From Sumerian Codes to
Computer Code:
A Formal Logic Perspective on Legal Theory, Normative
Systems and Information Technology
in a Historical Context
Notes by
Luigi
Logrippo
luigi@uqo.ca, logrippo@uottawa.ca
http://www.site.uottawa.ca/~luigi/
Started: 2009-08; Last updated: 2018.09.13
This work is dedicated to the memory of
Fritz Paradies, a lawyer and scholar from Frankfurt
and Amsterdam. In his self-published paper “Enthält
Cobol eine juristische Logik?”, written in the
mid-1960s, he expressed some of the ideas I mention below. But do we have a
basic philosophical bug here? Law is based on the idea that humans have free
will, something that computers are not
supposed to have! I still don’t have a good answer to this, but you might wish
to read on … and get lost in the similarities, as happened to Fritz and me.
Contents
1.2.2
Different types of norms, and different ways of representing them
1.2.3.The
difference between norms and programming language statements
2.
Sumerian and Babylonian codes (about 2000 BC)
2.1.2
Access control systems (ACS)
4.
Legal Logic in Roman Law, and Greek influences
5.
Early Medieval European Law: the Example of Salic Law
8.
Chinese law: the example of the T’ang code
9.1 Fraunce’s legal argumentation model
10.
Late Medieval European Law and Scholastic Logic
12.
19th Century legal theory in the West
13.
Hohfeld’s ontology of legal concepts
14.
From E-Commerce to E-Laws, E-Courts, E-judgments and Computable contracts
15.2.1
Consistency in logic and normative systems
15.2.2
Resolution of inconsistencies in normative systems
15.3 Completeness and closure norm
15.5 Deontic logic and deontic concepts
15.6 Contrary to duty obligations, Chisholm’s
example
15.7 Logic of action and agency
15.8 Machine learning, theory revision and common
law
16.
Concepts common to Computer Science, Software Engineering and Law
16.2 Refinement from requirements level to
operational level
16.6 Event projections and aspect-oriented design
16.7 Normative systems for e-societies
16.8 Laws, standards and the political process
17.
Argumentation models, Artificial Intelligence, and automated legal decision
systems
19.1 Logic programming and constraint logic
programming (e.g. Prolog, Constraint-Prolog)
19.2 Logic checkers and satisfaction algorithms
(e.g. Alloy)
19.3 State exploration (e.g. SPIN)
19.4 Theorem provers (e.g. Coq)
20.
What else is there (too much…)
Appendix
1. Tammelo’s “Manifesto of legal logic”
Feedback,
interventions and discussion
1. Discussion with Peter Denning (January
2010)
For many years I have been interested in
issues of legal logic, its history, and corresponding developments in
Information Technology (IT). Since I have studied law, then I have moved to IT
and now again I am interested in law, this document will include reflections
taken from the points of view of both areas.
The main purpose of this document is ‘notes to myself’, however I am making it
available to the world in case it might interest others. I am interested in
discussion, in hearing other views. Notable interventions are being added at
the end.
So this document is work in progress, and I
will keep updating it as I find sources, ideas and time. Expect conjectures,
incompleteness, inconsistency, rough text, lack of bibliographic references,
etc.
The terms norm and normative system
will be used often to refer collectively to the different types of rules, laws,
computer-based policies, etc., that will be considered here. In a well-known
1972 book Alchourròn and Bulygin
loosely define norms as statements that relate cases to solutions. The authors
did not intend to extend the scope of their definition beyond the social
sciences and law but clearly according to their definition norms and normative
systems exist in IT.
In 1993, Jones and Sergot
wrote:
“The general position which we here develop and
illustrate is that---at the appropriate level of abstraction---law, computer
systems, and many other kinds of organisational structure may be viewed as
instances of normative systems. We use the term to refer to any set of
interacting agents whose behaviour can usefully be regarded as governed by
norms. Norms prescribe how the agents ought to behave, and specify how they are
permitted to behave and what their rights are. Agents may be human individuals
or collections of human individuals, or computer systems or collections of
computer systems. Normative systems include systems of law, abstract models of
computer systems, and hybrid systems consisting of human and computer agents in
interaction.”
I subscribe to this view, with two
exceptions. First of all, are normative systems sets of interacting agents
(legal institutions), or sets of norms? This question, whether institutions or
laws have come first, has been extensively debated in philosophy of law and
therefore it should be avoided if possible. Isn’t it similar to the ‘chicken
and egg’ problem? In these notes, I am mostly interested in sets of norms.
Second, this view characterizes norms in terms of the deontic concepts of
obligation (‘ought to’) and permission. This is a common view, endorsed by the
best authorities. However normative reasoning is possible without deontic
concepts.
So the main emphasis of these notes is not
on legal logic and legal reasoning alone. It is on finding traces of actual use
of logic reasoning in applied legal contexts, and note correspondences with
methods in Computer Science, Software design and IT applications.
According to [Alchourròn,
Bulygin 1972] ‘The rules of inference have rarely,
if ever, been discussed by legal writers, who often are not aware of their
existence.’ But this is consistent with the role of logic in all
disciplines that use it, including mathematics and philosophy. Texts in
disciplines that use logic will very seldom include explicit logic derivations,
but faults in the use of logic will be pointed out and often will be considered
to invalidate the whole argument. In
many areas of law, the expectation is of ‘fairness’ rather than rigorous logic.
So logic tends to be invisible as long as it is correct. Legal thinking is
dominated by political, ethical, sociological and economic concerns. These
other disciplines, in relation with law, posit assumptions or domain axioms that are far more visible
than the inference rules of logic that are used to derive conclusions from
them. In other words, legal thinking is dominated by assumptions coming from
these disciplines, as well as from law and precedent. The coverage of these
assumptions is extended by using analogical thinking. After this, the
application of law to the specific case is often a simple deduction (e.g. a
syllogism) of which we are often not even aware.
Legal reasoning uses the same logic as all
other sciences, e.g.:
· Joe owes a sum of money to Mary or he
doesn’t (law of excluded third).
· All
taxpayers who make between $100K and $150K are in the 30% tax bracket; Alice is
a taxpayer who makes $125K; hence Alice is in the 30% tax bracket
(syllogism based on the property 100<125<150).
· If none of the accused are guilty, then
they are all innocent (deduction based on the definition: not guilty =
innocent).
Legal practitioners will not write in this
style, but will implicitly use these forms of reasoning.
Occasionally, fairly complex logical
reasoning can be found in judicial texts. Many such examples have been
published in the literature. Several are analyzed in plain language in [Tammelo 1978], and here is one (page 100,
please refer to the book for some background that is necessary in order to
fully understand this text):
For every m: if m
commits larceny then for some n:
m
takes n
and m
acts feloniously.
For every m: exactly if for some n:
m
takes n
and m
acts feloniously then m
commits a trespass.
For every m: if for some n:
m
takes n
and m
acts innocently and m
fraudulently converts n
to his use subsequent to the original taking and neither m is a servant and m commits embezzlement or m is an agent and m commits misappropriation nor m commits a bailee's larceny
then it is not that m
commits larceny.
Ashwell takes the souvereign
and Ashwell is innocent.
Ashwell fraudulently converts the souvereign
to his own use subsequent to the original taking.
Therefore, it is not that Ashwell is guilty of
larceny.
[Brewer 2012] includes several examples of
logical reasoning in judicial decisions.
[Stelmach, Brozek 2006] identify four historically established methods
used by legal practitioners and theoreticians: logic, analysis, argumentation
and hermeneutics. They claim that they are all useful and used, none being
subordinate to the others. The boundaries among these methods are not sharp.
So I will follow [Fraunce 1588]: “I sought for Logike in our Law, and found it as I thought”. Logic reasoning is identified by precise and complete definitions and clear logic inferences, as well as an explicit effort to maintain consistency (avoidance of contradictions).
The proponents of the use of formal logic
in the legal process have often pointed out that such use helps towards
predictability in the process, which is required for assuring the principle of certainty of law, proposed by Max Weber
among others as necessary condition for the achievement of economic goals. In
other words, the results of the legal process are more predictable and uniform
if the law is logically clear and consistent and the decisions are reached by
formal logical inference from the law and the established facts. Today, a
technological argument for the use of formal logic in the legal process is
provided by the fact that information systems are increasingly entrusted roles
of legal relevance and the most obvious mechanism for computers to draw legal
conclusions is logical deduction. In IT terms, the laws are the policies and
the established facts are the context. Examples are in e-commerce and privacy
protection systems, among others. Multi-agent systems are very similar to
social systems with their policies, which essentially have the function of
laws, but are inferred and enforced automatically.
With the availability of efficient Boolean
satisfaction (SAT) algorithms [Malik, Zhang 2009], many application
possibilities are now open.
There is no lack of theoretical works on
legal logic, going back to the 16th Century. If I have read well, the ideas of
logic formalization of legal thinking and even of automation of legal thinking
go back to Leibniz (1646-1716), but I haven’t been able to research this point
yet.
[Lorini 2003] and
[Kalinowski 1983] cite quite a number of publications
on the subject, accelerating towards the 18th, 19th and 20th C. I have seen
very few of these treatises, however most probably they take the word ‘logic’
rather loosely, with emphasis on argumentation.
But this is OK, good argumentation must be based on good logic, although
this connection may not be obvious. Starting in the 1920s, there has been
further acceleration of interest and papers and books have appeared, with different
orientations. Formal logic approaches to legal interpretation and deduction
were developed. Very significant research in formal logic of law was done in
the 1950s, see http://www.jstor.org/stable/2269771?seq=1
(consulted October 2009). This link contains reviews of books and papers by
Layman E. Allen and William Halberstadt. Layman Allen
may have been one of the first to apply modern formal logic for the
interpretation of a real law, the USA Internal Revenue Service (IRS) Code (what
better candidate?)
Lucien Mehl, a
French jurist and legal documentation expert, was perhaps the first person to
articulate the view of automation in the legal world, in a paper of 1959 [Mehl 1959]. His ideas were of course simple by today’s
standards, based on binary encoding of logic concepts. He viewed his ‘juridical
machine’ as an aid for the jurist and judge, rather than a substitute. However
in a paper published some decades later [Mehl 1995]
he recognized that in some cases legal decisions can be entirely automated.
This analysis is still valid many years later.
From 1959, there was a newsletter on logic
and law in the USA, it was called M.U.L.L. (Modern
Uses of Logic in Law) and was edited by Layman E. Allen (copies can now be
found in the WWW). This newsletter was soon swamped with papers on jurimetrics
and then changed name to ‘Jurimetrics Journal’. [Klug 1951][Tammelo
1969][Alchourròn, Bulygin
1972] are some of the first major monographs that have proposed and illustrated
the use of formal logic methods for the analysis of legal reasoning. [Narayanan,
Bennun 1998] contains several articles presenting the
view of the field at the end of the last century.
The philosophical basis of this direction
in the study of law may perhaps be traced to legal positivism, which had
different but partly converging developments in Austria, Germany, UK and USA.
[Haack 2007] provides ample background on this.
[Sartor 2005, Chapters 5 and 6] are
interesting chapters on Law and Logic. [Gabbay et al
2013] is a handbook that contains many useful chapters.
Nowadays, there are several international conferences or workshops which
deal with research on logic and law:
CLIMA (Computational
Logic in Multi-Agent Systems)
DEON (Deontic Logic in Computer Science)
ICAIL
(Intern. Conf. on AI and Law)
JURIX
(Intern. Conf. on Legal Knowledge and Information Systems)
NorMAS (Normative Multi-Agent Systems)
ReLaw (Requirements Engineering and Law)
Some
of the views presented here were published in [Logrippo 2007 and 2011].
The term ontology has a history in
philosophy. It has become a technical word in Computer Science, with a somewhat
different meaning, and it is in its CS meaning that I will use it. An ontology
in this sense is the definition of a set of concepts together with their
relationships. Various ways of representing ontologies are: sets of logical
axioms involving constants, data types, diagrams (e.g. UML diagrams),
conceptual taxonomies, etc. Many different, and very complex, ontologies can be
present in a legal system. Some can be explicitly defined in the law, others
can be considered to be understood, or ‘inherited’ from areas of knowledge that
are technical or common knowledge. For example, inheritance law involves (at
least) a family ontology, an ontology describing rights that the deceased may
hold, an ontology describing the objects on which rights can be held, and an
ontology describing the structure of testaments.
The role of ontologies in legal thinking is
debated [Sartor 2009]. [Breuker, Valente, Winkels 2004, 2005] present their views on the same
subject, including the conclusions of an extensive application study carried
out by their group.
Where should ontologies come from? They could
come from legal theory, however only informal, partial and often messy
ontologies are found in legal textbooks. Ontologies are also different from
textbook to textbook. Or they could come from a ‘grounded’ approach, e.g. from
processing the legal texts and deriving relationships in the terminology. In
the first case, we risk using
irrelevant ontologies. In the second case, we risk not seeing
what the concepts really mean because there is a lot of assumed knowledge in
legal texts. It seems that an intermediate approach is necessary [Fernández Barrera 2011].
A main problem with ontologies is that,
although they are needed to understand the law, often they are not part of the
law. In other words, the interpretation of the law can be heavily determined by
external concepts. Precision in the law itself won’t help if the necessary
ontologies are not well defined, but often to make these precise would involve
including segments of many sciences, as well also of many concepts that are not
defined scientifically. This problem
pervades much of legal thinking.
[Winkels 2010] is
a web page dedicated to information on legal ontologies. [Fernández Barrera 2009] is a presentation on legal
ontologies, showing some historical ontologies in graphic format. See also
[Valente 1995][Valente 2005][Van Engers
2008][Sartor 2011].
Legal norms can be stated in many different
ways, using the expressive power of natural language. As is normal for natural
language statements, usually there are several ways of expressing norms in
logic.
The analysis of [Dworkin 1978] given in [Verheij 1998] distinguishes between rules and principles in
the following way:
Rules: if
the condition of a rule is satisfied, the rule is applied and its conclusion
follows directly
Principles: a principle only gives rise to a reason for its conclusion if it
applies. Moreover, there can be other applying principles that give rise to
both reasons for and reasons against the same conclusion. A conclusion then
only follows by weighing the pros and cons.
In this view, reasoning with principles
leads to models of argumentation and types of logic that support the weighing
of arguments.
Personally, I have been inspired by the
concepts of implementations and requirements, current in software engineering
[Logrippo 2007]. Taking this view, a principle is a requirement, which can be
used to generate rules and to which rules can conform or not. Conflicting principles are due either to poor
legislative practices, or to the desire of the legislator to allow space for
different implementations. In this latter situation, eliminating the conflict
is indeed a matter of interpretation, which is not a strictly logical process
and can be done in several ways, including argumentation.
A rule, or ‘implementation” type of norm can be expressed as
Event-Condition-Action (ECA):
if Event and Condition then Action
meaning that if an event occurs, in the presence
of conditions that must be true on the context, then an action should follow.
If a nurse requires access to the X-Ray department, and she is working in the
Emergency Ward, and it’s between 22h and 06hrs, then permission will be given.
Whether
a syntactic occurrence should be listed as action or as part of the context
condition, this depends on the architecture and ontology that has been defined
for the system.
The
ECA style is widely used in IT in event-driven architectures, policy-directed
systems and rule engines. The ECA style can be immediately translated in
Horn-clause style, which is at the basis of the semantics of the programming
language Prolog and of its derivates.
Principles
are simple logical statements, e.g. “nurses can be given access to the X-ray
department only in exceptional circumstances”. Note that there is a difference
between a logical statement like A ^ B → C and a rule such as ‘If A ^
B then C’. The former is a logical statement, an implication; the latter is an operational norm;
it defines a state transition, with a side effect, by reaching a new state
where the postcondition of C is true. The logical
statement form is suitable for expressing principles,
the state transition form is suitable for expressing rules. ECA style is
operational, but the ECA norm makes the implication true.
ECA style allows forward chaining,
since in the new state new conditions are true and new actions can lead to
other actions. In the example above, when the nurse has been given access to
the X-Ray department, then new rules may come into play, by which perhaps she
can take X-Rays herself or she can ask a technician to take them for her. ECA style allows also backward
chaining, by which one can ask what are the possible actions and conditions
that can lead to a given state. E.g. what are the
actions and conditions that can lead to a nurse taking X-rays. Forward and
backward chaining can become very interesting in the presence of a rich
ontology. If we have a ECA rule If A ^ B then C and also
C → D is asserted in the ontology, then
all the consequences of D become possible after the state transition. If the
X-Ray department includes other equipment, then the rules for the use of that
equipment may become applicable.
A.J.I.
Jones, R. Kowalski, M.J. Sergot and their
collaborators have been the recognized pioneers in this line of thinking.
