® InfoJur.ccj.ufsc.br


paper prepared for the Conference on Expert Systems in Law, Bologna, 3-5 May, 1989

Ejan Mackaay, Daniel Poulin, Jacques Frémont, Paul Bratley, Constant Deniger

Ejan Mackaay, Daniel Poulin, Jacques Frémont, Constant Deniger
Centre de recherche en droit public

Faculty of law
Université de Montréal
Box 6128, Stn. A
Montreal, Canada, H3C 3J7
Tel.: (514) 343 7210,
FAX: (514) 343 2199
EMail: poulin@IRO.UMontreal.CA

Paul Bratley
Department of Computer Science and Operational Research

Université de Montréal
Box 6128, Stn. A
Montreal, Canada, H3C 3J7
Tel.: (514) 343 7478
EMail: bratley@IRO.UMontreal.CA

Financial support for this research has been provided by the Social Science Research Council of Canada and by the Fonds FCAR of the Quebec government under its programme of Actions structurantes.


1. Chomexpert

This paper is part of a research project to develop an expert system on Canadian unemployment insurance law. A prototype system dealing with the question of admissibility to the UI programme was implemented in Prolog on a Macintosh under the name Chomexpert[1]. The next phase of the project is the design of an expert system to deal with complex cases and `open textured concepts' in the Act. For the understanding of what follows it would seem helpful to outline the essential features of Canadian unemployment insurance law.

1.1. Unemployment insurance law

The core of unemployment insurance law is the Act[2]. Simplifying considerably, one might say that the Act declares eligible for benefits the person who during a so-called qualifying period - generally of 52 weeks prior to the claim - has been gainfully employed during a certain number of weeks - varying between 10 and 20, according to the category one belongs to (Sect. 17 and 18).

Once declared eligible, the beneficiary is awarded a benefit period - generally of 52 weeks (sect. 19). During this period, he or she may draw benefits for any week during which he or she is not gainfully employed. The first two weeks are a waiting period during which no benefits are paid. Subsequently, the total number of weeks for which benefits may be drawn is limited by the number of weeks of gainful employment during the qualifying period, with a maximum of 25 (Sect. 22). After this number has been exhausted, the insured may in some cases be entitled to supplementary benefits (depending among other things upon the regional unemployment rate).

Benefits are set at 60% of the average weekly earnings over the last 20 weeks of employment during the qualifying period, or over all weeks of employment where there are fewer than 20.

Time is not of equal importance in all fields of law. Bench-Capon and his fellow researchers note that it is of little consequence in the British Nationality Act but paramount in the supplementary benefits legislation[3]. This brief overview makes abundantly clear that that conclusion holds equally well for Canadian unemployment insurance law. The Act refers to qualifying periods, benefit periods, possible extensions of either, waiting periods, periods of disqualification, days excluded from benefit, prior benefit periods and so on. We must now examine how time was handled in the prototype version of Chomexpert.

1.2 Implementation of time in the prototype of Chomexpert

Chomexpert is programmed in Prolog and uses where possible declarative statements. The conditions for eligibility for unemployment insurance benefits can be adequately expressed using declarative statements.

Where the temporal aspects are concerned, this is not an interesting option. One need only imagine the number of declarative statements required to express the duration of the qualifying period (with all the variants the law provides) or the calculus of dates (to determine for instance how many weeks lie between the 11th of June 1988 and the 28 of February 1989) to see that a declarative approach would not readily lead to a tolerably efficient system. It has therefore been decided to represent this type of information by means of procedures.

