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Representing temporal knowledge inlegal discourseB. Knight a , J. Ma a & E. Nissan aa School of Computing and Mathematical Sciences , TheUniversity of Greenwich , London, SE18 6PF, UKPublished online: 10 May 2010.

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Information & Communications Technology Law, Vol. 7, No. 3, 1998 199

Representing Temporal Knowledge in Legal Discourse

B. KNIGHT, J. MA & E. NISSAN

School of Computing and Mathematical Sciences, The University of Greenwich, London SE186PF, UK

ABSTRACT This paper presents a formalism for representing temporal knowledge inlegal discourse that allows an explicit expression of time and event occurrences. Thefundamental time structure is characterized as a well-ordered discrete set of primitivetimes, i.e. non-decomposable intervals with positive duration or points with zeroduration), from which decomposable intervals can be constructed. The formalismsupports a full representation of both absolute and relative temporal knowledge, and aformal mechanism for checking the temporal consistency of a given set of legalstatements is provided. The general consistency checking algorithm which addresses bothabsolute and relative temporal knowledge turns out to be a linear programming problem,while in the special case where only relative temporal relations are involved, it becomesa simple question of searching for cycles in the graphical representation of the corre-sponding legal text.

1. Introduction

Temporal reference of statements is ubiquitous and plays a vital role in legaldiscourse. In fact, a staggering percentage of propositions involved in the legaldomain can be shown to be explicitly or implicitly time-dependent. Consider forinstance the following sample statements:

(1) the contract was signed at 11 a.m. on the 26th of August 1996;(2) the court was adjourned at 6 p.m.;(3) the trial lasted for 45 minutes;(4) he was in the hospital for 16 hours;(5) the car was stolen during the time when the driver was in his office;(6) the suspect was away from home after midnight;(7) it took him less than three hours to get home;(8) the sentence should be more than six years but less than 10 years;(9) he beat her for 20 minutes and left her at 21 p.m.; she then died at 21:30 p.m.

Here, several different types of temporal information are involved:

• Absolute temporal references, e.g. '11 a.m. on the 26th of August 1996', '6 p.m.',and '21:30 p.m.', which refer to points in time;

• Absolute temporal durations, e.g. '45 minutes' and '16 hours', which refer tosome certain amount of temporal granularity;

• Relative temporal references, e.g. 'during the time when the driver was in hisoffice' and 'after mid-night', which refer to times that are known only by their

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relative temporal relations to other temporal reference, which again, may beabsolute or relative;

• Relative durations, e.g. 'less than 3 hours' and 'more than six years but less than10 years', which refer to some uncertain amount of temporal granularity.

Time is a crucial aspect of legal evidence, concerning a story on which thecourt is called to decide. In a penal context, the events within the story underdiscussion fit in what Bernard Jackson has termed the 'semantics' of the story,in a semiotic perspective of 'anchored narratives' (Jackson, 1996; Wagenaar et al.,1993). Temporal reference also fits, however, at the contextual levels of theadministration of justice. The story as delivered in court is, to Jackson, the'pragmatics' of the story. Moreover, the legal domain aside, when it comes tonarratives in general, literary studies terminology distinguished between 'nar-rated time' and 'narration time'. Literary stories sometimes have a frame storyin which they are embedded. Back to court, the events that take place there are,of course, the story of the trial itself. However, around trials, there is thenitty-gritty of the administration of justice. There is also the history of the law,and of legislation. A corpus, in von Wright's sense, is a 'finite set of co-existingnorms' (von Wright, 1982). The corpus of norms evolves, and derogation, bywhich a norm is discarded from the corpus, has been a major topic for research(Bulygin, 1982; Alchourron, 1982; Martino, 1982) into deontic logic, in thephilosophy of law as well as in computing for law (Bauer-Bernet, 1986). Forexample, how to reason on precedents, given the evolution in time of legaldoctrine? (Berman & Hafner, 1995). This way, the problems associated withtemporal information (or, then, spatial information; Nissan, 1996) permeateeverything in life.

The problem of reasoning with temporal information in this mixture of formsis two-fold:

a. How to represent this kind of temporal knowledge.b. How to construct a reliable method of inference, based on this representation.