Normative
conditionals and their analysis are discussed in detail in [Sartor
2005, Chapter 20, 21].
It might be considered important to decide
which part of a legal system is ontology, and which part is ‘something else’.
For example, an assertion such as: Land transfer acts
are civil law acts could
be considered ontological, a classifying statement. But what about: Land transfer acts must be registered with the land registry. At first, this could be considered a
deontic statement, involving the concept of obligation. But
it could also be seen as a simple implication, part of an ontology, just like
the other assertion.
We
should note before we go on that there has been considerable discussion in
philosophy of law about the logical nature of norms [Lorini
2003, Kalinowski 1972]. According to some, norms
cannot be true or false as logical assertions can, and as example statements
such as ‘do not drive through a red light!’ are brought forward. But is this a
norm? According to what I have just said, I consider two kinds of norms. By way
of example:
‘no one should drive through a red light’,
‘debts must be repaid’, these are
statements that can be true in some legal systems, false in others. These seem
to be principles.
‘If someone does not pay debt, her properties
shall be sold and the proceeds distributed to her creditors’ can be read in
two different ways. One is as a logical implication, part of a legal ontology,
which can be true or false, and so it is a principle.
The second is an ECA rule or program, which establishes a postcondition
on the basis of a precondition. In this second case, the pre- and post-conditions
can be true or false at different states in the system, but the program does
not have a truth value. This is an operational rule.
However
the statement: ‘ECA rule X is a valid
rule in a given legal system’ can indeed be true or false, but it is not a
norm, most likely it should be taken as a meta-norm.
So
there are several possible interpretations for a legal statement, which one(s)
should be preferred depends on the preferred type of reasoning. Philosophers may dwell on such distinctions
for a long time but I am inclined to think that these distinctions don’t matter
in principle. Simpler is better whenever computers are involved. A typical
logic analyzer or theorem prover won’t make any difference regarding the
provenance or the nature of different logical assertions.
Needless to say, legal texts contain many different types of norms; in
addition, laws can be classified in different ways according to the purpose of
the classification. Our purpose is logical structure. So the discussion above
doesn’t even scratch the surface of the subject.
An
important fact about legal norms is that they can be decomposed into norms of
different types, for example a norm directed to the subject, and another directed
to the enforcer. I call the first the Moses norm, and the second the Hammurabi
norm (in ECA-atyle). Example: “Parking on Rideau
Street is punished by an amend of $10”. The Moses norm
here is: ‘Thou shall not park on Rideau Street”. The Hammurabi norm (for the
police officer or the judge) is: “If anyone parks on
Rideau Street, he or she will be punished with an amend of $10”. Both norms can
be violated, but the first can be violated by the subject, while the second can
be violated by the enforcer. Clearly, each type of violation can have cascading
effects with the activation of other norms. Interesting, if a subject is also
an enforcer, he can, of course, violate both norms.
I
haven’t yet found any reference on this topic, so I will try my best to get in
hot water.
Intrinsic
in the concept of norm is that it can be violated. Hence the semantic of ‘norm’
should include a non-deterministic choice (the ‘free will’) which, in the case
of violation, leads to consequences. These can be as simple as flagging the
fact that a violation has occurred. This flag can trigger other norms.
In
traditional programming languages, the semantic of statements does not include
this possibility. Statements are executed in sequence, and choices are
deterministic.
Several
modern programming languages include constructs that specify nondeterminism or
exceptions (e.g. in Java: try, catch, finally). However these must be
specifically programmed.
The
best programming model for norms can perhaps be found in logic programming
languages, where statements can succeed or fail according to the truth or
falsehood of preconditions, independently of the order in which they are
written.
Sumerians
and Babylonians are well-known for their scientific knowledge. But also their
legal codes are written precisely in a rigorously uniform style. The code of Ur-Nammu is said to
precede Hammurabi’s by some 300 year and is presumed to be the earliest legal
text extant. However since Hammurabi’s code is more complete, we will
concentrate on this one, which is written essentially in the same style.
Here is one of Hammurabi’s almost 300 rules (from http://www.wsu.edu/~dee/MESO/CODE.HTM, consulted September 2009):
If
any one agree with another to tend his field, give him seed, entrust a yoke of
oxen to him, and bind him to cultivate the field, if he steal the corn or
plants, and take them for himself, his hands shall be hewn off.
This rule, like many other rules in this code, is written in ECA style:
· The Event here is: If any one
steals the corn or plants, and take them for himself,
· The Condition is: If that person
has agreed with another to tend his field, give him seed, entrust a yoke of
oxen to him, and bind him to cultivate the field
· The Action is: His hands shall be
hewn off
Not only this, but in many rules the event itself consists of three
elements:
· Subject: in this case anyone
· Verb(s): in this case steal
and take for himself
· Object(s): corn or plants
As well, the Action may contain simple ‘algorithms’ to decide the
penalty, this is seen in other rules.
It would be possible to dwell further on the logical structure of these
rules. In the case of the rule given above, it can be seen that the Condition
defines a ‘precondition’ for the rule to be applied. It can be further analyzed, in this case it describes an existing legal
relationship between the main legal Subject (any one) and another legal Subject
(another), as well as an object, the field. In its turn, the field contains
‘corn or plants’, The Verb is the ‘trigger’ , the
event that causes the rule to become applicable in what otherwise is a normal
legal situation.
It has been very interesting for me to see that a legal system can exist
at an elementary structural level that is also well known in IT.
Many later codes do not show such uniformity. They show mixtures of
rules in ECA style with other rules that are written in various other styles,
notably often not explicitly mentioning the consequences of actions, such as
violations.
On the negative side, there is in this code a lack of conceptualization.
Each rule considers a specific case only, without attempts of generalization.
There are no explicit ontologies. There are no subject headings in the code, although rules concerning similar cases are often
grouped together (e.g. articles 215-225 group rules applying to physicians).
This leads to a multiplication of rules to consider individual cases. The only
legal concept to be found in the rule above is the concept of theft, which
depends on the concept of property, and neither is defined. Several other rules
make reference to an implicit ontology that reflects the Babylonian social
structure, from priests to slaves, etc. So forward chaining is very limited,
although there may be some: e.g., trivially, if someone is executed for an
offence, then inheritance rules come into consideration.
It would be an interesting project to study this code in order to
complete this analysis, and better identify the ontologies and the basic
structural principles it is based on, to the extent to which they can be
identified.
The aim of ancient legislators using the ECA style was probably to give
examples to the ruler’s delegates, the judges. It has been speculated that the
articles of these codes were decisions actually taken by the rulers. Surely
other situations would present themselves that did not exactly match the given
patterns. What would the judges do in these cases? Probably infer by analogy,
as judges still do today. Modern codes explicitly leave space to judges’
discretion to determine circumstances and dose decisions, and this might have
been implicit at that time. This may not be appropriate in simple cases where
it is desired to obtain automatic judgments [Logrippo 2011].
We shall see that the ECA style has been often used in the history of
legislation, as an effective and simple legislative style.
There is a striking similarity between the style of the Hammurabi code
and the style in which firewall rules are written. A firewall is a part of a
computer system or network that is designed to block unauthorized access while
permitting outward communication. Essentially, firewalls monitor communication
lines and block or authorize entry to data packets showing certain
characteristics, such as address of origin or port of destination.
Firewalls are programmed by sets of rules written in ECA style. Most
rules are of the type: if a packet having such characteristics is received,
then it should be blocked at the firewall, or it should be forwarded to
the destination. Just as it may have been done in the code of Hammurabi,
firewall rules are added by the system administrator when the need presents
itself. Each rule is on its own and there are no general principles or
definitions in a firewall system.
But in sets of firewall rules the order is important: at the arrival of
a data packet, the set of rules is scanned top-down, the first applicable rule
is executed, and then the next packet is taken into consideration. Other
applicable rules later on are not used, so specific rules must appear before
more general ones, more important rules before less important ones. Instead in
codes of law all rules are equally important and if two rules are applicable
for a given situation, both may apply or some conflict-resolution strategy will
have to be applied, usually by a judicial authority.
In both firewalls and systems of legal rules, there is a ‘closure norm’.
In the case of firewalls, the closure norm is often: if no rule applies for
a given incoming packet, then reject it. In the case of legal systems, the
closure norm is often: the action is not legally relevant, nothing to do
(e.g. the legal maxim: nullum crimen sine lege, no crime
without law).
ACS are also characterized by ECA rules.
Typically, these are used to protect or limit access to resources, such as
computer files or also physical resources, such as rooms or equipment. A
typical rule in an ACS could state: nurses can access only the files of
patients in their wards, and only during their work hours; or: in the
army, only officers can access documents classified as ‘top secret’.
As in the Hammurabi code, ACS rules are often written in the fixed
style:
(subject, verb, object, condition, action)
For example: (if a <clerk> <requires access> to the <bank
safe><from 0:00h to 7:00><deny>).
A type of ontology that is used in some ACS is the role ontology, and
the best known conceptualization of this is provided in the theory underlying
RBAC (Role-Based Access Control). Here, roles are essentially functional
positions in organizations, to which users can be associated (e.g. Director of
Marketing, Chief Surgeon, emergency doctor, etc.). Access rights are associated
to roles, and then users are associates to roles. Role hierarchies with access
right inheritance can be defined.
A standard computer language has been defined for ACS, by the standards
organization OASIS, is XACML. It is related to the access control method ABAC,
Attribute-Based Access Control.
The XACML standard defines mechanisms for deciding access and enforcing
access, comparable to a judicial system. Two main components of the XACML
system are the ‘Policy Decision Point’ and the ‘Policy Enforcement Point’.
Exchange messages are defined between these points.
XACML allows the user to set meta-rules to resolve potential conflicts
between rules: Deny-Overrides, Permit-Overrides, First-Applicable, Only-One-Aplicable, Lower-Role-Overrides.
[Barker 2012] develops a logic framework for core concepts in access
control. He also states: “In future work,
we intend to consider the type of more general authorization model requirements
that Jones and Sergot have considered and their
representation of rich forms of non-standard access control models within our
framework.” He cites among others [Jones, Sergot
1992]. He died in 2012, unfortunately.
A lesson that may be drawn from these analogies is that, just as legal
systems have evolved from the simplest ECA structures into complex structures
involving ontologies, many types of legal rules, etc. ,
firewalls and access control systems will also evolve in similar ways.
Legal systems have been developed for a very long time, and so they are very
sophisticated. However comparable IT systems are more precisely defined, tuned
for automatic decision-taking. Precision and complexity may head towards
convergence in time. Convergence will likely be first achieved for legal
systems that are meant for automatic implementation. Privacy protection systems
may be among the first to witness such convergence.
With respect to Sumerian and Babylonian codes, the code that according
to the Bible was given by God to Moses shows two important characteristics: use
of deontic concepts and higher level of abstraction.
Thou shalt not steal…
Remember the Sabbath day…
are typical rules of this code. Deontically,
the first can be written as: it is prohibited to steal; and the second: it is
obligatory to remember the Sabbath day. These are the only two deontic
modalities used in this code, namely permission is not used. However an implicit
understanding of permission seems to be present: that obligatory actions are
permitted, that forbidden actions are not permitted.
Opposite to the Hammurabi code, this code ignores the judicial authority
and speaks directly to the individual. However in order to enforce it, a
judicial authority may be necessary, with corresponding norms.
To see the consideration of large classes of behaviors, consider again
the norm: Thou shall not steal. There
are quite a few specific scattered norms corresponding to this one in the
Hammurabi code: e.g. 6, 8, 14, 22, 23, 24… However in each case the Hammurabi
code dictates the consequences of each specific type of theft, which are left
unspecified in the Moses code. In engineering terms, one could say that a rule
written in the ‘Moses style’ is a requirement, to be implemented in the
‘Hammurabi style’.
I am getting into things I don’t know now, but perhaps one could view
the Talmud as an implementation or refinement of God’s code.
Another interesting legal concept that is related to Moses is
delegation:
Exodus
18:
17:
And Moses' father in law said unto him, The thing that
thou doest is not good.
18: Thou wilt surely wear away, both thou, and this people that is with thee:
for this thing is too heavy for thee; thou art not able to perform it thyself
alone.
19: Hearken now unto my voice, I will give thee counsel, and God shall be with
thee: Be thou for the people to Godward, that thou mayest
bring the causes unto God:
20: And thou shalt teach them ordinances and laws, and shalt shew them the way
wherein they must walk, and the work that they must do.
21: Moreover thou shalt provide out of all the people able men, such as fear
God, men of truth, hating covetousness; and place such over them, to be rulers
of thousands, and rulers of hundreds, rulers of fifties, and rulers of tens:
22: And let them judge the people at all seasons: and it shall be, that every
great matter they shall bring unto thee, but every small matter they shall judge:
so shall it be easier for thyself, and they shall bear the burden with thee.
A couple of interesting legal concepts can be found here: one delegates
powers that one already has; and one delegates to lower-rank subjects who have
the ability to take the responsibility. There is no mention of another
constraint: that in order to delegate a responsibility, one should have the
power to perform such delegation.
Delegation in law is discussed in detail in [Sartor
2005, Chapter 5].
People who think that legal logic is irrelevant need to look no further
than Rome for an argument in their favour. Roman legal thinking has dominated
legal thinking in much of Western Europe for millennia, up to our days. Roman
lawyers invented many of the legal concepts still used today, and in many cases
their solutions to private legal issues were the same as the ones of today. Yet
pragmatic Romans were quite uninterested in logic, in fact scornful towards it,
as they were towards much of philosophy and pure sciences. Philosophers were
often banned from Rome, and had either to teach out of town, or present
themselves as teachers of something else, such as rhetoric. However there was
at least one philosophical persuasion that had a deep and lasting impact on
Roman society, this was Stoicism. Roman scholars of law were exposed to
Stoicism, including its logic component, probably through their schools of
rhetoric, and this will have the consequences that we will note below. The role
of Stoic philosophy in the development of Roman law is discussed in [Wright
1983], but also see [Watson 1995] for an opposite opinion. It can be debated to
what extent this philosophy had influence on the spirit of the law and on the
legal logic.
I would say that the contributions of Roman legal theory to legal logic
were two: the development of the first legal ontologies and the development of
analogical thinking.
Opposite to the Romans, the Greeks were the inventors of formal logic in
the Western world, and held philosophy in great esteem. They were also among
the first peoples to recognize the importance of the rule of law in society.
But they did not develop a memorable legal theory of their own.
It is believed by some that early Roman legal codes were influenced by
pre-existing Greek codes. What is left of the Law of the XII Tables of the 5th C. BC are modern reconstructions based on
citations written centuries after the tables had disappeared. On this basis,
this does not seem to be a remarkable document from the logical point of view.
It is well-organized, each of the 12 tables dealing with a different subject
heading, but it shows a low level of conceptualization. There is no
uniformity of styles and while in some cases consequences of violations are specified,
in others are not. It uses indifferently ECA style or deontic statements.
A much later source is the Institutes of Gaius, a law manual, see http://faculty.cua.edu/pennington/law508/roman%20law/GaiusInstitutesEnglish.htm. It was written in the 2nd Century AD,
probably on the basis of earlier manuals (Gaius=Caius was a very common
praenomen in Rome but no other famous Romans are known to us with this name only:
so it has been questioned whether Gaius was the name of a real person, or
perhaps a traditional name attached to a compilation). Somehow
this manual had a very long life, since it was re-worked by Justinian in the 6th
Century AD, and by others in legal texts of the early Middle Ages. In spite of
its practical nature, it shows considerable conceptualization and it is
probably the first legal source that is based on ontologies, in fact it starts
with a single ontology that is supposed to include all legal concepts. At the
highest level, Gaius presents a tripartite division of private law (ius) into persons
(personal status), things (property, succession and obligations) and actions
(forms of action and procedure). Notice the echo of the concepts of subject,
object and verb already noted in Sumerian law, and which is still used today in
access control theory, as mentioned. There are many progressive subdivisions
that work towards elementary legal concepts. For example, persons can be free
men or slaves. Free men can be born free or freed. The latter can be Roman
citizens, Latins, or ‘dediticii’. And so on. Things
can be of human law or sacred, etc. Although the ontology developed by Gaius no
longer applies today, his method of creating tree-structured legal ontologies
is still used. This method has its foundations in the diairesis
(=conceptual distinction, classification of concepts) of Greek philosophers. Diairesis starts with general concepts and obtains more
specific ones by distinctions. Concepts are defined by their position in the
tree. Diairesis was known to the Stoics, and it is an
interesting coincidence that Marcus Aurelius, the Stoic emperor, was a rough
contemporary of Gaius. Graphical representations of parts of Gaius’ ontology,
as well as of more modern legal ontologies, are given in [Fernández
Barrera 2009] [Fernández Barrera 2010].