While this approach at first blush appears to solve the problem, it has the disadvantage of obscuring the logic of the expert system. All through the formalisation of the legal rules there are calls to procedures for handling the temporal questions. McCarty aptly expresses the disadvantages of procedural representation of legal knowledge:

`First, [...] the interaction between the user and the program here is extremely rigid. There are, as practical matter, only few fixed paths through the statute, and the program controls absolutely the order in which these paths are explored. [...] A second limitation arises from the fact that it contains no explicit representation of the legal rules, but instead represents rules implicitly [...] Finally, and closely related, there is the difficulty of modifying the system whenever the legal rules are modified.'[4]

Procedures can be used only in a preset way, declarative knowledge in a variety of ways. Procedures are difficult to modify and the rules of knowledge become less readable as a result. On the whole, these considerations lead to the conclusion that procedural representations are to be avoided where possible in expert systems.

The reason for using procedural representations frequently stem from the nature of the provisions to be formalised. The Unemployment Insurance Act contains a good many provisions of a procedural nature which could not be easily represented in a declarative manner. Winograd favoured the embedding of procedural knowledge within declarative representations:

It is an obvious fact that many things we know are best seen as procedures, and it is difficult to describe them in a purely declarative way. [...] In using procedures we trade some degree of flexibility for a tremendous gain in the ease of representing what we know about processes. [...] The strongest support for procedural representation comes from the fact that it works.[5]

No doubt some procedural representations will have to coexist with declarative ones in a field such as unemployment insurance law. But they ought to be kept to a minimum. To this end it will be essential to have a mechanism for handling rules which have a temporal dimension, failing which one has to to resort to such tricks as were used in the prototype of Chomexpert. In the current program all mechanisms relating to the computation of dates are brought together in a specialised module. The predicates computed in this module are subsequently available for use in expressing legal rules.

It is our hunch that a specialised module for handling all temporal aspects offers promise. To determine what such a specialised time module might look like it seems essential to examine what AI research in general has discovered with respect to the handling of time.

2. Research in artificial intelligence on the formalisation of time

2.1. General artificial intelligence approaches to the formalisation of time

Artificial intelligence aims at representing all activities attributed to human intelligence. It was therefore to be expected that AI researchers would broach the question of how to represent time in human affairs. This question has first been addressed in studies dealing with natural language and with planning problems, no doubt because of the fundamental rôle time plays in these fields. It would seem relevant to survey key elements of this research in order to identify insights which may be useful for the representation of time in law.

a. J. McCarthy

During the sixties already, one of the pioneers of artificial intelligence, Mr. John McCarthy, explicitly integrated the handling of time in his proposals for intelligent systems. In his Advice Taker [6], the situation is the basic element. Each situation describes a complete state of affairs at some instant of time. Causality is represented by actions which move the world from one state to another. Each action creates a new state and changes time.

This calculus of situations entails several problems, the most important of which is known as the frame problem: after each event or action the entire state of the world must be specified, even the elements which have not changed from the previous state. The system can only consider one event or action at a time. It does not encompass the notion of duration for transformations of states of the world.

b. McDermott

To correct some of the drawbacks of McCarthy's proposals, McDermott has elaborated a first order temporal logic. His aim was to develop a robust temporal logic which could serve as a framework for programs that have to take time into account.[7] McDermott's logic is based on two key ideas: openness to the future and continuity of time. It allows for several possible futures from a given initial state and it encompasses progressive and continuous change.

The system defines what happens or may happen by means of a partially ordered set of states which are snapshots of the world. Each state has a time of occurrence which is a real number. States are structured in chronicles. Each chronicle is a complete possible history of the universe. From the present time onward, chronicles branch out into the future, each branch representing one of the possible futures.

States and chronicles are the support for facts and events. Facts change truth value over time; they designate states for which they are true. For instance, the fact ON(A, B) designates the state in which block A is on top of block B. An event is represented as a set of intervals during which it takes place[8]. In contrast to his predecessors, McDermott does not assimilate events with changes of the world. An event may leave the world unchanged.

McDermott's logic is non-monotonic, in that the addition of a new fact may invalidate earlier conclusions. Moreover, facts may be assigned a duration. Such facts are true so long as their lifetime has not been exhausted.

McDermott's temporal logic, to our knowledge, has not yet been implemented in a functional system. Development of such a system must no doubt await further advances on non-monotonic logics.

c. J.F. Allen

Within the research surveyed here, the temporal logic of J. F. Allen has drawn the widest attention.[9] Contrary to McCarthy and McDermott, in whose systems the instant is the primitive term, Allen takes the interval as primitive element of time. This decision is justified by the consideration that `the majority of events described take place over a time interval. Thus our representation is designed to maintain these interval relations conveniently and concisely'[10]. Allen gives the example of finding a letter. At first sight this is an instantaneous event; yet upon further examination, it can be decomposed, showing a beginning and an end[11] In more recent work, Allen has added time points and moments. Yet the interval or the period remains the basis of the system.

Allen's approach is to develop a specialised inference engine for temporal relations, termed the time specialist. The time specialist considers neither absolute time nor the duration of the intervals, but merely the relations between intervals. Allen has reduced these to seven basic types, six of which allow for an inverse relation (in parentheses):

    x equal o                       xxxx

    x before o (o after x)          xxx   oooo

    x starts o (o started-by x)     xxx

    x finishes o (o finished-by x)     xxx

    x overlaps o (o overlapped-by x)  xxxx

    x meets o (o met-by x)          xxx

    x during o (o contains x)         xxx

The time specialist handles these relations and `propagates' them. Thus, if a, b and c are intervals and the system is being told that a meets b and that b before c, it will infer that a before c.

Allen's ontology consists of properties, events and processes. These elements have different relationships with time. Properties hold for the duration of an interval and for any sub-interval comprised within it. They are termed homogeneous. Events occur during an interval and occupy the entire interval in such a way that no single sub-interval can be identified which comprises them. Processes are a somewhat odd category of elements. They can be said to occur during an interval even though they do not occur during the entire interval, but merely during a substantial number of sub-intervals. An example is the statement `I have been walking during t'. The statement does not cease to be true should I have briefly stopped during my walk in order to examine a flower[12].

Shoham has pointed out some logical difficulties with Allen's system[13]. Allen's system has nonetheless given rise to a number of artificial intelligence projects. Among these, the work of Ladkin[14], Vilain and Kautz[15], Sadri[16] as well as Kowalski and Sergot[17] deserves to be mentioned.

d. Kowalski and Sergot

Kowalski and Sergot have proposed an event calculus whose purpose it is to allow for reasoning on events and time in the context of logical programming[18]. The system is aimed at data base management and natural language processing. One of the authors has tried to implement these ideas in a legal expert system[19].

The events which are `calculated' in this system are those that mark the beginning or the end of a period during which a given relation holds. Where relation holds for a time period, the system assumes that it holds for any time point during that period. Relations are therefore considered to be homogeneous with respect to time.

One of the advantages of the system put forth by Kowalski and Sergot is that additions to the knowledge base are additive. It is not necessary explicitly to erase information from it. This is taken care of by the added precision stemming from new information about the beginning or end of a period. For instance, one may represent the fact of Paul's being hired at the Lab by the statement hire(Paul, Lab, E1), time (E1, 1/1/89). If it is asked, on the 20th of January, whether Paul is working at the Lab, the system would reply in the affirmative since it has no knowledge of an event putting an end to the employment. Should it subsequently be informed that Paul was fired on the 15th of January (fire(Paul,Lab, E2), time(E2, 15/1/89), the same question put to it would trigger a negative answer, without the information about the hiring having been explicitly erased.

Past and future are handled perfectly symmetrically in this system. Information about particular events may be provided in any order. Furthermore, it is not necessary that an absolute time reference is assigned to each event; only their relative order matters. Since events are distinguished from the instants during which they take place, several may occur simultaneously. Events may be only partially ordered. It is not necessary that the relationship of an events to all other ones be known.