It is interesting to note that Gaius presents rights as incorporeal
things. In fact, they can be held and transferred like corporeal things. How can this be connected with modern Hohfeldian
concepts of duty, privilege, and the different ‘actions’, this I haven’t
figured out yet.
Tree-structured ontologies of this type have implicit the concept known
in computing as inheritance: if a
concept A subdivides in A1, A2 … An then clearly
everything valid for A is also valid for each of A1… An. If a legal question
comes up concerning a freeborn citizen and the question can be answered in more
general terms for all free men, then this latter answer applies.
An interesting section of the Institutes is the one where Gaius explains
the Roman system of judicial ‘formulae’: [Poste 1875] discusses how formulae
can be understood in terms of syllogisms. I won’t explain how the formula
system worked, since there are explanations on this in the web (a good source
may be the Institutes themselves, see Book Four, starting in paragraph 39).
Essentially, for each type of litigation there were pre-set formulae consisting
of several parts where the main elements of the litigation were expressed in
precise, stylized language. Formulae could include, in fixed sections: the
subject of litigation, uncontested elements, elements
to be proven, possible results of the litigation, etc. The formula was set up
by a magistrate and then the judge (essentially an arbitrator) had to decide on
specific predetermined questions and among specific predetermined outcomes. The
judge’s mandate was often limited to determine the facts and then choose the
corresponding outcome according to the formula. Today, stylized formulae are
used in legal documents such as land transfer acts, but not normally in
judicial procedures. It seems that if we want to think of automated tools to
speed up the judicial process, such as in the e-commerce context, this would be
a good method to study [Logrippo 2011].
The formula process was preceded by another, called ‘lege
agere’. This ancient and not well documented type of
process was characterized by the fact that specific gestures had to be
performed and specific words pronounced. Gaius mentions that this type of
process became unpopular for this formalism and rigidity and also for the
limited number of possibilities it proposed. A minimal error, apparently even
an error of pronunciation, could lead to the loss of a case. Does this sound familiar
to computer people?
The main legal legacy of Rome is the Corpus
Iuris Civilis. The part
that interests us is the Digesta
or Pandectae.
This is a very large (a volume of 1 000 large, tightly printed pages)
compilation of excerpts of writings of jurists, covering civil law, compiled by
order of Justinian in the 6th Century AD. The excerpts are from
writings of the 3rd Century, but edited to reflect the changed laws
and thinking. This document is well organized, with major titles divided in
subtitles, etc., and many of these titles are similar to the ones that we find
in modern texts of civil law.
Examples of explicit logic reasoning or inference are pretty well
impossible to find in the Digesta. Logical operators
such as if, and, or, forall,
exists are much more difficult to find in these texts than they are in
modern legal texts.
The legal excerpts collected in the Digesta
center on the solution on legal cases, or quaestiones. Unlike the cases of
modern common law, these were often manufactured for the sake of discussion, in fact many of them seem to be artificial.
Perhaps they should be called ‘legal scenarios’. Analogical thinking is
paramount. This often consists in finding other similar legal scenarios and
then coming up with a solution that takes care equitably of all the similar
scenarios.
In other words, Roman jurists of the period documented in the Digesta were not interested in how to set up legal problems
in logical terms. Rather, they were interested in reasoning by analogy with a
concept of equity. They proposed intuitively persuasive solutions to legal
scenarios, based on law, precedent, economic and social principles. This
corresponds to a lack of interest in logic, accompanied by a keen interest in
rhetoric, or the art of persuasion.
Equity and the intent of the law, based on analogy, were the
main principles of interpretation in Roman law, rather than the letter of the
law [Bruncken 1917]. Many Roman legal texts can be
read in this way: here is an interesting case (legal scenario, quaestio) to
solve. Here are similar (analogous) cases. There is a common pattern, and an
equitable solution for all these cases is so-and-so. The solution may come from
a law or another known principle that applies to some of the cases in the
similarity set. Similarity of cases does not mean real-life similarity; it
means that the cases involve similar rights or obligations.
This method of analogical thinking based on equity and rhetoric is still
today very commonly used in legal reasoning.
The legal system documented in the Digesta is
a compromise between conceptualization and practical considerations.
[Watson 1995] points to the paradox of ‘high conceptualization and small extent
of systematization’ for there was prestige in finding intuitively convincing solutions
for specific problems but none in systematizing. He cites
Digesta 50.17.202. Javolenus, Epistles, Book XL. Every definition in the civil law
is subject to modification, for it is rare that it may not be overthrown.
So definitions are rare in the Digesta and
when they are present they are expressed in rather awkward terms. Watson
further cites Digesta 26.1.1 and a text by Aulus Gellius (Noctes Acticae 4.1.17, not part
of the Digesta) to
illustrate this point. Concepts were useful to the extent where they could
establish predictability in the system. Much of the conceptual systematization
of Roman law was really done in the 19th C.!
The majority of legal opinions in the Digesta
are written in an informal ECA style. Sketchy explanations are often introduced
by the word ‘quia’=
since, because. Here is an example (some translations in this section are from http://www.constitution.org/sps/sps.htm).
29.7.
8. Pomponius, On Sabinus,
Book II. If a testator, after having bequeathed a tract of land, should dispose
of a part of the same, it is held that only the remaining portion is due to the
party to whom it was left; because even if an addition was made to said land
the legatee would profit by the increase.
I selected this citation almost at random, but then by
examining it I found it to be a good example of the occasional shortcomings of
legal thinking in the Digesta. Pomponious
has posed a quaestio,
thought of a similar scenario, and posited an equitable solution for both
scenarios, based on economics. His argument (because
…) is more rhetorical than legal. I
have asked the question of two Ottawa lawyers
[1], and promptly they both came up with a clearer legal reason for the same
conclusion: the author of a testament retains the full right of disposing or
acquiring any properties until death, hence the legatee can find herself with a
part, more or nothing at all. Pomponius could easily think of this reason, but decided to present one that
perhaps he felt to be more convincing.
Apparently brilliant, but legally ill-conceived statements such as this
may be the price that Roman lawyers paid for not being interested in legal
conceptualization.
Here is another example:
7.1.12.
Ulpianus, On Sabinus, Book
XVII. Julianus presents the following question in the
Thirty-fifth Book of the Digest. If a thief plucks, or cuts off ripe fruit
which is hanging upon a tree, who will be entitled to a suit against him for
its recovery; the owner of the land, or the usufructuary?
And he thinks that as fruit does not belong to the usufructuary
unless it has been gathered by him, and not when it was separated from the land
by another person, the owner has the better right to bring an action for its
recovery; but the usufructuary has a right to an
action for theft, for it was to his interest that the fruit should not have
been removed.
Perhaps I should not have used this text, because the
concept of usufruct will be mysterious for some of my readers (usufruct gives
the usufructuary the right to enjoy the fruits of a
property, most normally land, while the property remains with someone else).
Also there are several concepts at work that are discussed in previous and
following sections. According to Julian, the property of the fruits separated
by someone who is not the usufructuary is of the
owner of the land. We note that the last part of the statement is justified (by
Julian) in economic terms, by the interest of the usufructuary
(an equity-related concept), rather than in legal terms. In the next several
lines (not shown above) Ulpian tries to answer the question by discussing
situations that in the view of him and other lawyers are similar (but not
obviously so). His conclusion remains
unclear to me, after having read it in the original Latin and in English and
French translations: both the ownership and the right of action remain in
suspense (in pendenti).
It seems that this was considered to be a difficult case.
Julian’s opinion demonstrates a fairly usual reasoning
process used in jurisprudence: an economic concept (interest) that has legal
consequences. I have read somewhere that
the right of property of the North American natives on their land was legally
questioned because of the fact that their economic organization (primarily
hunting-gathering) did not make an efficient use of the land.
There are lots of concepts in Roman juridical
thinking, fuzzy as they often are. Forward and backward chaining are possible,
but difficult to use because the definitions were so shifting. [Watson 1995] notes that Roman jurists used the
distinction between genus and species (see above the mention of diairesis in Gaius): “Quintus Mucius
distinguished five genera of tutela and different
genera of possession, and Servius three genera of tutela and four genera of furtum”.
The notion of type inheritance is implied: there are rules that apply to tutela in general and which also apply to its five
genera, unless there are particular reasons to the contrary.
Book 50, Title 16 of the Corpus is particularly
interesting from the logical point of view, it is entitled: On the meaning
of words and it includes many rules and definitions, some of logical
interest.
Here is a well-known passage that elucidates the three possible meanings
of the word ‘aut’ = ‘or’
[2]
50.16.124
Proculus libro secundo epistularum
The
following words, "So-and-So or So-and-So," are not only disjunctive,
but subdisjunctive in their signification. They are
disjunctive; for example, when we say, "It is either day or night,"
for having suggested one of two things, the other is necessarily impossible,
since to suppose one disposes of the other. Therefore, by a similar form of
words, an expression can be subdisjunctive. There
are, however, two kinds of subdisjunctives; one where
in a proposition both things cannot be true, and neither of them may be; as,
for instance, when we say, "He is either sitting or walking," for as
no one can do both these things at the same time, neither of them may be true,
for example, if the person should be lying down. The other kind of disjunctive
occurs in a statement where of two things neither may be true, but both of them
can happen to be; for instance, when we say "Every animal either acts or
suffers," for there is no animal which neither acts nor suffers, but an
animal may act and suffer at the same time.
Modern propositional logic of course knows about these
three meanings. The disjunctive operator is the exclusive OR or XOR operator; the first subdisjunctive
is the NAND operator, better known as the negation of the conjunction; and the
best known is the second subdisjunctive, which
nowadays is denoted by the ubiquitous logical operator ‘v’.
A close analysis of this explanation shows other
interesting points, e.g. the writer alludes at the rule ((A|B) ^ A) → ¬B,
where | is the exclusive or operator. This is hardly a significant logical
discovery, however. The same law holds for the first subdisjunctive
NAND, but Proculus does not mention it. This may be
the reason why the NAND is considered as a case of disjunction, in fact it is
the disjunction of the negation of the two operands.
So there doesn’t seem to be much that could be
recognized as predicate calculus or syllogism in the Digesta,
but here we have an explicit explanation of propositional logic operators.
Aristotelian syllogistic logic, involving predicates and quantifiers, appears
to be hardly known in ancient Rome. Apparently at more than one point in
history Peripatetic philosophers teaching such doctrines, or even all
philosophers, were considered dangerous and banished from the city… But I have
mentioned the importance of Stoic philosophy [Wright 1983] and part of Stoic
philosophy was what we call today propositional logic. In the text above, Proculus probably cites from some rhetoric textbook
inspired by the Stoics. The fact that this was standard knowledge is confirmed
by the fact that the term ‘subdisjunctive’ was also
known in medieval times, but only in the last of the meanings described above,
which is the one of the modern operator ‘v’.
[Watson 1995] reaches essentially the same conclusions
and rightly notes that this passage is presented in a
vacuum: no applications of the logical laws cited by Proculus
are given, neither in the context of the passage itself nor probably in any
other part of the Digesta.
[Copi 1979] explains how
Latins used vel for the modern operator ‘v’, aut for XOR, and
similar views have been expressed by others, even in Latin texts. This is wrong
according to Proculus.
An interesting section of the Digesta
mentions a legal paradox related to the ‘Lex Falcidia’.
See on this [Artosi, Sartor
2016].
The Digesta also cite a
number of legal rules that show the beginning of a trend towards the legal
conceptualization that will be developed hundreds of years later. Many of these
rules became brocardi in the later middle ages. One can
recognize fragments of deontic and other modal logic in statements such as the
following:
Title 17: Different
rules of ancient law.
50.17.55.
Gaius, On Wills Relating to the Urban Edict, Book II.
No one is considered to commit a fraud who does what
he has a right to do.
50.17.151.
Paulus, On the Edict, Book LXIV. No one commits a wrong against another unless
he does something which he has no right to do.
50.17.185.
Celsus, Digest, Book VII. No obligation is binding
which is impossible.
Concerning delegation, the following text is of
interest:
50.17.54.
Ulpianus, On the Edict, Book XLVI. No one can
transfer to another a right which he himself does not possess.
There are also rules to solve inconsistencies between
laws, such as:
50.17.80.
Papinianus, Questions, Book XXXIII. In all legal
matters, the species takes precedence of the genus, and whatever has reference
to it is considered of the most importance.
This rule acquired great importance in the many
centuries when the Digesta had the authority of
Common Law but could be derogated by specific laws of local authorities: in toto iure generi
per speciem derogatur,
see the discussion on consistency.
50.17.100.
Gaius, Rules, Book I. Any obligation contracted under one law is annulled by a
contrary law.
Presumably the contrary law would be a following law, in
time. This seems to be lex posterior derogat legi priori, discussed elsewhere.
It would be interesting to dissect the arguments of
the Roman jurists from the logical point of view: formalizing the ontologies
they are based on, as well as the detailed logical reasoning.
If any historians of Roman laws happen to read this text, I would like
to ask them: was there a progression of legal thinking in Rome that went from
formalism at the beginning, towards freer interpretation based on equity later?
I seem to recognize such evolution from some of the points discussed above:
formalism in the ‘lege agere’
process; formalism still (although possibly progressively less pronounced) in
the formula process; formal ontologies such as Gaius’, which could date from
much earlier times. But then later legal thinking, as documented in much of the
Digesta, avoids definitions and strict deduction in
favor of analogy and equity. Logical methods are replaced by argumentation and
persuasion.
The dissolution of the Roman Empire led to a multiplication of laws,
called leges barbarorum,
which contained a mixture of elementary Roman law concepts with the concepts of
the traditional laws of the invaders, most of them of Germanic origin. They
were usually written in a form of Latin. Understandably, the conceptual level
was elementary.
Much of the medieval Frankish Salic Law (about 500 CE) is written in ECA
style, however the implied ontology is complex,
inherited from both Roman law and Germanic laws. The rules are separated in
chapters: there is a chapter about murder, one about property etc.
The Talmud is a collection of Jewish texts of various ages, compiled
around 200-500 CE. It contains legal texts of considerable logical
sophistication. There are web resources and publications on this; a standard
reference is [Jacobs 2006].
I have heard about studies on the logic of Islamic law, but
unfortunately my ignorance on this is very deep.
Here are some rules found in the Koran [3]. They appear to be written in variants of the ECA style
God
recommends that a son receive twice as much as a daughter.
If
it were more than two women then they receive 2/3rds of inheritance;
if it was an only female she receives half and to his parents 1/6 each;
if he has no children then his mother takes 1/3;
if he has siblings then his mother gets 1/6;
these rules apply to moneys left after satisfying the will and debts to man
and god
to men you have 1/2 what your wives leave if they don’t you have
children; if she had children then you get 1/4 of what is left after the will
or debt.
Your
women get 1/4 of what you leave if you don’t have any children after satisfying
your will and your debts to God and man.
If
man or woman passes away and they have 1 sibling female or male they receive
1/6; if there was more than one sibling they
split the third of the inheritance
Medieval Arabic and Persian philosophers were very familiar with
Aristotelian logic. We all know that much Arabic mathematics was developed in
order to solve the fractions given above in complex cases. It would be
interesting to know whether logic conceptualization or logic deduction was used
by medieval Muslim jurists. However by the little I have read I seem to
understand that analogical thinking was paramount, as in the case of Roman
jurisprudence. [Hallaq 1997] seems to be quite
interesting but I haven’t read it.
[Sowa, Majumdar 2003] discuss analogical
reasoning in Islamic law and especially the contribution of Taqi
al-Din Ibn Taymiyya.
[Joerden 2010] presents several diagrams to
illustrate the relationships between concepts of Islamic law.
Citing from: http://www.tobenot.com/students/061/guides/04_cosmopolitan/03_culture_society/resources/Ebrey_116-131.pdf (viewed Nov. 2009):
‘The
earliest of these [codes] to survive intact is the T’ang
code, issued in 653. This code contains laws on criminal matters like theft and
murder, civil matters like inheritance and ownership of property, and
bureaucratic procedures like transmittal of documents.’
This law is remarkable for its clear
style and the intricate decisional procedures it describes. Essentially it is
ECA, with few legal concepts. But in terms of computer science, one can
recognize well-known concepts such as function calls with parameters, loops
with arithmetic, if statements, case statements etc. These are found especially
in the Action part, where there are rules to calculate the penalties.
Here are two articles:
In
cases in which someone at first hit a person for some other reason, and then
snatched his goods, calculate the value of the stolen goods to apply the law on
robbery by force. When death resulted, the sentence is exile with labor. When
he took the goods by stealth, use the law on robbery by stealth, but increase
the penalties one degree. When killing or injuring resulted, apply the laws on
intentional battery.