The event calculus proposed by Kowalski and Sergot avoids the frame problem mentioned earlier. It does so, as the authors themselves state it, `by qualifying relationships with time periods instead of global situations. Time periods associated with different relationships have different names even if they have the same duration'[20]. A change in the temporal dimension of a relation does not entail a change in the rest of the base.

Kowalski and Sergot's work is related to Allen's in their focus on the period. Their event calculus is similar to Allen's interval calculus. Sadri has shown that Allen's system can be modified so as to include the features that distinguish it from Kowalski and Sergot's event calculus[21].

e. Shoham

Focusing on temporal problems in the context of planning, Shoham has proposed a temporal logic which he terms Chronological Ignorance. It is a modal non-monotonic logic. In Shoham's view a theory about time must have the following features: `1. A language for describing what is true and what is false over time, what changes what remains constant; 2. A way of defining and reasoning about rules of "lawful change" in the above language'[22]. Shoham's proposal contains the precise syntactic and semantic specification of a temporal logic capable of handling the problem of prediction in artificial intelligence.

Shoham's aim is to resolve two essential problems for predictions in the context of planning, to wit the qualification or frame problem and the extended-prediction problem. The first problem arises because of the need, in a machine with a finite capacity, to find a compromise between the quantity of information to be held for predictions of the type P1(t1) => P2(t2) with t1 <= t2 and the reliability of those predictions. The problem is, in other words, to determine how to make solid predictions of the future without considering the past in its entirety.

The second problem, that of extended prediction, has to do with the focus of prediction. One can predict the immediate future, which leads to a great number of predictions as soon as one wishes to forecast a somewhat further removed future; or one can attempt directly to predict the far removed future, which, however, imparts a measure of defeasibility to the forecast.

The creation of an automatic theorem prover in a system such as Shoham's is no simple task. So far Shoham's work has contributed more to placing temporal reasoning upon a solid theoretical footing than to its implementation.

f. Evaluation

The ideas of McCarthy, Allen and Kowalski/Sergot have been implemented in practical systems. Those of McDermott and Shoham are still removed from practical implementation. They are, however, promising on a theoretical plane.

What interest do these proposals have for expert systems in law? The answer depends on peculiarities of the law and on what type of formalisation one wishes to pursue. On the first aspect, we shall have more to say in the next section of this paper. With respect to the second aspect, if one wishes to model the deep conceptual structure of the law, the richness of representations which are possible with the proposals of McDermott and Shoham may well be indispensable.

For a more `mundane' expert like Chomexpert, such richness may not be necessary. A subset of the temporal logics described above may be sufficient to add substantially to what can be expressed in the knowledge base. In many instances legal expert systems draw conclusions from past events, but do not need to project into the future, as is required in the planning exercises envisaged by McDermott and Shoham. Hence the systems developed by Allen and by Kowalski/Sergot would seem to be adequate for law. A further advantage is that their systems lend themselves to rapid implementation. In further work on Chomexpert, we plan therefore to start from Allen's ideas about the time specialist. While Allen's inference engine is not very efficient, it can easily be operationalised. Its content will have to be adapted to the requirements of the law, since, as we shall see in the next section, law behaves quite differently from the temporal logic envisaged by Allen.

2.2. Formalisation of time in existing legal expert systems

The prototypes of legal expert systems which have been constructed to date all embody choices with respect to the handling of time. In some cases, the choices reflect ideas stemming from the general AI research reviewed above. The choices are a function of the field of law covered and the tasks assigned to the system. In systems mainly geared to classification, i.e. that identify the nature of the legal problem involved in a case, questions of time management would seem to be of lesser importance. By contrast, where the system developer aimed at providing the program with a conceptual deep structure, the representation of time had to be much more elaborate.

The literature on the existing expert systems in law contains some thoughts on the question of time management. L. Th. McCarty deals with it in his articles on Taxman[23]. In his recent paper on Permissions and Obligations, he envisages three levels of discourse, first the ordinary language describing different states of the world, the second one an action language in which one can pass from one state to another in time.and the third one a deontic language[24].

Gardner, in her thesis about the formalisation of American contract law, adopts a representation of time reminiscent of the calculus of states proposed by John McCarthy[25]. DeBessonet, too, gives some thought to the representation of time, in his formal language for the Louisiana Civil Code[26]. Bench-Capon and his team intend to adopt the event calculus of Kowalski and Sergot in their work on Supplementary Benefits Legislation.[27]

Most recently, Nitta and his team have explicitly considered the representation of time in their formalisation of the Japanese Patent Act. They have developed an interval logic for temporal reasoning[28]. This approach appears to us to be particularly promising.

3. A lawyers' view of the formalisation of time

Intuitively, every lawyer knows how time is handled in the law. Dates, delays, limited periods of time seem to abound in any field of law. The subject seems trivial. Yet, lawyers would seem hard pressed to express in an abstract way their knowledge of how time is used in law. Is it that the ubiquity of the phenomenon obscures their view of its rôle? Or is it a more complex subject than a casual glance might suggest?

3.1. Real time and legal time

The view we wish to put forward here is that, as with its language, the law borrows much of its concepts for handling time from common usage, yet takes the liberty to modify them to suit its needs. Legal time resembles in form time as it is used everyday. Yet its substance is several shades removed from everyday usage, all the more so as the legal system grows in complexity.

Two examples may illustrate the point. Where a sale is rescinded because of latent defects in the object sold, the contract is deemed never to have existed: history is rewritten retroactively. A shipwreck may stretch over a considerable period of time. If an inquiry is held into the conduct of the captain during the shipwreck, time is examined in its duration. Yet the law treats the shipwreck as an instantaneous event for the purpose of determining, for instance, within what period the victims have to state their claims or, for inheritance purposes, at what time exactly a passenger has died. A period of time is collapsed into a instant in law.

What this means is that time in relation to law must be seen at two levels. There is what one might call real time, composed of instants, periods, events and actions which people refer to in ordinary usage. The law itself constructs a different time - one might call it legal time - which draws its input from real time, but draws it selectively and may transform it in the process. In legal time, moreover, some inferences - such as retroactive effects - are admissible which would be excluded in real time.

If our thesis is correct, we must investigate how legal time is constructed from real time and what inferences are allowed in it[29].

3.2. Preliminary exploration of legal time

In this subsection we illustrate how elements taken from real time are transposed into legal time. The examples are taken from the Canadian Unemployment Insurance Act on which Chomexpert is based. It would seem that the phenomena illustrated here are equally found in other areas of law and in other advanced legal systems.

a. Transposition of real time into legal time

(i) Units of time

Real time is measured in seconds, minutes, hours, days, weeks, months years, centuries and so on. Law borrows these units, but it may choose to ignore some and to redefine others.

In the Unemployment Insurance Act the basic unit used is the week, days serving as secondary units. The Act defines the week as `a period of seven consecutive days commencing on and including Sunday'[30], which corresponds to common usage. A week of unemployment, however, is defined as `a week in which [a claimant] does not work a full working week'[31]. This provision is further qualified by the second sub-section, which states `A week during which a claimant's contract of service continues and in respect of which he receives or will receive his usual remuneration for a full working week, is not a week of unemployment, notwithstanding that the claimant may be excused from the performance of his normal duties or does not in fact have any duties to perform in that time.'[32] A working week, by contrast, is defined in expansive fashion: `A working week of a claimant [...] is a number of hours, days or shifts normally worked in a calendar week by persons in his grade, class or shift at the factory, workshop or other premises at which he is or was employed'[33].

Days are similarly redefined in legal time. A `working day' is `any day of the week except Saturday and Sunday'[34].

(ii) Time in non-chronological order

Time flows from the past through the present to the future. The law does not in all circumstances respect this chronological order, as is evident in the case of retroactive effects.