Those
who plant public or private land they do not have rights to are liable to a
beating of thirty strokes for the first mu or less, increasing one degree for each five mu. After the penalty reaches one hundred strokes, it
increases a degree for every ten mu. The maximum penalty is one and a half years penal servitude. The
penalty is reduced one degree if the land had been uncultivated. If force was
used, the penalty is increased one degree. The crops belong to the government
or the owner.
The Normans who conquered England in
the 11th Century used Frankish and other Germanic laws that were
influenced by Roman law. England was ruled by an Anglo-Saxon legal system that
had evolved under other influences, but was also essentially Germanic and
Roman. After the conquest, a new legal system was started in England that was
based on custom and precedent, with limited conceptual background. This is what
we know as the Common Law system, distinguished from the Civil Law system of
Roman descent. However in the 16th C. the
Common Law system came under the influence of Roman law jurisprudence and it
acquired many concepts from it. In many matters of civil law, the decision
reached under the Common Law system or under the Roman Law system can be similar today, although the justification (precedent vs.
written code) might be very different.
It seems to me that from a logical
point of view there is little difference between interpreting a precedent and
interpreting a legal opinion found in the Digesta.
A very special position is occupied
by the work of Abraham Fraunce [Fraunce
1588]. Aspects of this work are briefly discussed in [Gray, Mann 2003]. These
authors say: ‘Fraunce was a forerunner of legal knowledge engineering. [His] case diagrams are
not unlike the extensive structure of the Latent Damage Law legal advice tree
constructed by Capper and Susskind four hundred years later.
’
This is a good paper to read for people wanting to see an example
of logic-based legal argumentation. As expected, Fraunce’s
argument is based on powerful assumptions, which are used to reach conclusions
by simple syllogisms.
There is much literature on the logical analysis of
judgments and precedents, but I won’t be able to dwell on this subject at this
point.
Much could also be said about common law systems seen
as learning systems. I’ll mention this later.
Here is another huge hole to be
filled. In the late middle ages, jurists and cultivated people in general were
well informed in Scholastic logic, including the Aristotelian syllogism that
was adopted and developed by the Scholastics. Initially, such doctrines came to
the West through Arabic translations of Greek texts. Did this knowledge have
any influence on legal thinking? This would be interesting to see.
[Bruncken
1917] mentions that late Medieval and early Renaissance jurists considered that
their work consisted in finding for every situation an applicable principle in
the Digesta, which completely denatured the way Roman
jurists considered the same matter.
These jurists tried to conceptualize
what they read in the Digesta, without understanding
the culture that created the text. This led to complications in some cases, by
which they were sometimes vilified (namely by Rabelais, obviously not
interested in complex reasoning).
Medieval jurists emphasized the need
of conceptualization by distilling and using many short mnemonic statements
called brocardi, which essentially were taken as
axioms from which conclusions could be drawn. An example is:
Semel heres, semper heres:
once heir, forever heir
meaning that once one has accepted an inheritance, this
cannot be changed – or otherwise, one cannot be heir for a limited period. This
can be represented in terms of the ‘henceforth’ temporal logic operator:
heir → □ heir
Some such statements were already present in Roman texts, and many of them
are still in use, even in countries outside of the immediate influence of Roman
law. Most of the short Latin texts that I have included in this text were known
as brocardi.
Leibniz (1646-1716), a philosopher, mathematician and jurist, was perhaps
the first person who thought of formalizing the rules of legal thinking.
Apparently he believed that an algebra or logic could be developed to this end.
His contribution to deontic logic is briefly mentioned in the
appropriate section below.
I understand that the ideas of Leibniz on this subject are scattered
among several of his works. So far I haven’t had the time of finding a good
summary of these ideas. If someone can help (in almost any west-European
language) thanks!
In the 19th C there was a great effort on systematization of
legal theory in continental Europe, comparable to advances in sciences and
engineering in the same period. Scattered laws were unified in single codes of
law, the Napoleonic Code being the main example. Roman law remained the base,
however many concepts that are said to come from Roman law were clearly
formulated for the first time in this period.
In fact, it is striking to compare a modern textbook on Roman law with
an ancient textbook such as the Institutes of Gaius. They describe the same
system, but the modern texts are more conceptual and less case-driven. Modern
texts also try to describe the historical development, rather than a fixed
system.
Some lawyers promoted syllogistic reasoning at this time, others
abhorred it.
Mathematical logic started to be developed at the same time, but was
essentially ignored by legal philosophy until the 1950s.
Since these notes are being written in Canada, I should mention the work
of Pierre-Stanislas Bédard
(1762-1829) a Québec politician, journalist, lawyer and judge. He is a
well-known personality in the history of Québec and general information on him
is available on the web. He is believed to be the author of a manuscript “Traité du droit naturel démontré
par des formules algébriques”,
which unfortunately has not reached us. Note that this work was done in
complete isolation, and Bédard’s dates make him an
absolute pioneer in this area. A short report on my examination of a notebook
by Bédard can be found here.
Much of modern western legal theory
is constructed in terms of legal concepts that have been developed over the centuries,
mainly on the basis of Roman law – although other legal system also knew them.
The American jurist Wesley Newcomb Hohfeld developed a well-known ontology of these concepts [Hohfeld 1913]. I follow the presentation of [Sergot 2001 or the enhanced version appeared in Gabbay et al. 2013, see also Sartor
2006]. In fact, the model I will describe should probably be called Hohfeld-Sergot. The concepts are presented in two squares:
the obligative square is as follows:
Right,Claim-----correlative----------Duty
| |
| |
opposite opposite
|
|
| |
No-right, no claim---correlative----
Privilege,Liberty
The potestative square is as follows:
Power-----correlative----Subjection,
liability
| |
| |
opposite opposite
|
|
| |
Disability-correlative---Immunity
The connection between the two
squares is given by the fact that the rights, duties ... in the obligative set generate powers, subjections... in the potestative set that can change rights, duties, etc. One
subject’s right may be protected through that
subject’s power to activate a sanction against
another subject. This is turn can create other rights, duties, etc.
Example (from Hohfeld): The correlative of X's right that Y shall not enter on the land is Y's duty not to enter; but the correlative of X's privilege of entering himself is Y's "no-right" that X shall not enter. (My addition): If Y
violates the duty, X has the power to take Y to court.
Example (from Hohfeld):
X commits an assault on Y by putting the latter in fear of bodily harm; this
creates in Y the privilege of self-defense, that is,
the privilege of using sufficient force to repel X's attack; or, correlatively,
the otherwise existing duty of Y to refrain from the application of force to the person
of X is, by virtue of the special operative facts, immediately terminated or
extinguished.
Example (from Hohfeld):
X, a landowner, has power to alienate to Y or to any other ordinary party. On the
other hand, X has also various immunities against Y, and all other ordinary parties. For Y is
under a disability (i. e., has no power) so far as shifting the legal interest either to
himself or to a third party is concerned.
Example: If a subject A has a right of accessing a data base, then the provider B of the
data base has a duty to make it available, and A has the power of asking access, to which B is subject. However if the database is provided by B on a purely
voluntary basis, A has no right to which corresponds the privilege of B to make it available. A is not able to ask for access, and B is immune from A’s claims.
These concepts can be defined in
terms of deontic concepts of obligation and permission [Sartor 2005 Ch. 19 and 22, 2006, 2008]. See also [Wenar 2011, Saunders 1989].
Many important legal concepts are
based on the concepts just mentioned. Hence, the precise formal expression of Hohfeld’s ontology continues to be the subject of
interesting research.
[Joerden
2010] presents various networks of legal concept, not related to Hohfeld’s and mostly related to criminal law.
However these conceptualizations are not well-known in legal
practice, nor in legal theory. Hohfeld’s ontology has
been criticized by some [Corbin 1921], usually without proposing other
possibilities. It is well-known among legal logic researchers, who are
interested in precise formulations of legal concepts. As we have read in the
citation of Javolenus, lawyers can question any
conceptualization that is not written in the law, and even for these, their
exact meaning can be discussed. In legal logic, we can only derive conclusions
that are valid if the conceptualization is accepted. Putting this in another
way: lawyers can very well refuse conceptualization that do not help them win their
case, and judges can refuse conceptualizations that they do not see as helpful
for their understanding of the social and economic factors that may lead to a
decision. But
us, the Computer people, need conceptualizations to write our algorithms; the Hohfeld conceptualization is one that we can understand and
use – subject to human refutation, of course.
The court system could be considered
as a human-directed system for analog-to-digital conversion. It converts from
continuous reality made of infinite nuances into discrete judicial decisions
stating who is right and who is wrong, who gets what rights, imposing discrete
penalties, etc.
The need for rapid decision of
litigation in contexts of E-commerce or privacy protection may lead to E-laws,
to be enforced automatically by E-courts. Suppose for example that a web query
tries to access an external data base, but the database access control system
denies access on grounds of privacy protection. The requesting agent may have
been programmed to appeal this decision by automatically sending a query to an
electronic system set up by a body such as a Privacy Commissioner. The latter,
after considering the privacy status of the requesting agent and of the data
being requested, may prescribe that access should be provided. This e-judgment would be sent to the data
base access control system, which would immediately allow access. Today, this
is not realistic because it depends on much relevant information being
electronically available: the status of the requesting agent, the status of the
information requested, and the data access laws. Further, the e-judgment
mechanism would have to be programmed. However, all these things are possible
and in fact necessary, so it can be foreseen that one day they will be in
place.
This point is developed in [Logrippo 2011].
It is interesting that some referees of [Logrippo 2011] or of
its variants have thrown themselves in eloquent, involved and cultivated
disquisitions about the complexity and possible unfeasibility of e-judgments
and e-courts, from the social and legal point of view.
They starts with the obvious view that e-judgments, based on
electronically established facts and clear, unambiguous law, seem to be
possible now already. For example, the tax office already issues automatic
assessments that have the force of judgments, although it is not recognized as
that (solve et repete). My
idea is that this concept can slowly (perhaps very slowly) be extended to many
other fields, for which examples are given in the paper. Such rapid e-judgments
will always be appealable to a human court, of course. This evolutionary view
does not pretend to solve at this point complex problems that arise in the
general case: the desirability in general of e-courts, the mechanics of
e-judgments, etc. In my view, solutions to these problems will grow slowly, as
the applications of the concepts of e-courts and e-judgments will grow.
Probably e-courts and e-judgments initially will follow very straight logical
procedures, more similar to what is now done by the tax office than to what
many researchers involved in legal logic are envisioning.
I have touched a raw nerve here: the
fear of societies regulated by computers, while it should be clear that the
path to such evolution will be regulated and controlled by the society.
More discussion on this topic is in
the Feedback section at the end of this paper.
[Narayanan, Bennun
1998] contains some articles presenting views on the use of AI methods for
automatic judgments.
[Benyekhlef,
Gélinas 2005] is a detailed study of application and
consequences of on-line conflict resolution.
[Surden
2011] is a very interesting, very detailed legal theory article that attempts
to precisely identify the characteristics of the areas of law where automatic
judgments may be possible. It is
worthwhile to cite from its conclusions:
Within
the legal literature, this Article pushes back against the view that automation
of legal analysis is not possible in any area of law, by providing a means to
identify relatively determinate portions even amidst a background of
indeterminacy. One observation is that although the task of the lawyer in
performing legal analysis mostly involves professional judgment, there is some
small subset of legal analysis that is relatively mechanical. A rough heuristic
is that where the task of the lawyer is approximately mechanical, it is more
likely to be (eventually) automatable via computers.
The article does not take a position
on whether automation is desirable or possible, but it notes possible gains in
efficiency. It includes detailed discussion of the existing literature on the
subject, and is therefore a good starting point for other reading.
A similar position was taken fifteen
years earlier by one of the pioneers of the idea of automation in the legal
process, Lucien Mehl [Mehl
1995], a jurist. He mentioned then the existence in the legal world of acts
where the decision-taker is essentially bound, and he says that in such cases
it doesn’t matter if the decision is taken by man or machine. He further
mentions the fact that automatic decisions can always be documented by
explaining their reasoning, and can be appealed to human authorities.
In IT, distributed resolution
mechanisms exist, see for example [Crespo 2007].
[Surden
2011b, Surden 2012] is developing a theory of
‘Computable contracts’. “A computable contract is a contractual obligation that
has been formulated such that a computer system can both interpret and
determine whether the obligation has been complied with”.
A similar concept of contracts
exists in the framework of the Open Distributed Processing Reference Model,
ODP-RM [Putman 2001]. An interesting paper with application to e-commerce is [Merz 1998].
In its general outline, the proof
process used in law is the same as the proof process used in mathematics and
logic. Basic principles are postulated, some will come from the law, others are
established facts and others yet will come from common knowledge, common sense,
ethical principles, etc. The proposition to be proven is broken into simpler
propositions, and these are broken into simpler ones recursively until one gets
to propositions that can be considered to be self-evident (the axioms). All the
nodes of the proof tree must be taken care of. Any weak links can be
challenged. This process is discussed in [Sartor
2005, Ch. 27].
In classical logic, a system is
consistent if there is no statement A for which it is possible to prove both A
and not A. Different rules can cover the same cases with contradictory
effects. One rule allows access, another prohibits it. One rule
prescribes a minimum penalty of life, the other allows immediate release.
Inconsistencies can be immediate between laws, or can be the result of logical
derivations. This situation of course cannot be confused with the similar case
in which two rules can be applied, but their results are compatible (e.g. one
norm stipulates a repayment, another stipulates a fine).
Inconsistency is the only real limit
of logic. A system of assertions (legal or otherwise) is consistent if and only
if a logical model can be found for it.
Should legal system be consistent?
This question may seem absurd to logically-oriented readers. If so, they better
read [Haack 2007] for discussion and bibliography on this subject. The question
and its answers are not as simple as they are in purely logical systems. However one can ask what is the effect of inconsistency on
the principle of certainty of law.
As mentioned in [Logrippo 2007],
there can be several types and levels of norms in a normative system. Some
norms may specify general requirements, others may
specify actions and consequences. Some norms may be at the meta-level. Of
course, inconsistencies can exist between such levels.
In classical logic, in an
inconsistent system anything can be derived, because an inconsistency is false
and from false anything can be derived (ex falso quodlibet). Therefore, any inconsistency has
global implications. However this conclusion is insignificant in practice. If
an enterprise database contains an inconsistency, users normally still believe
the rest, although the more inconsistencies are found, the more confidence will
decrease. If an inconsistency is found in rules for a complex game, players
will still play the game according to the remaining rules. Therefore
the users of an inconsistent system tend more to isolate the inconsistent part,
than to say that since the system is inconsistent then any rule applies. And in
those cases that are not flagrant, users try to iron out inconsistencies by
means of interpretation, i.e. by trying to show that norms that appear to be
mutually inconsistent apply to different cases. In other words, it may be
possible to interpret the norms in such a way that the inconsistency
disappears. This is a main occupation for judges and lawyers. In Computer
Science there is a literature on the topic of inconsistency in databases and
inconsistent data sources.
[Breuker,
Valente, Winkels 2005] show, with interesting
examples,
Some normative systems have built-in
conflict resolution strategies. For example, we have seen that in firewalls the
first applicable rule is executed, and the others are ignored.
In access control systems, similar to
legal systems, all rules in the rule set must be considered when deciding
access. This raises the possibility of inconsistencies, if two or more rules
lead to different conclusions. XACML allows the system administrator to set
these meta-rules. Five such meta-rules are defined, and they are known as: Deny
overrides, ordered deny overrides, permit overrides, ordered permit overrides,
and first applicable. The last one is essentially the same that is used in
firewalls.
Legal systems also have rules for
resolving inconsistencies, e.g. in Western jurisprudence, some overriding
principles of a quite different nature have been known for centuries, of which
the best known are the chronological rule, the specialization rule, the
hierarchical rule, and the rule of competence.
The chronological principle (lex posterior derogat priori) states that among two laws at the
same level, the most recent prevails on the previous one. In fact, it is
normally assumed that the successive rule is abrogated by the previous rule. Note
the difference between the case where a law is abrogated and the case where the
law is declared invalid. In the former case, the law can still have had valid
effects during the time of its validity. In IT, the posterior norm will have to
be implemented. In an access control system this norm may still be void if it
is less restrictive than the previous one, since such systems implement deny
override independently of the time in which the regulations came into effect.
So if Alice is denied access to certain files, and then later she is allowed,
the previous rule will stay in effect unless it is removed. Semantic checks at
the time of the introduction of the second rule may point out the existence of
the previous rule to the Security Administrator, who will have to remove one of
the two rules.
Annulment of a norm can be often
impractical in IT systems, because it implies that all the effects of the
annulled norm will have to be rescinded. This means rolling back the whole
system to the state where it was when the norm started to be implemented, but
still keeping the effects of all other norms [Governatori,
Rotolo 2008].
The specialization principle (lex specialis derogat generali) states that a law covering
specific cases takes precedence over a law covering the general case.
Now, this seems to be clear if the general and specific law are in the same
text, or if the special law has followed the general law. However this
principle has sometimes been strengthened to claim that a specific rule takes
precedence over a following general rule (lex posterior generalis non derogat priori speciali). This principle seems to
contradict chronological principle, but such are the discussions of lawyers… To
see how this could work in IT, suppose that Alice, a nurse, was given access to
the financial records of her hospital’s patients. A subsequent hospital
regulation states: nurses do not have access to such information. This
regulation can be implemented immediately if the hospital has an access control
system based on RBAC. Normally the access control system will start denying
access to Alice. However a semantic check at the time when the second rule is
enacted may bring the previous rule to the attention of the Administrator, with
a question: do you wish to keep Alice as an exception?
The hierarchical principle assumes a
hierarchy of norms (lex superior derogat inferiori). For example, in Canada the Charter of Rights and
Freedoms takes precedence over other laws, whether precedent or successive. In
IT, the priority of the higher law will not be automatic. Suppose that in a
consulting company Allan has access to both Chrysler’s and GM’s files. At a
later stage, the Chinese Wall policy is enacted, by
which consultants who work in behalf of a company cannot access files related
to a competing company. This policy will have to be implemented in terms of
detailed access control rule, otherwise it will have
no effect in the access control system.
The competence principle may limit
the validity of laws with respect to certain territorial domains or spheres of
competence. For example, in the province of Quebec it is allowed for cars to
turn right on a red light, but in the city of Montreal, which is in Quebec,
this is not allowed. The traffic laws of Iowa are not applicable in Pennsylvania,
etc. According to some this principle can be assimilated to the specialization
or the hierarchical principle.
There is no priority among these
principles in legal systems and so in some cases more than one of them can be
applied. So there can be meta-principles that regulate the priority between
these principles. It could be decided that hierarchy takes precedence over
chronology; this would be a case where a previous higher law takes precedence
over a successive lower law. Or we saw above the case where a hierarchically
higher law takes priority over a successive specialized law. These are the
things lawyers get their money for.
Apart from these principles, the
main method for resolving apparent inconsistency in law is to make
distinctions. This method takes advantage of the fact that legal definitions
are often imprecise and will say that mutually inconsistent rules apply to
different cases. To separate the cases, reference is often made to the
intention of the law. Similarly, if an inconsistency is found in IT policies,
it can be resolved by separating cases.
In all cases, there is question of
whether the application of the chosen resolution algorithm or principle may
betray the intention of the author of the norms, who may not fully understand
all existing conflicts and their possible solutions. So inconsistencies should
be seen and understood.
There is an important difference
between resolution rules for IT systems and resolution rules for legal systems.
In IT, the rules are applied automatically by a program. In legal practice,
they are guidance for jurists, lawyers and ultimately the judges who apply
them.
An interesting discussion of the use
of ‘preferences’ to resolve inconsistencies in law and ethics is presented in [Sartor 2005, Ch. 7, see also Sartor
1992].
What does it mean for a legal system
to be complete? Much has been written on this subject by philosophers of law,
and I should remember the extensive monograph [Conte 1962].
Some very easy cases can be resolved
by combinatorial analysis. For example, assume an access control system in
which rules are of the type (S,V,O) → P, for
subject, verb, object, permission. A typical rule in this system could be: if
subject A requires to read file X, then this should be permitted. If there are
k subjects, m verbs, n objects, then such as system is complete if and only if
there is a rule for each of the k x m x n possible combinations. Such systems
usually include rules stating that all accesses that are not explicitly
permitted will be blocked, This is a closure norm.
Closure norms can be implicit or explicit, in fact most often they are implicit. Consider for
example the description of a game such as chess. It includes the description of
all possible moves, plus an implicit closure norm stating that no other moves
are allowed. Or consider a criminal law system. In the Western world, it is
usually assumed to include a norm stating that all behaviors not explicitly
disallowed are allowed. No crime without law, nullum crimen sine lege. Closure norms make the system complete. However the
Judaic or Christian legal systems do not seem to consider Moses law ‘closed’,
since they seem to prohibit many behaviors that are not obviously considered in
Moses’ law (but see the discussion on arguments a fortiori, etc).
Another IT example of closure norm is in firewalls that won’t let packets get
through unless there is an explicit permission rule for the specific packet
type. But in Linux routers the implicit closure rule is positive (let pass
through unless explicitly dropped) because the main function of a router is to
forward, not to block.
Can the closure norm be derived? It
seems that when the rule system contains only positive rules, then the closure
norm is negative, and vice-versa. This may have to do with the purpose of the
system, whether the purpose is to permit or to forbid. I am not sure what could
be said about systems that contain both positive and negative rules.
In some systems there can be closure
rules at different levels. For example, in a company
there could be a closure rule that applies to executives, e.g. all information
access is allowed to executives even if no specific rule is present, however
for everyone else the closure rule is to deny access. Closure rules can be
different by department. I have seen examples more complicated than this.
However, whenever there are closure norms, there may be question of
whether those who specified policies have forgotten something. So this question
always makes sense: does the system, including the closure norms, correspond to
the intentions of the system designer, e.g. the legislator, the system administrator?
Considering all combinations can be difficult or impossible when
conditions are added to rules. There can be complex conditions involving
intervals where infinitely many values are possible: quantities, temperatures,
etc. E.g. file X can be accessed only when the authorization of the requestor
is more than $10,000, and only if the requestor sends the request from certain
GPS coordinates.
So another way to look at completeness is to ask whether the system has
all the rules that are required by the security officer’s or the legislator’s intention.
Intention is a well-established concept in software engineering and jurisprudence.
Here is an example from law: suppose that Moses wants to find out
whether Hammurabi has in fact condemned all types of theft. Then Moses should
develop a classification (an ontology) of all behaviors that for him are theft,
then he should go through Hammurabi’s law to see
whether they are all considered.
Here is an example from IT: suppose that in an enterprise, the Bell-La Padula information protection method must be implemented by
means of an access control system. To verify this, it has to be checked whether
all cases prevented by Bell-La Padula are covered by
access control rules. For example, it has to be checked whether there is an
access control rule to prevent Alice, a private, from reading ‘top secret’
files.
A way to ensure that a system of rules is complete with respect to
intentions can be to provide a language to specify directly intentions,
providing an ontology to define all cases to consider, and then automatically
compiling the detailed rules, if this is possible.
Since legal reasoning is informal, incompleteness can be difficult to
distinguish from inconsistency. This is because when there is no immediately
applicable rule all sorts of other rules can be brought in the discussion.
Legal relevance is a related concept. Blowing your nose may be irrelevant from the
point of view of the law of your country or baseball rules. It will be relevant
if you are participating in a etiquette context.
Completeness and closure are considered in detail in [Sartor 2005, Ch.
18].[Breuker, Valente, Winkels
2005] present an interesting discussion showing that it can be quite difficult
to determine completeness and consistency in real systems of norms, since the
underlying ontologies are not given.
We have seen that in some systems there are implicit meta-rules by which
some rules take the priority. I.e. in firewalls, the rules that come first take
the priority. This is not justifiable in logic terms, because order has no
importance in logic. Similarly, in legal system all norms are equally valid
unless otherwise said.
Defeasible logic is a logic well-known in AI
and to researchers on legal logic. It can be seen as a logical mechanism to
manage inconsistency and exceptions. It is a non-monotonic logic first proposed
Donald Nute. It involves three types of propositions:
• Hard rules: these specify that a fact is always a consequence of
another: all packets from spammers.com must be refused.
• Defeasible rules: specify that a fact is typically a consequence of
another: all packets from nuisance.com must be refused
• Defeaters: specify exceptions to defeasible rules: packets from
luigi@nuisance.com must be accepted.
Therefore, before applying a defeasible rule, it must be checked for
defeaters. Defeasible logic provides a framework for specifying exceptions and
priorities. Interestingly, it is difficult to find hard rules in nowadays’
legal systems, a fact that creates a lot of work for lawyers and judges…
The closure norm can be seen as a defeasible norm [4]. It exists in the system, but can be defeated by any other norm. It
applies only if no other norm applies. If defeasible logic
is not used, the closure norm can be constructed as the norm that applies when
the conjunction of the negation of the premises of all other norms is true, and
this conjunction may be very lengthy indeed. However, I have mentioned
elsewhere that some normative systems can have different closure norms for
different roles, levels or departments. I am not sure how to construct such
mechanisms by using defeasible logic.
Interesting methodological observations on the relation between
defeasible logic and classical logic can be found in [Soeteman
2003].
[Sartor 2005] presents a history of this
concept tracing it back to Aristotle. To justify the need of defeasibility in
law, Aristotle starts from the fact that the law must be universal, but this
must be tempered by the need to consider special cases. But in pragmatic terms,
defeasible reasoning finds its justification in the practicality of grouping
cases. If a group that covers a majority of situations can be found, the other
situations can be described as exceptions. This fact is well-known in
programming: many modern programming languages have the concept of exception.
It helps making programs clearer and more efficient.
We mentioned that the Moses code uses the concepts of obligation and
prohibition, but this is not a use of deontic logic. Deontic logic deals with
the relationships among the logical modalities ‘obligatory’, ‘permissible’,
‘forbidden’ etc. There are several variations of deontic logic, however most of
them state the duality between permission and obligation, i.e. a behavior x is
obligatory if and only if the negation of x is not permitted:
O(x) = ¬P¬(x) or ¬O¬(x) = P(x)
Another commonly stated law is that permission is the negation of
prohibition, written F here:
P(x)
= ¬F(x) or O¬(x) = F(x)
There are good articles on deontic logic in the Stanford Encyclopaedia
of Philosophy and in Wikipedia. The latter article mentions the following about
its history (this has been found on August 31, 2009 and of course it may
change):
Philosophers
from the Indian Mimamsa school to those of Ancient
Greece have remarked on the formal logical relations of deontic concepts
and philosophers from the late Middle Ages compared deontic concepts with
alethic ones. In his Elementa juris naturalis,
Leibniz notes the logical relations between the licitum,
illicitum, debitum, and indifferens are equivalent to those between the possible,
impossible, necessarium, and contingens
respectively.
The mention of these insights by Leibniz is very interesting, because
part of Leibniz enormous culture were law and ethics, in addition to logic,
mathematics, etc. See also [Kalinowski 1972][Joerden 2010].
In Hilpinen (1981) there are essays by von
Wright and by Knuttila, where there is discussion on
the history of deontic logic. The second author analyzes some sources going
back to the 14th century, and claims that the basic laws of modern
deontic logic where known at that time. However the authors cited were
philosophers with interests in theology and ethics, not law.
The beginnings of the modern history of deontic logic are dominated by
the thinking of Mally and
von Wright. A discussion of early work in this area is in [Kalinowski
1972].
A belaboured problem in deontic logic is the matter of paradoxes, i.e counterintuitive propositions. It seems that almost
none of the many systems of deontic logic invented so far is free of them. The Web Stanford Encyclopaedia of Philosophy
has a good article on deontic logic, which includes a discussion of
paradoxes. Its final conclusion is : Clearly, there is a lot of work to be done. This phrase was still there in the revision dated
April 2010.
[Sartor 2005, Chapters 17 ff]
present a pragmatic-legally oriented view of deontic logic.
Deontic concepts have different meanings, depending on whether they relate
to machine behavior or human behavior. If I tell a machine that it is
obligatory to do something, e.g ‘all incoming
messages must be acknowledged’ the machine will do it unless it is broken or
badly implemented. However if software requirements say that some software
behavior is obligatory, this is an obligation for the implementer. She may
implement it wrong, perhaps entailing consequences for her.
Similarly in law obligation implies necessity if this can be achieved
entirely within the legal system, without human intervention. For example, if
polygamy is legally prohibited in a country, then it is legally impossible. If
a legal act, such as purchase, has certain obligatory legal consequences, such
as transfer of property, then the latter will happen. But if a law says that a
certain behavior is obligatory, then this or may not be executed by an
individual, perhaps entailing consequences.
In other words, obligation of human action is usually implemented as: do
it, or else. It can be broken. Obligation not depending on human action means
necessity. The concepts are so different that different terms should perhaps be
used; a possibility would be to talk about implication or casual dependency and
not obligation in cases where obligation means necessity [Boella,
van der Torre 2004].
For example, if a specification says: upon reception of message X,
message Y must be sent: this requirement seems to be expressed better as a
simple implication or as a temporal logic statement than as a deontic logic
statement.
Deontic logic is based on a ‘square of oppositions’, described in the The Web Stanford Encyclopaedia of Philosophy; see
[Beller 2008] for experimental validation of this square. This square is homomorphic to the
well-known square of propositional functions and quantifiers,
see [Copi 1979]. [Joerden 2010]
shows that more complex deontic models can be built as hexagons, octagons, etc.
In fact, he shows that such complex deontic models are used in Islamic legal
theory.
Some adventurous designers of a Mitel telephony system tried ad one
point to design a system based on obligations that could be broken with
penalties, then the choice of the action to be taken would be determined by a
comparison of penalties. Apart from this, I am unaware of applications of
deontic logic in practical IT, although current research aims at applying it to
express policies in multi-agent systems. I am unaware of automated tools
specifically designed for deontic logic, although these can be obtained by
adding axioms to standard logic tools.
I respect the work done with deontic logic, and I am also convinced that
deontic logic laws such as the ones mentioned at the beginning of this section
are basic for legal and ethical thinking in many legal cultures. Deontic logic
can be used to advantage to formalize normative texts that use deontic
concepts. However, many normative texts do not use them. I also wonder whether
higher order logics wouldn’t be more flexible and powerful. Constant higher
order predicates can be used to express deontic concepts. This would avoid us
all the peculiarities and the varieties of modal logics and would make tools
for higher order logics immediately useful for research on legal reasoning.
There will be some discussion on this further in this
document.
There is a considerable literature on using combinations of deontic
logic and defeasible logic to express norms. The discussion is sometimes based
on examples such as the following one [Prakken, Sergot 1969]:
There
must be no fence (i.e. it is forbidden to have fences)
If
there is a fence, then it must be white
There
is a fence
The obligation on the second line is often called a ‘contrary to duty’
obligation, which means a secondary obligation that becomes active after
another obligation is violated. So the assignment of a penalty would be a
contrary to duty obligation. This example is based on a more complicated
example presented in [Chisholm 1963]. Several papers have discussed different
formalizations of examples of this type.
I understand that this reasoning can be useful for examples such as the
one above, but many laws and regulations are expressed in (or can be translated
to) simpler terms. Consider for example the following article from the Hammurabi
code:
If anyone agrees with another to tend his field, give him seed, entrust
a yoke of oxen to him, and bind him to cultivate the field, if he steal the
corn or plants, and take them for himself, his hands shall be hewn off.
Would it be reasonable to translate it to the following:
If anyone agrees with another to tend his field, give him seed, entrust
a yoke of oxen to him, and bind him to cultivate the field, he must not steal
the corn or plants, and take them for himself. If he does this, his hands shall
we hewn off.
Logically, this is more complicated and so there should be a good reason
to do this. This reason might be to achieve uniformity in contexts where some
other rules are already expressed by deontic statements.
Unfortunately, one finds several authors who claim that there are
‘right’ and ‘wrong’ formalisms to solve these problems, a type of discussion
that I cannot accept, given that conceptual frameworks have their advantages
and disadvantages, can do certain things but have limitations. In addition, the
applicability of different frameworks depends on how the problems are stated
initially, and what type of conclusions one is interested to draw.
Much discussion in this area is based on contrived examples, which are
not clearly related to legal texts or legal reasoning.
In recent decades, there has been very considerable work on logics of
action and agency, and some of the concepts have been applied to express legal
concepts. A good reference is: ‘The Logic of Action’ in the on-line Stanford
Encyclopedia of Philosophy. I find the situation confusing because there are
several different proposals.
Common law is defined in various ways as a system of law developed on
the basis of precedents established by judges. Common law is thus the result of
an ongoing process. In Artificial Intelligence, the areas of machine learning and theory revision seem to provide the
tools necessary to study and model this process. In intuitive terms, at some
system state, there is a certain set of established rules, which can be
expressed in some form of logic. A new judicial decision causes a state
transition, into a new state defined by a new set of rules, including the rule
just introduced. We now have three cases. The new rule can be independent of
the previous ones: in this case, it can be simply added. Or it can be implied
by the existing ones: in this case, the new rule is unnecessary, redundant. It
is also possible that the new rule is inconsistent with the existing ones. To
avoid this inconsistency, the system of rules will have to be adjusted: this is
theory revision.