The Unemployment Insurance Act offers the example of the insured being excused for a delay in claiming benefits: `When a claimant makes an initial claim for benefit on a day later than the day he was first qualified to make the claim and shows good cause for his delay, the claim may, subject to prescribed conditions, be regarded as having been made on a day earlier than the day on which it was actually made'[35].

Other provisions may give rise to complex non chronological processes. `Where a benefit period is established for a claimant but benefit is not payable or has not been paid in respect of that benefit period, the benefit period may, subject to prescribed conditions, be canceled by the Commission and deemed not to have begun'[36]. This provision gives the Commission discretion to cancel historical facts, to rewrite history. This is one of the instances in which legal reasoning gives rise to a non-monotic logic: the addition of a new fact invalidates a fact established earlier and the inferences based on it.

(iii) Transformation of intervals into instants

In the shipwreck example we have already encountered the phenomenon of events having a certain duration being considered as a single instantaneous facts for certain purposes. A similar remark could be made for other types of accident.

b. Conclusion

The preliminary exploration of how time is used in the law - in such a technical branch as unemployment insurance law - suggests that while in form time in law looks like time in the real world, the law introduces subtle differences between the two. Legal time is an abstraction -sometimes differential- of real time; some terms are redefined for legal purposes; the law allows in some instances past events to be retroactively modified. The conclusion from this preliminary investigation is that temporal logics developed for the real world may not be fully adequate for law.

4. Proposal for handling time in a legal expert system

On the basis of the foregoing considerations, we plan to adopt the following structure for our legal expert system. At the root there is the Prolog interpreter. The second level is a temporal inference engine, such as the time specialist envisaged by Allen. This inference engine allows one to define, at a third level, one or more temporal logics, one of which may be particularly suited for expressing legal knowledge about time. All these instruments are used in formulating the knowledge bases. The structure is represented in the following diagram

Diagram 4.1.
Architecture of an expert system based on temporal logics

4.1. The planned time specialist

We implemented in Prolog a preliminary version of temporal inference engine similar to Allen's and are now validating it. The program shares with Allen's the ability to `propagate' temporal information relating to intervals. It differs form Allen's in several respects. We have modified the engine so that it can explicitly use absolute time references (such as dates). In legal applications temporal information is frequently `dated'. The absolute time reference allows to specify the relationships between intervals and to reduce the amount of computation necessary to `propagate' temporal relationships.

A second difference stems from the fact that the law frequently uses the duration of intervals[37]. The inference engine must take account of this use and we have partially integrated it in our program.

A third difference is the algorithm used for `propagating' temporal relationships. For Allen's algorithm, analysed by Vilain and Kautz, the number of operations required in the case of one interval being added to the network is a cubic function of the number of intervals already registered in the network[38]. The algorithm we are implementing would reduce this to a quadratic function.

Our time specialist further contains a set of procedures for the computation of dates.

4.2. A two-pronged non-monotonic temporal logic

As we have argued above, the law appears to use for temporal relations a metric which differs in some respects from that of ordinary usage. Just where these differences lie will have to be studied in more detail. To accommodate them, our system would have to encompass a legal as well as an ordinary temporal metric.

Legal reasoning appears to be non-monotonic in some instances, as we saw in sub-section 3.2. The system must be able to handle this aspect too.

We are not yet able to specify such a two-pronged non-monotonic temporal logic. Yet even with a small sub-set of such a logic out time specialist would be able to express legal rules must more easily than the Horn clauses used in Chomexpert. To illustrate the advantage, let us look at how rules are represented in the prototype of Chomexpert:

if Condition1
and Condition2
and Condition3
and Conditionn
then Conclusion

where Condition1,2 etc. and Conclusion are Prolog terms. These terms represent concepts of the unemployment insurance universe and may contain variables. Rules referring to duration and more generally those involving temporal phenomena cannot comfortably be represented by such means.

A temporal logic such as sketched above would allow us to use `richer' rules. Time would explicitly described and acted upon in the time specialist. In this set-up, rules might look like the following:

if Condition1 holds_on Interval1
and Condition2 holds_on Interval2
and Conditionn holds_on Intervaln
and Interval1 relationl Interval2
and Interval2 relationk lnterval3
and duration_of Interval3 is n days
then Conclusion holds_on IntervalC

where Condition1,2 etc. and Conclusion are Prolog terms and Interval1,2 etc. and relation1,2 etc. would be respectively the intervals associated with terms describing the domain and the relations between such intervals derived from Allen's calculus.

We believe that rules of this kind would allow one more easily to describe the phenomena of unemployment insurance law. Let us look, by way of example, at the problem of determining the `qualifying period' for those who have suffered some unemployment during the previous year and have already been entitled to an earlier benefit period. The relevant sections of the Act read as follows:

Sec. 18. (1) [...] the qualifying period of an insured person is the shorter of

(a) the period of fifty-two weeks that immediately precedes the commencement of a benefit period under subsection (1) of section 20, and
(b) the period that begins on the commencement date of an immediately preceding benefit period and ends with the end of the week preceding the commencement of a benefit period under subsection (1) of section 20.

Sec. 20. (1) A benefit period begins on the Sunday of the week in which

(a) the interruption of earnings occurs, or
(b) the initial claim for benefit is made,

whichever is the later.

The relationship among the various periods and points in time can be graphically represented as follows:

Diagram 4.2.
Computation of a new qualifying period
where there has been a previous period of benefit

One first checks the date of `interruption of earnings'(1, below) and makes sure that it occurs before the initial claim (2,3). The system no verifies whether there has been a previous period of benefit in the fifty-two week preceding the claim (4-6). If so, the new qualifying period is set (9) to begin at the start of the previous benefit period (8) and to end at the time when the claim was made (7)

rn (User Case)

if interruption_of_earnings occurs_on momentA (1)
and initial_claim occurs_on momentC (2)
and momentA -(before)-> momentC (3)
and new intervalstandard -(meets)-> momentC (4)
and new intervalstandard duration_is 52 weeks (5)
and intervalbenefit/previous -(during or finish)-> intervalstandard (6)
and new intervalqualifying -(meets)-> momentC (7)
and new intervalqualifying -(start)-> intervalbenefit/previous (8)
then new qualifying_period holds_on intervalqualifying (9)

4.3. Assessment

The approach proposed here is similar to Nitta's[39] in that it uses Prolog to implement a temporal logic specifically geared to legal reasoning. The idea of using a two-pronged non-monotonic logic goes beyond Nitta's approach.

Our time specialist owes much to Allen's work. The use of duration in the context of an interval based temporal logic has been mentioned by Allen, but not, to our knowledge, been implemented. The same is true of the use of absolute time references of intervals.

5. Conclusion

This paper is part of an on-going research project for developing an expert system (Chomexpert) on Canadian unemployment insurance law. One of the salient feature of this field of law is that it relies heavily on dates, periods and other elements of time. Time cannot comfortably be formalised by means of the declarative statements normally used for describing the knowledge base of expert systems. In the prototype of Chomexpert the calculus of dates has been implemented by means of procedural statements brought together in a specialised module.

The use of procedural statements which can be called up from within declarative statements has the disadvantage of making the description of the rules of the knowledge base less transparent. For this reason, it was felt that the question of time should be studied more closely to determine if a representation more in line with the usual expert systems logic could be developed. In the general AI literature the question has been studied with respect to planning systems and with respect to natural language understanding. The examination of this literature shows a divergence between approaches that `work' or could be implemented, but do not necessarily do justice to all aspects of reality, and those which aim for theoretical purity at the expense of the promise of immediate implementation. In our further work we draw in particular on work of the former category.