In 2012 the USA Supreme Court stated that the "The Affordable Care Act's requirement that certain individuals pay a
financial penalty for not obtaining health insurance may reasonably be
characterized as a tax". So now we know a new fact, and the USA tax
ontology has acquired a new component, with all the logical consequences. All
legal concepts and rules that apply to taxes in general now apply to this new
tax.
The same ideas apply to other systems of law which can be influenced in
some way by judicial decisions. In fact, even the legislative process can
introduce inconsistencies, causing the need of theory revision.
I don’t know much on this, if some of my readers can find references, I
would be pleased to cite them and learn more.
In IT, much study has been generated by a particular type of
inconsistency, called Feature Interaction (FI). This subject attracted the
attention of designers of telephony features, when they realized that the
combination of several features led in some cases to problems, because one
feature could disrupt the intended effect
of another. This could occur on one end of the system, or, worse, between end
points.
An example of distributed FI between end points is the following:
suppose that Alice does not want Bill to be called from her phone, so it puts Bill’s
number on her Outgoing Call Screening list. Don can contradict the purpose of
Alice by putting Connie’s phone on Call Forward to Bill. Now Don can call Bill
from Alice’s phone by calling Connie, and these calls will not be blocked. FI!
Note that there is no error here: each feature worked as expected but the goal
of one feature (or intention of a user) was defeated. Also note that this is
not easy to fix, because of the distributed nature of the system. Two possible
solutions are equally awkward. One would require Alice’s phone to communicate
to Connie’s phone her list of blocked phone numbers at the time of call; but
surely Alice doesn’t want this to happen! A second would be for Connie’s phone
to ask Alice’s phone for permission to forward. But does Connie want this to
happen?
So the concept of intent is
just as relevant here as it is in law..
FIs have been identified in many systems that are not telecom. Examples
exist in security features, home electronics features, etc. They also exist in
enterprises and law, in fact it is easy to find legal
examples similar to the telecom example above. Such examples occur in cases of
delegation, among others. I like this example [5]: Alice does not want her credit card number to be
divulged to third parties. It does business with a company who promises
confidentiality. However this company subcontracts Connie, who, possibly
unaware of the confidentiality issue, may leak the information. This problem is
easier to fix, since a good law would force all companies to be responsible
about transferring private information to reliable parties only.
A more general case of this problem can be stated in the following way.
In a component-based system, some components may have mutually inconsistent
requirements. How can this be detected, can they still be combined?
Two types of detection have been studied: in static detection, the
feature interaction is detected by formally analyzing the specifications, or
policies. This is similar to detecting inconsistency in a normative system.
Static detection can be followed by static resolution, a process where
inconsistencies are ironed out (akin to performing revisions in legal systems).
Dynamic detection is done at execution time, if mechanisms have been put
in place to issue an alarm when a FI is about to occur. Some sort of judicial
process can then be executed, where the processes involved in the FI submit
their needs to an arbitrating entity, who decides who can go ahead. This
arbitrating entity must be provided with all necessary information, and this
can be a difficult thing to do in a telecom system.
A series of workshops and conferences has been dedicated to this topic,
they started in 1992 (proceedings by IOS Press). [Calder et al. 2003] is a good
starting point to study the topic.
Law was invented of course in order to avoid and solve conflicts and so
methods to do this are well-known in the legal domain [Bench-Capon, Prakken 2008]. Unfortunately some such methods are
impractical for IT, where response times must be very fast and systems are very
distributed, without central authorities. The two examples above show this.
Software engineering includes concepts that are also known in law, and
for a very long time. Some of these have already been discussed implicitly.
Here are some more. Can we conclude that computer science and software
engineering are the exact sciences that are most related to jurisprudence?
I have suggested that certain types of legal norms can be read as
programs. The next question is: what is the entity that should execute these
programs? In certain cases (e.g. Hammurabi code or T’ang
code, see below) it is clear that the norms are programs for the judicial
authority. In others it is clear that they are programs for individuals who
find themselves in certain circumstances, or want to reach certain results. But
these two aspects are like the two sides of a medal. In practice, many legal
statements are written in a generic style, and both aspects are present at
once. Suppose that a country wishes to eliminate theft. The principle is stated
as: theft is prohibited. This is implemented (refined) in a law, perhaps
stating that theft is punished by jail. This law can be seen as a program for
judges, to send thieves to jail. However individuals wishing to go to jail see
the same law as a program that enables them to achieve their goal.
This situation is mirrored in Software Engineering. For example, the
description of an access control mechanism can be used to program the mechanism
itself, or the procedure to gain access.
One of the referees of one of my papers has stressed “the necessary inequivalence between laws and computer code”. In some
sense this is obvious, but there are also strong relationships.
How does one refine Moses norms to Hammurabi norms? How does one
translate a requirement into a rule? How can it be recognized that a proposed
refinement is in fact correct? Please refer to the section on deontic logic for
discussion on implementation of deontic concepts.
The concept of meta-theory (which is a theory about another theory) was
invented by logicians and mathematicians at the beginning of the 20th
C. This concept is well known in software theory. Isn’t the constitution
of a country a meta-law? It talks about how laws are created, about the
validity of laws, etc. It is a law about laws.
Another example is the case of laws that state conditions that company
regulations must satisfy.
The concept of meta-law has been known for a long time, but I haven’t
found any solid reference on the subject.
One difficulty in the formalization of legal concepts is that they often
traverse several of these layers.
The concept of conformance and compliance is well-known in software
engineering, especially in relation to software testing and protocol testing. A
specification document may identify compulsory and optional features of a product.
The product will have to satisfy these requirements,
as well it might have additional characteristics.
Similarly, a company regulation will have to satisfy law requirements.
We have done some research on this, and we have treated conformance checks as
consistency checks between different levels of law. But surely this subject
needs more research.
Layering of protocols is a fundamental concept in telecommunications
protocol engineering. Similar concepts are used in law. I’ll take an example
from international affairs, where it is customary that a head of state
communicates with another head of state by sending a message via an ambassador.
So a head of state wants to send a message to her peer entity, another
head of state. For her, this is direct communication however in reality this
has to go through numerous underlying steps. Her office will submit the message
to the Department of External Affairs, including instructions. The Department
of External Affairs is a service provider for the head of state. It provides a
well-defined service, which is transmittal of messages to other heads of state.
But this is not done directly. External has inside itself another service
provider, the External Relations Office. This office performs a well-defined
service, which is transmittal of messages to embassies around the world.
Although the office thinks in terms of direct communication to the ambassadors
abroad, this is not done directly, it is done through
an underlying service provider, and so on up to a lowest level that actually
transmits the information. So initially the message goes down a hierarchy up to
the lowest level. At each level, a layer consisting of an addressed envelope
and instructions to the peer entity abroad is added to the message. When the
package gets to the other country, it will start going up towards the other
head of state. Each level will strip the envelope directed to it and read the
instructions directed to it from its peer in the other country. Eventually the
message will get to the ambassador, who will strip the envelope and read the
instructions directed to her. She now knows that she has a message to be
delivered to the other head of state. What will be left of the package at this
point will be the envelope directed from the first head of state to the other
head of state, containing the initial message. This can now be delivered, the
other head of state will tear the initial (which is also the final) envelope
and read the message.
(Note that in this structure the two Departments of External Affairs do
not communicate, since ambassadors can visit heads of state directly.)
Telecom protocols work just like this.
Here is an example of projections of actions on different normative
dimensions: a group of business people play bridge
while discussing deals and signing contracts. Some of their actions project on
the normative dimension of bridge rules, others project on the normative
dimension of civil or common law, others may be relevant on the ethical
dimension. Some of their actions may project on two or more dimensions.
Aspect-oriented design is an application of similar thinking.
Societies are ruled by laws and customs. Those who do not abide by them
are punished or emarginated. Electronic societies can span the world and these
enforcement methods may not be effective, as we all know by our constant fight
against spam and viruses. Similarly, we can get into what appears to be a bona
fide electronic agreement with a party, and then we are helpless when we see
that the party does something we don’t believe was agreed.
A model for peer-to-peer agreements and electronic societies may be
provided by international law, which is constituted mainly of customs and
multilateral conventions.
Collaboration of distributed systems can only be achieved if they all
use certain common mechanisms. For example, interprocess
communication in a set of distributed processes depends on all the processes
using common synchronized methods. Such tacit agreements constitute
customs.
In law and society, many customs exist that are respected by all who
want to be considered reliable citizen. For example, if Alice lends a book to Bob,
Bob is supposed to check back with Alice if she wants to lend it to Carl.
However in telephony Bob can automatically forward to Carl a call from Alice
without checking with her. So Alice may find herself talking to Carl, although
she may have Carl on her incoming call screening list. This is a well-know
example of interaction of telephony features that is possible because of
violation of a rule that is well understood in society, but not so in
telephony.
Unequal agreements with network entities such as Skype, who dictates
terms of operation, may be similar to protectorates. Consortia such as Apache,
where participants can collaborate in the evolution of the system, are more
similar to alliances. In computing systems we can have multi-faceted situations
where a user can be simultaneously in many such agreements, again creating the
possibility of inconsistencies. People routinely click the ‘Accept all
conditions’ box, happily no one compares all clauses that have been accepted.
Network entities will associate with other entities they trust, and this
will establish societies of mutual trust. Concepts and modes of operations will
be created in these societies, some of which will slowly gain acceptance, thus
enlarging the societies. The concept of Web of Trust is an application of this
idea.
The political process that produces both laws and IT standards may have
an effect on logical clarity. Each party may have a clear logical idea of what
the law or the standard should say, but in order to reach consensus it may be
necessary to express the law in a way that allows several interpretations. It
is then to implementers (judges or programmers) to decide, and this may lead to
a long period of incertitude.
One of the first argumentation models in legal reasoning are the charts
proposed by law scholar John Henry Wigmore in the
early 20th C. These charts are intended to show the structure of
informal legal arguments. They are not based on formal logic but have been
presented as an early form of Bayesian Networks. Much information on this can
be found in the Web.
[Klug 1951] discusses the following models of argumentation used in the
legal process: ‘argumenta a simile (=
analogical), e contrario,
a majore ad minus, a minore
ad majus, a fortiori, ad
absurdum’, all known with Latin names because of their very long history
not only in the legal world, but also in philosophy and ethics. Klug cites
different definitions given by different authors for each of them, along with
legal examples, and attempts to provide different interpretations in logic.
[Haack 2007] discusses the role of abduction
in legal reasoning. These thinking models are also common in science, however
in modern science they are used as the source of conjectures, to be
corroborated by experimentation or more precise analysis. Argumentation models,
as well as the relation between argumentation and inference, are discussed in [Sartor 2005 Ch. 26 ff.].
Here are some simple examples [6].
In
the Qu’ran, the use of wine is forbidden because of
its intoxicating effects. Islamic tradition then forbids the use of
intoxicating drugs. According to Klug’s definitions, this is an application of
the argument ‘a minore
ad maius’ (from minor to major), or possibly of the
similar argument ‘a fortiori’ (for stronger reasons). This reasoning can be
modeled in logic with the help of an ontology, which in this case is a partial
order between intoxicating media, including the fact: wine < drugs. Then we
need an axiom, e.g:
x< y →
(Forbidden(x) → Forbidden(y))
If
we wish to model the fact that performing a more serious offence involves a
more serious penalty, then we need an ontology for penalties, with a partial
order among them, and a corresponding axiom.
Similar
reasoning can be used in IT. For example, suppose that in an enterprise
Confidential files are password-protected, however Top-Secret files are not. The
enterprise’s security policies can be considered incomplete by this reasoning.
This can be implemented in a completeness checking program by using the same
idea: partial orders between document classifications and protection schemes,
as well as an axiom.
Other
argumentation schemes mentioned by Klug can be modeled in similar ways, at
least in their simpler uses. In each case, the main task is to create
satisfactory ontologies, for example an ontology of similarities in the given
domain in the case of reasoning by analogy.
Note
that the use of these arguments in criminal law requires to nuance in some way
the principle ‘no crime without law’. In principle, almost every behavior can
end up being considered to be legislated by analogy or similarity. This also
can make it impossible for law to be incomplete [Conte 1962].
The
argument ‘ad absurdum’ corresponds to the proof by contradiction and can be
modeled in logic by showing that if the contrary of the desired conclusion is
assumed, then a contradiction is derived, or no logical model exists for the
system.
Often
in the legal literature one can find argumentation models that are based on
complex intuitions that are difficult to formalize. It is also common for
several of the mentioned argumentation models to be used at once, packed
together in short phrases, so a detailed analysis may be necessary to
tentatively recognize reasoning patterns.
This
is where Artificial Intelligence methods have their place. For example, one can
try to automate analogical thinking by calculating degrees of similarity of
legal situations. An AI-oriented view of legal reasoning is presented in the
book of [Sartor 2005]. This book analyzes many types
of legal reasoning with an AI approach.
I
have found the most convincing explanation of analogical thinking in computer
science terms in [Sowa, Majumdar 2003]. This paper
claims that deductive, inductive and adbuctive
thinking are applications of analogical thinking, which is explained in terms
of conceptual graphs. It cites the 14th-C Islamic jurist and legal
scholar Taqi al-Din Ibn Taymiyya
for his analysis of analogical thinking in law, and for his comparison of the
latter with Aristotelian syllogism.
While
classical deductive logic produces certitudes, argumentation models produce possibility
and probability. This observation establishes their place in the legal
process. Since the latter must produce a
decision, argumentation models must be enclosed in deductive processes
expressed in classical logic [Soeteman 2003]. This
situation is similar to the one found in automated control systems. For
example, consider a nuclear reactor shutdown system: it takes a number of
continuous parameters, which indicate the likelihood of a meltdown: pressure,
temperature, and possibly a database of dangerous scenarios; it must produce a
binary decision, shutdown or not.
Legal
decision systems are discussed in [Yannopoulos, Reed
1997][Oskamp, Tragter 1997]. The construction of such systems is possible
in limited areas of law, where definitions are precise and rules are clear. I
briefly mention the role of AI in legal decision-making in [Logrippo 2011].
A
comprehensive survey of the role of logic in computational models of legal
arguments, with many citations, can be found in [Prakken
2001]. This paper develops a view based on four layers: a logical layer
(constructing an argument); a dialectical layer (comparing and assessing
conflicting arguments); a procedural layer (regulating the process of
argumentation); and a strategic, or heuristic layer (arguing persuasively).
The
possible use of AI methods to model the common law system was mentioned
earlier.
Strangely,
the discipline of Legal Logic is now considered by many as
part of Artificial Intelligence, see [Bench-Capon et al. 2012].
There
is a lot of research on argumentation frameworks, focussing on formalizing how
arguments can attack or reinforce each others [Dung 1995]. This theory is quite
elegant but if there is no basis on the semantics of the arguments and their
basis in law, it becomes empty of contents.
Some laws must be implemented in software. In other words, software
requirements have to be derived from laws and implemented in software. This
process is particularly important in areas such as: fiscal law, e-commerce law,
privacy law.
Essentially, the law has to be translated into some formalism for
expressing software requirements in some software development methodology, e,g, UML. This is called
‘requirement extraction’. When this is done, the normal software development
process can take over. So the research in this topic focuses on the requirement
extraction phase [Hassan, Logrippo 2009].
The yearly RELAW workshop, an affiliated workshop of the IEEE
Requirement Engineering conference, is dedicated to this topic, and its
proceedings can be found in the IEEE database.
This
section will discuss automated deduction tools. The tools I will consider fall
in the following categories:
I
have already mentioned that legal thinking is dominated by political, ethical,
social, economic concerns. In the western culture, equity and the intent of the
law remain two main interpretation criteria. Argumentation models, which lead
through ‘discourses’, or chains of arguments, that are plausible, intuitively
‘logical’ but have no formal logical basis, dominate the legal process, see
[Haack 2007] (a remarkable philosophical paper with many references), also [Kalinowski 1983][Sartor 2005]. In
principle argumentation models can be expressed in formal logic with the help
of suitable ontologies, although complexity and consistency may be challenges.
As we have already mentioned, argumentations are dominated by complex
assumptions or domain axioms (the ontologies), connected by simple logic, which
may all be left unspecified, possibly because they are too complex to specify.
This type of legal thinking has been modeled by using artificial intelligence
methods. However one might wonder to what extent mechanising traditional legal
thinking will perpetuate its faults, among which are occasional obscurity,
unpredictability and inconsistency. Although human judgment is necessary in
many areas of law, in others clarity, predictability and consistency, as well
as simplicity, are just as necessary. I have already mentioned the growing
areas of e-commerce and privacy protection, where decisions of legal relevance
must be reached and enforced impersonally and at electronic speed. It seems to
me that clear formal logic methods should be used in these areas.
If
one could map out various methods of reasoning in various areas of the legal
process, surely one could find areas where formal logic is prevalent. The
believer might detect an extremely slow process of increased conceptualization
in legal thinking over the millennia, conceptualization which is a necessary
premise for the use of logical inference methods. Already for some time now, in
the fiscal legal systems of many countries we have very clear conceptualization
and inference rules, so that initial assessments, fines, etc. are calculated by
computer.
‘Classical’,
two-valued logic seems to be prevalent: either one owns something, or one
doesn’t. Either one is guilty, or one isn’t. However probabilistic thinking can
also be used in the chain of reasoning.
Probably
the most comprehensive book ever written on legal reasoning is [Sartor 2005], an 844 pages volume. It features chapters
analyzing many types of legal reasoning. Happily, it is also very well written
and pleasant to read, with good examples on almost every page. I could have
cited it much more. A good ‘motivational’ article for this general research
area, with many suggestions for research and many references, is [Bench-Capon, Prakken 2008]. A more recent and very useful survey paper
is [Bench-Capon et al. 2012]. Other comprehensive recent books, covering many
subjects discussed above, are [Haage 2005] [Stelmach, Brozek 2006] [Joerden
2010]. This flurry of substantial publications witnesses the increasing
attention that our field is receiving.
I can’t resist concluding all this without attempting my own philosophy, which I will base on social and scientific communication concepts (one of many possible explanations). Many processes of social communication are based on reproducibility. Natural sciences and engineering are based on reproducibility and predictability. However a person’s reasoning is based on chaotic processes that depend on many things that go on in the person’s mind. So a person must state her reasoning in a way that she and others can understand and verify, reproduce, remember. Logic and mathematics are built on concepts and processes that many people are able to understand and reproduce, so they are good means to communicate in certain environments and situations. Predictable and reproducible processes, such as scientific and engineering processes, can be based on logic and mathematics. Other ways to communicate exist, for example some are based on feeling and sentiment, and they can also produce understanding and predictable, reproducible results; this is the area of social sciences and other areas such as argumentation. Legal thinking stands at the intersection of several of these reasoning and communication processes.
Ilmar Tammelo (Narva, Estonia, 1917 –Sydney, Australia, 1982) wrote some
of the first books on the use of modern formal logic for the analysis of legal
reasoning. [Tammelo 1978] contains a number of
interesting examples taken from real-life judgments. The book concludes with the
following text which is worth citing in full:
The
nature and role of legal logic can be epitomized in the form of the following
manifesto:
(1) Legal logic is indispensable for any rational treatment of legal
problems.
(2) Legal logic is complementary to other disciplines of fundamental
legal thought.
(3) Legal logic is not a source of the material contents of law but an
instrument of legal thought.
(4) Legal logic is a prerequisite of utilisation of modern technology in
the field of law.
(5) Legal logic is indispensable for promoting expediency, efficiency,
and integrity in legal reasoning.
(Note: This list is a personal jumble,
it includes publications that I have found useful, as well as others that I
would like to know better. A great majority are available in the web; but I
have also cited certain sources that are difficult to find. Needless to say, it
is quite possible that better sources exist in many subjects and if so I would
like to know from my readers).
Carlos Alchourròn, Eugenio Bulygin
(1972): Normative Systems. Springer.
Alberto Artosi,
Giovanni Sartor (2016): Leibniz as a jurist. In: The Oxford Handbook on Leibniz, Oxford
Handbooks on Line. http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199744725.001.0001/oxfordhb-9780199744725-e-38?rskey=8DOFg7&result=4
Steven
Barker (2012): Logical Approaches to Authorization Policies. In: Logic
Programs, Norms and Action
LNCS 7360, 2012, 349-373.
Trevor J.
M. Bench-Capon, Michal Araszkiewicz, Kevin D. Ashley,
Katie Atkinson, Floris Bex, Filipe Borges, Danièle Bourcier, Paul Bourgine, Jack G. Conrad, Enrico Francesconi,
Thomas F. Gordon, Guido Governatori, Jochen L. Leidner, David D.
Lewis, Ronald Prescott Loui, L. Thorne McCarty, Henry Prakken,
Frank Schilder, Erich Schweighofer,
Paul Thompson, Alex Tyrrell, Bart Verheij,
Douglas N. Walton, Adam Zachary Wyner (2012): A
history of AI and Law in 50 papers: 25 years of the international conference on
AI and Law. Artif. Intell.
Law 20(3): 215-319
Trevor J.M.
Bench-Capon, Henry Prakken
(2008): Introducing the Logic and Law corner. Journal of logic and computation,
18(1), 1-12
Sieghard Beller (2008): Deontic reasoning squared. In B. C. Love, K.
McRae, V. M. Sloutsky (Eds.), Proc. 30th Annual Conf.
of the Cognitive Science Society. Cognitive Science Society, 2103-2108.
Karim Benyekhlef, Fabien Gélinas
(2005): Online dispute resolution. Lex Electronica (10), 2, 1-129.
Guido Boella and Leendert van der Torre
(2004): Fulfilling or violating obligations in multiagent
systems. IEEE/WIC/ACM International
Conference on Intelligent Agent Technology (IAT 2004) 483-486.
Joost Breuker, André Valente, Radboud Winkels (2004): Legal Ontologies in Knowledge Engineering
and Information Management. Artificial Intelligence and Law 12: 241-277.
Joost Breuker, André Valente, Radboud Winkels (2005): Use and Reuse of Legal Ontologies in
Knowledge Engineering and Information Management. In: V.R. Benjamins
et al (Eds): Law and the Semantic Web, LNAI 3369,
36-64.
Scott
Brewer (2012): Introduction to basic concepts for the study of logic in legal
argument. Summer School in Law and Logic. https://lawandlogic2012.wordpress.com/
Ernest Bruncken (1917): Science Of Legal
Method, Boston Book Company. Chapter IV, Sections 3 and 4
Muffy
Calder, Mario Kolberg, Evan
H. Magill, Stefan Reiff-Marganiec (2003): Feature
Interaction: A Critical Review and Considered Forecast. Computer Networks,
41(1) 115-141.
CBC -
Canadian Broadcasting Corporation (broadcast by Paul Kennedy) (2011): http://podcast.cbc.ca/mp3/podcasts/ideas_20111019_45513.mp3
Gaetano
Carcaterra (1996): Corso di filosofia del diritto, Bulzoni Ed.
Roderick M.
Chisholm (1963): Contrary to duty imperatives. Analysis, 24(2), 33-36.
Amedeo G.
Conte (1962): Saggio sulla completezza degli ordinamenti giuridici. Giappichelli.
Arthur
Corbin (1921): Jural Relations and Their
Classification. Faculty Scholarship Series. Paper 2873.
http://digitalcommons.law.yale.edu/fss_papers/2873
Rui G.
Crespo, Miguel Carvalho, Luigi Logrippo
(2007): Distributed Resolution of Feature Interactions for Internet
Applications. Computer Networks 51 (2) 382-397.
Irving M. Copi (1979): Symbolic Logic. Prentice-Hall
Phan Minh
Dung (1995): On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person
games. Artificial Intelligence 77 (1995) 321-357.
Ronald
Dworkin (1978): Taking rights seriously. New impression with a reply to
critics. Duckworth, London.
Meritxell
Fernández Barrera (2009): Legal ontologies -
Historical origins and state of the art. http://lexsummerschool.files.wordpress.com/2009/09/sate-art-legal-ontologies.pdf (Consulted Jan 2011).
Meritxell
Fernández Barrera, Giovanni Sartor
(2010): Classifications and the Law: Doctrinal Classifications vs.
Computational Ontologies. EUI Working Papers LAW No. 2010/10. July 2010. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1698686 (consulted Jan 2011).
Abraham Fraunce (1588): The Lawyer's Logic, reprinted by The Scolar Press Limited, Menston,
1969. Original title: Lawiers Logike.
Dov Gabbay, John Horty, Xavier
Parent, Ron van der Meyden, Leendert
van der Torre. Handbook of Deontic Logic and Normative Systems. College
Publications, 2013
Guido Governatori, Antonino Rotolo (2008): Changing legal systems: Abrogation and
Annulment. in: R. van der Meyden,
Leendert van der Torre (Eds.). Deontic Logic in
Computer Science, DEON 2008, Proc. of the 9th
International Conference, DEON 2008. LNAI5076, Springer, 3-18.
Pamela N.
Gray, Scott Mann, S. (2003). The Fraunce (1588) model
of case-based reasoning. In Proceedings of the 9th
international Conference on Artificial intelligence and Law (Scotland, United
Kingdom, June 24 - 28, 2003). ICAIL '03. ACM, New York, NY, 89-90.
Stefan Gruner (2010): Software Engineering Between Technics
and Science: Recent Discussions about the Foundations and the Scientificness of a Rising Discipline. J.l for General Philos. of Science / Zeitschrift
für allgemeine Wissenschaftstheorie 41/1, 237-260, Springer Verlag, June 2010.
Susan Haack
(2007): On Logic in the Law: “Something, but not All”. Ratio Juris, 20 (1),
1-31.
Jaap Hage (2002). What to expect from legal logic?. J. Breuker e.a.
(eds.), Legal Knowledge and Information Systems. Jurix
2000: The Fourteenth Annual Conference. IOS-Press, Amsterdam, 77-87
Jaap Hage (2006): Studies in Legal Logic. Law and Philosophy
Library, Springer, 2005.
Wael B. Hallaq (1997): A history of Islamic legal theories: an
introduction to Sunni usul al-fiqh.
Cambridge University Press (available in Google Books)
Waël
Hassan, Luigi Logrippo: A Governance
Requirements Extraction Model for Legal Compliance Validation. In Proc.
IEEE 17th International Requirements Engineering Conference (RE'09): RELAW
Workshop. Atlanta, GA. Sep. 2009.
(Electronic proceedings, 6 pages)
Risto Hilpinen, (Ed.) (1981): New Studies in Deontic Logic –
Norms, Actions, and the foundation of Ethics. University of Turku, Turku,
Finland: D. Reidel Publishing Company.
Wesley
Newcomb Hohfeld (1913): Some Fundamental Legal
Conceptions as Applied in Judicial Reasoning. Yale Law Journal 16. This classic
paper is available in a number of contemporary re-printings.
Louis
Jacobs (2006) : Studies in Talmudic Logic
and Methodology, Vallentine Mitchell Publishers.
Anthony
J.I, Jones, Marek J. Sergot (1992): Formal
Specification of Security Requirements Using the Theory of Normative Positions.
In: Deswarte, Y., Quisquater,
J.-J., Eizenberg, G. (eds.) ESORICS 1992. LNCS, vol. 648,
pp. 103–121. Springer, Heidelberg (1992)
Anthony
J.I. Jones, Marek J. Sergot (1993): On the
characterisation of law and computer systems: The normative systems
perspective. In: Deontic Logic in Computer Science: Normative System
Specification, J.-J.C. Meyer and R.J. Wieringa (Eds), Wiley.
Jan C. Joerden (2010) : Logik im Recht, 2te Aufl.,
Springer.
Georges Kalinowski (1972): La logique des normes. Presses
Universitaires de France.
Georges Kalinowski (1983) : La logique juridique et son histoire. In Simposio de Historia de la Logica. Anuario Filosofico de la Universidad de Navarra Pamplona, 1983, vol. 16, no1, pp. 331-350. http://dspace.unav.es/dspace/retrieve/4798/license.txt (consulted December 2009).
Ulrich Klug (1951): Juristische Logik, Springer-Verlag.
Luigi Logrippo (2007): Normative Systems: the Meeting Point between Jurisprudence and Information Technology?
In: H. Fujita, D. Pisanelli (Eds.): New Trends in Software Methodologies,
Tools and Techniques – Proc. of the 6th SoMeT 07. IOS
Press, 2007, 343-354.
Luigi Logrippo (2011): From
e-business to e-laws and e-judgments: 4,000 years of experience. CYBERLAWS 2011, Proc. of the Second
International Conference on Technical and Legal Aspects of the e-Society,
Guadeloupe, Feb 2011, 22-28.
Giuseppe Lorini
(2003) : Il valore logico delle norme. Atlantica Editrice.
Lucien Mehl (1959) Automation in the legal world: from the machine
processing of legal information to the "Law Machine". National
Physical Laboratory Symposium No 10, Mechanisms of Thought processing (2
vols.). London: HMSO.
Lucien Mehl (1995) À
quelles conditions une décision juridictionnelle, administrative ou privée,
peut-elle être totalement ou partiellement automatisée? Publ.
de l’assoc. québecoise
pour le développement de l’informatique juridique.
Sharad
Malik, Lintao Zhang
(2009) : Boolean Satisfiability – From Theoretical Hardness to Practical
Success. Comm. ACM 57 (8), 76-82.
Michael Merz, Frank Griffel, M. Tuan Tu, Stefan Müller-Wilken, Harald Weinreich,
Marko Boger, Winfried Lamersdorf
(1998): Supporting Electronic Commerce Transactions with Contracting Services.
Int. J. Cooperative Inf. Syst., 249-274.
Ajit
Narayanan, Marvyn Bennun : Law, Computer
Science and Artificial Intelligence. Intellect, 1998.
Anja Oskamp, Maaike W. Tragter (1997): Automated Legal Decision Systems in
Practice: The Mirror of Reality. Journal of Artificial Intelligence and Law. 5
(4), 291-322.
Edward
Poste (1875): Elements of Roman law by Gaius. Clarendon Press. Pages 522-530.
Henry Prakken, Marek Sergot (1996):
Contrary-to-Duty Obligations. Studia Logica, 57, 91-115.
Henry Prakken,
Giovanni Sartor (2001) :
The role of logic in computational models of legal argument – a critical
survey. In: A. Kakas, F. Sadri (eds.): Computational logic from logic
programming into the future. Springer-Verlag 2001.
Janis R.
Putman (2001): Architecting with RM-ODP. Prentice-Hall
Jean Ray
(1926) : Essai sur la structure logique du code civil français. Alcan (Paris).
Giovanni Sartor (1992): Normative conflicts in legal reasoning.
Artificial Intelligence and Law 1: 209-235 (Kluwer).and Law 1: 209-235,
1992.rtificial Intelligence and Law 1: 209-235, 1992.
Giovanni Sartor (2005): Legal Reasoning: A Cognitive Approach to the
Law. Published as Chapter 5 in: A treatise of legal philosophy and general
jurisprudence, Springer (available on-line on the Springer site).
Giovanni Sartor (2006): Fundamental legal concepts: a formal and
teleological characterization. Artificial Intelligence and Law 14 (1). See also a related presentation: http://deon2008.uni.lu/Sartor.pdf
Giovanni Sartor (2009): Legal concepts as inferential nodes and
ontological categories. Artificial intelligence and Law, 17: pp. 217–51.
Giovanni Sartor, Pompeu Casanovas,
Mariangela Biasiotti and Meritxell
Fernández-Barrera (2011): Approaches to Legal
Ontologies – Theories, Domains, Methodologies. Springer.
Kevin W.
Saunders (1989): A Formal Analysis of Hohfeldian
Relations, 23 Akron L. Rev. 465.
Marek J. Sergot, Fariba Sadri, Robert A. Kowalski, Frank R. Kriwaczek, P. Hammond, H. T. Cory (1986): The British
Nationality Act as a Logic Program, in Comm. ACM, 29 (5), 370–386.
Marek J. Sergot
(2001): A Computational Theory of Normative Positions. ACM Trans. on Comput. Logic, 2(4), 581-622.
Jerzy Stelmach, Bartosz Brozek (2006): Methods of Legal Reasoning. Springer.
John F.
Sowa, Arun K. Majumdar (2003).
Analogical Reasoning. In: A. Aldo, W. Lex, & B. Ganter,
eds. Conceptual Structures for Knowledge Creation and Communication, LNAI 2746,
Springer-Verlag, pp. 16-36
Arend Soeteman (2003): Legal Logic? Or can we do without?
Artificial Intelligence and Law 11, 197-210.
Harry Surden (2011a) The Variable Determinacy Thesis, 12 Columbia
Science and Technology Law Review 1, (91 pages), (April 2011)
Harry Surden (2011b): Computable Contracts (Presentation) http://www.youtube.com/watch?v=KLAE_SKMeAY
Harry Surden (2012): Computable Contracts. UC Davis Law Review,
Vol. 46, No. 629, 629-700.
Ilmar Tammelo (1969): Outlines of Modern Legal Logic. Franz
Steiner Verlag, Wiesbaden 1969.