The question then arises to what extent the temporal logic developed in the general AI literature is well adapted to legal reasoning. In exploring how the law uses time, we discovered that while the terms used to deal with time (days, weeks, months, periods, moments) are generally those of ordinary usage, their meanings may differ from it. The law may redefine terms to suit its needs and allows for operations on time which would be inadmissible in ordinary usage. In giving retroactive effect to the annulment of a contract or other act, for instance, the law effectively modifies the relations among events that have already taken place. The exploration of the use of time in law leads us to the conclusion that one must distinguish between real time and legal time. Legal time appears to call for a non-monotonic logic.

In further work on unemployment insurance law, we are implementing in Prolog a separate module for handling temporal relations, more or less in line with the approach taken by J.F. Allen. Within this module, two temporal logics have to be developed to handle the relations in real time and in legal time. We are only at the beginning of our study of what these logics may look like. Already it seems obvious that an inference engine enriched to allow for explicit declaration of temporal information would offer a appreciable gain in ease of expression of legal rules and transparence of the knowledge base.

6. Bibliography

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Allen 1983
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Allen, J. F. Towards a General Theory of Action and Time, (1984) 23 Artificial Intelligence 123-154
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Allen, J.F. and Hayes, P.J., Short Time Periods, Proceedings of the 10th International Joint Conference on Artificial Intelligence, 1987, pp. 981-983
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Allen, J.F. and Koomen, J.A., Planning Using a Temporal World Model, Proceedings of AAAI-1983, pp. 741-747
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Atias, Christian, Epistémologie juridique, P.U.F., 1985
Bauer-Bernet 1986
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[1] Poulin 1988. Retour.

[2] Revised Statutes of Canada (1985), Ch. U-1. Retour.

[3] Bench-Capon 1987, p. 195. Retour.

[4] McCarty 83, p. 282-283. Retour.

[5] Winograd 85, p.360. Retour.

[6] McCarthy 1968, p. 304. Retour.

[7] McDermot 1982, p. 103. Retour.

[8] McDermott, 1982, p. 110. Retour.

[9] Allen 1981, 1983, 1984 and 1985. Retour.

[10] Allen 1981, p. 222. Retour.

[11] ibid. Retour.

[12] Allen 1984, p. 135. Retour.

[13] Shoham 1988. Retour.

[14] Ladkin 1986, 1987, 1988. Retour.

[15] Vilain/Kautz 1986. Retour.

[16] Sadri 1987. Retour.

[17] Kowalski/Sergot 1986. Retour.

[18] ibid. Retour.

[19] Sergot is one of the co-authors of Bench-Capon 1987. Retour.

[20] Kowalski/Sergot 1986, p. 74. Retour.

[21] Sadri, 1987, pp 121-168. Retour.

[22] Shoham 1988, p. 1. Retour.

[23] McCarty 1977, pp. 340-342 (for Taxman I) and McCarty 1983 and 1986 for more recent work. Retour.

[24] McCarty 1986. Retour.

[25] Gardner 1987, pp. 92-3. Retour.

[26] DeBessonet 1986, pp. 377-382. Retour.

[27] Bench-Capon 1987, p. 195. Retour.

[28] Nitta 1988, pp. 332-334, 346 Retour.

[29] The problem appears to be similar with regard to legal language. Here the use of fictions has been studied. See Fuller 1967. For instance, a manufacturer is deemed to have known the defects of his product. For the purposes of the Consumer Protection Act in Quebec, the importer is considered to be the manufacturer, where the latter has no establishment in the province (art. 1(g). Retour.

[30] Act, Section 2(1)y. Retour.

[31] Act, Section 21(1). Retour.

[32] Act, Section 21(2). Retour.

[33] Unemployment Insurance Regulations, sect. 44 (1). Retour.

[34] Unemployment Insurance Regulations, sect. 45. Retour.

[35] Act, sec. 20 (4). Retour.

[36] Act, sec. 20 (5). Retour.

[37] See examples given in paragraph a (i) of subsection 3.2. Retour.

[38] Vilain/Kautz 1986. Retour.

[39] Nitta 1987 and 1988. Retour.