Ilmar Tammelo (1978): Modern Logic in the Service of Law.
Springer-Verlag.
André
Valente (1995): Legal knowledge engineering - A modelling approach. IOS Press.
André
Valente (2005): Types and Roles of Legal Ontologies. In: V.R. Benjamins et al. (Eds.): Law and the Semantic Web, LNAI
3369, 65-76.
Bart Verheij, Jaap C. Hage; H. Jaap Van Den Herik (1998): An integrated view on rules and principles.
Artificial Intelligence and Law, 6 (1), Mar. 1998 ,
3-26.
Alan Watson
(1995): The Spirit of Roman Law. University of Georgia
Press. Chapter 12: A Central Indefiniteness; and 13: Legal Isolationism III.
Radboud
G.F. Winkels (2010): Legal ontologies. http://www.lri.jur.uva.nl/~winkels/LegalOntologies.html
(Consulted Jan 2011).
Tom Van Engers, Alexander Boer, Joost Breuker,
André Valente (2008): Ontologies in the Legal Domain. Chapter 13 of: Digital Government. Springer.
Leif Wenar (2011): Rights, The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.) http://plato.stanford.edu/archives/fall2011/entries/rights/. Consulted April 2014.
George
Wright (1983) : Stoic midwives at the birth of
jurisprudence. Am. J. Juris. 169 1983, 169-188.
Georgios N.
Yannopoulos, Chris Reed: Modeling the Legal Decision
Process for Information Technology Applications in Law.
Kluwer Law International, 1997.
2. Mirella Capozzi and Carlo Cellucci of the University of Rome helped me with the
interpretation of this text
6. Thanks to Sofiene Boulares for the two
following examples
This section includes feedback I have received from
identified people and from anonymous referees. Such feedback contains valuable points
of discussion and so it should not remain hidden in my personal files.
http://cs.gmu.edu/cne/denning/
In
skimming the introduction, the following thoughts occurred to me:
(1)
US law now has algorithms written in to it.
The IRS code,for
example, contains algorithms for computing the deductions Congress has decided
to allow. As far as I can tell, they
embed the algorithm because in their conference committees they negotiated
using spreadsheets ("Well, I'll support your amendment if you'll reduce
the tax loss according to our spreadsheets.") They play with the numbers on the spreadsheet
until the bottom line comes out right.
By that time there is no longer a "principle" involved in
arriving at the amount of the deduction, so they instead just state the
algorithm.
(2)
There is an attitude among lawmakers that they are writing algorithms to
control (govern) society. They try very
hard to anticipate all the little ways people might try to circumvent the
intent of the law and write in clauses to block those actions. They literally think they are
"programming society". But of
course there is a huge difference between programming a computer (a
deterministic machine) and governing a society (a network of conversations and
practices that can take unpredicted directions at any time). There is a huge danger in failing to make
the distinction and a hubris in thinking that programming society is
possible. Laws seem to work better when
they state their intent and give their principles, than when they try to
prescribe or block behaviors.
Here are some tentative answers to your insightful remarks:
Your remark (1): In software, we
know how to keep track of principles. They are expressed as invariants whose
truth must be maintained, or as goals that must be achieved. So something can
be done for tax legislation, as well, if the legislators can agree on what the
principles are. A model checker can try to see whether the principles have been
respected in the algorithm. But what happens in bad law mirrors what happens in
bad software: it gets complicated, details take over, and no one can figure out
what the invariants are, or even what the program is really supposed to do. In
OSI protocols, every protocol had to have a service specification. But same layers were poorly designed, and
there was little difference between the protocol specification and the service
specification. Similarly for Internet protocols: if there are any service specifications at all,
they are usually encumbered by protocol details. Poor design IMOMO. Many areas of engineering are more advanced than IT (or law) in this
respect, and this would be a long discussion…
Your remark (2). Lawmakers *are* writing algorithms to control certain
behaviors in society. Now we get into politics, but almost every political
philosophy asserts that certain behaviors must be controlled, programmed.
Already the ancient lawmakers I talk about tried to do this, and you can read
the little programs in the Hammurabi code, or in the Chinese T'ang code. Of course, this can get intrusive and the
society as a whole must decide where this should stop.
You
say that there is a difference between programming a deterministic machine and
programming social behavior. This is
very true, and I touch on this when I talk about deontic concepts. Humans have
free will, machines are not supposed to have it. A malfunctioning human must be
corrected; a malfunctioning machine can be stopped. This distinction has many
consequences. It is a point that must be retained. But, I claim, there are
*certain areas* of law where determinism, efficiency and certitude are
important. Commerce law may be one, tax law and privacy law may be two others.
It's for us to decide. Human mechanisms may be set up to review doubtful
outcomes, to see whether the human concept of what should happen is reflected
in certain outcomes. The 'necessary distinctions' you talk about must be made,
but according to me they should be inside law, they should separate one type of
law from another. Technology offers possibilities, but distinctions must be
made to decide where and how they should be used. A car can be used to drive to your cottage, or
to drive into a crowd.
This
paper has undergone several revisions, and was submitted in two versions to a
couple of venues (one version was published in CYBERLAWS 2011, but the version on my web site is enhanced with respect to
conference version).
Some
of the referee comments are quite interesting and worth considering. One important point seems to be the
following: Your (my) view is either trivial or too ambitious. On one hand, e-judgments are already a
reality (see traffic tickets, tax assessments). If we go beyond that, we run
into insurmountable difficulties such as:
• The
inevitable ambiguity of the law, which supports the law’s capability to evolve
and be reinterpreted in various ways; hence it is very rare that law can be
specified precisely. So it remains to be seen whether e-commerce laws (for
example) can ever be specified in precise ways.
• Difficulties
to interpret all sorts of evidence: precise, unambiguous evidence is very rare.
Is it? I think I have some good examples of precise evidence in the paper, but
this is to be discussed further.
• The
examples in the paper refer to easy cases. Quite right. I don’t advocate
using e-judgments in difficult cases. Some of my legal contacts tell me that
much of law is easy drudgery.
• “Legal
scholars have for over a decade recognized that there are reasons to think that
the automation of legal reasoning will result in the denial of due process, the
overenforcement of unfair laws, and profound
injustice.” This seems to be an overreaction, since in my view e-judgments
would only be first-degree judgments, immediately appealable. Abuse of concept
is always possible but since most technologies have good and bad uses,
technologists keep developing them.
• “It
is naive to assume that the proposal will be taken as such. As the traffic
speeding example shows, digital legal practice may rather evolve stepwise, and
not from some grand design. Maybe that is also that the author aims at, but
does not make such perspective explicit. It has to be accepted piecemeal and
evolve accordingly in phase with political, social and legal developments. The
limiting factor here is whether and where current views on technology really
enable such a development and practice, and that is where the technical issues
come in.” I quite agree. My proposal is futuristic but, I think, worth
discussing in principle, read on.
One
of the referees mentioned a number of important open research issues. I will
report them textually below:
• The
structure of legal reasoning (argumentation, legal assessment methods, legal
drafting (consistency checking; simulation, etc.)
• The
representation of law, the representation of (legal) cases and the mapping of
the former to the latter, i.e. the relationship between legal knowledge and the
understanding of what happened (or may happen) in the world.
• Both
issues face the more fundamental and theoretical problems of adequate knowledge
representation formalisms, and completeness and consistency in reasoning. The
issues are here:
• The
deontic nature of law and its representation.
• Law has
to deal with a real world so we cannot make closed world assumptions and
therefore completeness cannot be acquired (maybe even more that in more
technical domains). AI has learned how to cope with (some of) these problems in
practical senses, which is not simply using `heuristics' as the author thinks.
Knowledge representation in law is a hot issue, where e.g. ontologies are used
to capture the meaning of legal terms in a consistent way (i.e. as specified,
intended and, or used in law; not different from law as the author assumes;
only in a different way).
• These
insights reflect back on legal theory but also on legal practice, e.g. in
drafting law. Practically, it means that where machines are good at -exhaustive
(reasoning) procedures-, where humans easily fail, and vice versa (e.g. in
using large amounts of common sense knowledge in particular to understand
causal relationships in human actions). Therefore, the issue has shifted
towards the question how machine reasoning and human reasoning can be used
complementary to achieve a higher degree of accuracy in legal reasoning (e.g.
in testing new legislation using simulators).
• Laws
themselves are justified by political, and/or moral and ethical beliefs.
However, legal reasoning finds its justifications in law itself. These
justifications (and if necessary explanations) go often by the name of
`argumentation structure' which bring events and states identified in the
description of cases into relation with statements of law. The (logical)
foundations of these
argumentations are not undisputed.
One of the referees also had the following valuable
list of references. They are all worth reading, but I highly recommend the
essay by Surden, which is the most recent and covers
several of the others. BTW the referee mentions that these references are to be
considered for the “necessary inequivalence between
law and computer code” (which is an obvious point, isn’t it?).
• Samir Chopra & Lawrence White, A Legal Theory for Autonomous Artificial Agents (U. Michigan
Press 2011)
• Danielle Keats Citron,
"Technological Due Process," Washington University Law Review (2008)
• James Grimmelmann,
"Regulation by Software," Yale Law Journal (2005)
• Lawrence Lessig,
"The Law of the Horse: What Cyberlaw Might
Teach," Harvard Law Review, (1999)
• Lawrence Solum,
"The Interpretation/Construction Distinction," Constitutional
Commentary (2010)
• Harry Surden,
"The Variable Determinacy Thesis," Columbia Science & Technology
Law Review (2011)
My conclusion: in spite of many practical and
theoretical issues (in fact, because of these) e-judgments are an interesting
concept and worth studying, both from the legal and the technological point of
view.
The Referee wrote:
My main problem with the paper is that the underlying
language is based on first-order logic and it is well know that first-order
logic is not appropriate to represent legal reasoning. There are cases where deontic distinctions
are necessary (how do you distinguish if something is just factual, permitted,
obligatory or prohibited). Also, first-order logic cannot handle reasonig about "violation" but in some areas (for
example compliance with business contracts) being able to handle violations and
compensation for violations is absolutely required. (see
Guido Governatori. Representing Business Contracts in
RuleML. International Journal of Cooperative
Information Systems 14 (2-3): 181-216, 2005.)
Second the paper seems to ignore work on business
process compliance based on deontic logic approaches, claiming there are no efficient
approaches (this is not true), see for example:
Guido Governatori. Law,
logic and business processes. In Third International Workshop on Requirements
Engineering and Law. IEEE, 2010.
Guido Governatori, Antonino Rotolo: An Algorithm for Business Process Compliance. JURIX
2008: 186-191.
Guido Governatori, Antonino Rotolo: A conceptually rich model of business process
compliance. APCCM 2010: 3-12
and on business process compliance in general:
Guido Governatori and Shazia Sadiq. The journey to business process compliance. In Jorge
Cardoso and Wil van der Aalst, editors, Handbook of Research on BPM, IGI
Global, 2009.
L.L.’s answer:
The
referee starts by saying that “first-order
logic is not appropriate to represent legal reasoning”, and then adds that “there are cases where deontic distinctions
are necessary’” (I agree with the second statement, but I think that the
first one is too generic). He goes on by saying that that first-order logic
cannot handle reasoning about violation and compensation! This last part is
strange since it seems obvious that one can represent cases of violation and
compensation by using simple implications, see the Babylonian codes mentioned
at the beginning. Entire legal systems
have been built on this basis.
The
referee clearly refers to the ‘results’ of long discussions in the legal logic
area, after which some researchers got convinced that deontic logic is
necessary for the formalization of legal texts, while others remain
unconvinced. See the section above on deontic logic.
Many
scientists agree that is useful to see how far one can go with a simpler tool
until a more complex tool becomes necessary. Dijkstra often warned against
cracking an egg with a sledge-hammer. Einstein warned to keep concepts as
simple as possible (but not simpler!) Should we use an electronic microscope
when a regular microscope is sufficient or perhaps even better?
It
is well-known that much legal reasoning can be appropriately formalized in
first-order logic. For many centuries, syllogism (a constrained form of
first-order logic) was considered to be sufficient. [Sergot
et al. 1986] use Horn clauses (a subset of first order logic) to reason about
the British Nationality Act. [Sartor 2009] uses
first-order logic in most of his book. Many other papers and books on legal
logic do not use deontic logic. Tax laws of many countries have been
implemented in programs without using deontic logic, although tax laws use the
concepts of obligation, prohibition, permission.
To
extend the referee’s comment, it could be said that it is also well-known that
deontic logic is not appropriate to represent legal reasoning, because there
are so many aspects of legal reasoning that cannot be represented in deontic
logic. Since law pretty well covers all aspects of human experience, all tools
of logic and mathematics may be needed in the study of aspects of different
laws. If I have to determine how many apples I am owed
given that Alice borrowed 5 and returned 3 I don’t need deontic logic, but I
need elementary arithmetic ….
So
I cannot believe a blanket statement that “first-order
logic is not appropriate to represent legal reasoning” because “there are cases …” etc.
I
remain of my opinion that first-order logic is appropriate for much legal
reasoning, it is more easily understood (than deontic or higher order logics),
it has many good tools, and so we should get as much as we can from it, before
we go into more complex formalisms. It is of course clear that deontic logic
can be a good tool for certain types of legal reasoning, I respect the work
done with deontic logic, and the papers cited by the referee. But higher order logic, and many other forms of logic and
mathematics, have even more potential.
In
the area of requirement extraction for software design (which was the subject
of my paper), it remains to be seen what place deontic logic will have. How
much deontic logic was used for the translation of tax codes into computer
code?
I
come from a research area (design and verification of real-time systems and
network protocols) where a variety of formalisms has been used for many years:
extended finite state machines, process algebras, Petri, nets, predicate
calculus, temporal logic, model-checking, and others. Each of these formalisms
has a school, and members of schools have occasionally implied that only their
formalism was the “right” one. More constructively, some researchers have
attempted to combine formalisms, by showing the advantages of using, say, Petri
Nets with temporal logic. Each formalism is useful for certain types of
reasoning. The work continues and often there are interesting new insights,
thanks also to these fruitful combinations.
I
don’t expect this debate to be settled soon: how many generations did it take
to settle calculus or gravitation theory? And still progress is being made in
these areas.
I
would like to continue with some examples. Consider the following norm:
(1) “Parking on Rideau Street beyond one hour
is punished at the rate of $10 for every hour in excess”.
Suppose
that we have a set of norms that is written entirely in this style
(essentially, the ECA style discussed earlier). It is possible to reason about
this code and derive all useful legal consequences by using only simple logic
plus simple arithmetic. Surely, one could rewrite such norms by using deontic
operators, e.g.
(2) “It is obligatory to punish parking in
Rideau Street beyond one hour at the rate of ...”.
But
would this help? Or one could state the following fact:
(3) “It is forbidden to park on Rideau Street
for more than one hour”.
By
doing this we have lost some information but, by using deontic logic, we may
able to derive other facts such as:
(4) “It is permitted to park for one hour on
Rideau Street”.
Suppose
now that a set of norms is written by using deontic modalities, such as:
(5) “Parking downtown is forbidden beyond one
hour”.
(5) alone is next to
useless because it does not specify the consequences of violations (people will
continue parking downtown as long as they want). It will take life by adding
ECA norms specifying consequences such as (1) above. To do this, we need a
small ontology specifying what are the downtown streets.
Supposing that the downtown streets are Rideau, George and York, then (5) is
implemented by three ECA rules, e.g.:
(6) “Parking on Rideau Street beyond one hour
is punished at the rate of $10 for every hour in excess”.
(7) “Parking on George Street beyond one hour
is punished at the rate of $5 for every hour in excess”.
(8) “Parking on York Street beyond one hour
is punished at the rate of $2 for every half hour in excess”.
After
this is done, simple syllogisms are sufficient to derive the judgments. It can
be questioned if (5) is still useful, if not as a guideline.
The
interesting case is the one where we have norms of both types. Such are many
codes, ancient and modern. In this case, deontic norms can be useful in order
to specify properties of sets of ECA norms that can lead to interpretation and
completeness checks. For example, in the situation above, suppose that (5),
(6), (8) are norms, but (7) is not.
There is a problem with the law, something was forgotten, and the
legislator or the courts will have to remedy this in some way. This seems to
imply that deontic logic belongs to some sort of “meta-legal” level.
By
using the concept of ‘contrary to duty obligation’ mentioned earlier, example 1
becomes:
(1’)
“It is forbidden to park on Rideau
Street for more than one hour. If this is done, the perpetrator is punished at
the rate of $10 for every hour in excess”
This
rephrasing can be useful in some contexts, useless in others. Depending on what
one wants to do …
Exercise:
try to rephrase Hammurabi’s code in this fashion.