First of all, we need to decide what objects are we going to take as the primitivefor our ontology of time. There are three known choices: points, i.e. instants oftime (McCarthy & Hayes, 1969; McDermott, 1982), intervals, i.e. periods of time(Bruce, 1972; Allen, 1983), or both points and intervals. In addition, there are twodifferent approaches to the characterization of intervals. The first takes intervals asderived structure constructed out of points (Bruce, 1972), and the second simplytreats them as primitive objects without any underlying conceptions about theirending/internal points (Allen, 1983, 1984). Noticing that temporal references areoften referred to as intervals, Allen's contention against time points is that nothingcan be true at a point, for a point is not an entity at which things happen orare true (Allen, 1983). Furthermore, in a time model where only points areaddressed as primitive, time intervals have to be defined as derived structuresout of points. This can lead to the so-called Dividing Instant Problem (DIP)(van Benthem, 1983; Galton, 1990; Vila, 1994), which is in fact equivalent tothe problem involving in characterizing the open/closed nature of intervals.For instance, suppose Jack was home alone over time interval U, and then Raywent into his house and stayed there over time interval h. Intuitively, I2 isimmediately after 7i. If intervals h and h are constructed out of points, bydefinition there will be a point, say P, at which h, and h meet each

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Temporal Knowledge in Legal Discourse 201

other. The question is how to decide whether Jack was home alone or wasaccompanied by Ray at the point P. In terms of ontology it is a matter ofdeciding whether interval ii (symmetrically h) is closed at point P or not. On theone hand, if both interval h, and interval I2 include point P, then Jack would beboth 'home alone' and 'accompanied by Ray' at the same time point P, which iscontrary to common sense. On the other hand, if neither \\, nor I], includes pointP, then Jack would have been neither 'home alone' nor 'accompanied by Ray',which is again absurd. The third decision takes one of the two intervals as 'open'and the other one as 'closed' at point P, so that they can sit conveniently nextto each other, seems arbitrary and hence unsatisfactory, since there is nothing tochoose between whether ii or l-i should be taken as open (closed) at point P.

Nevertheless, many common-sense situations suggest the need of includingtime points in the temporal ontology as an entity different from intervals. Forinstance, it is intuitive and convenient to say instantaneous events, e.g. 'Thecourt was adjourned at 4 p.m.', occur at time points. Hence, for generaltreatments, it is appropriate to include both points and intervals as primitives inthe underlying time model, for making temporal reference to instantaneousphenomena with zero duration, and periodic phenomena which last for somepositive duration, respectively.

The paper is organized as follows. In Section 2, a simple discrete time modelis presented, which will be utilized as the underlying temporal basis for makingtemporal reference to legal statements. Section 3 introduces a schema forrepresenting temporal knowledge which allows an explicit expression of timeand event occurrences. Section 4 presents a necessary and sufficient condition forthe consistency of any given set of temporal relations, which will play the roleof the consistency checker as respect to the corresponding statements. Section 5demonstrates the application of the inference mechanism to legal statements interms of some typical examples. Section 6 concludes the paper.

2. The time model

In Poulin el al. (1992), an expert system was described, which adopts a temporallogic for expressing legal rules and information. In Ma & Knight (1994), ageneral time theory has been proposed which can solve the DIP by means ofaddressing both intervals and points as primitive time elements. However, as fortemporal treatment in legal discourse, a discrete time model seems to be usuallysufficient, since any legal text must be given in terms of a finite set of statements.In this section, we introduce a simple discrete time model which will be utilizedas the temporal basis for making temporal references to legal statements.

We denote the fundamental time line as a triad (P, Meets, Dur), where P is anon-empty set of objects which are called prime time. Meets is a binary orderrelation over P, and Dur is a function from P to Ro+, the set of non-negative realnumbers. For any prime time element p in P, we call Dur(p) the duration of p.Intuitively, if Dur(p) > 0, we shall call p a prime interval, otherwise, p is called apoint.

Additionally, we assume that P is similar to N, i.e. the set of natural numbers.In other words, there exists a one-to-one mapping between the elements of P andN, which preserves the order relation. Such a mapping is called a similar function.Hence, Meets in fact represents the immediate predecessor relation over P. Inwhat follows, we use Meets(plrp2) to denote that prime time px is the immediate

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predecessor of prime time p2. Also, we impose the following axiom whichensures that two points cannot meet each other:

(P)Vpj,p2 e PQAeetsfa, p2) => Dur(pj) > 0 v Dur(pz) > 0)

From the property of the similar function, we have:

• P is a discrete collection of prime times which is well ordered by the binaryrelation Meets;

• P has no limit elements;• the fundamental time structure is linear, not branching from any time into

either the past or the future;• the fundamental time structure is unbounded in the future;• the fundamental time structure excludes circular times.

It is important to note that prime intervals and points have no internal structure.In other words, the elements of P are all non-decomposable, even though someof them (i.e. the prime intervals) may have positive duration. In fact, primeintervals are similar to Allen and Hayes' moments (Allen & Hayes, 1989). In thispaper, we shall use the term 'moment' and 'prime interval' interactively.

Based on the fundamental time structure we define the corresponding closureT whose elements are generally called times, which may be decomposable. Wedenote the elements of T as t (possibly indexed), and use Dur-r to denote, as theextension of Dur, the function from T to Ro + , so that Dwj assigns to eachelement in T a non-negative real number. Correspondingly, we call a time t aninterval if Dur-rft) > 0 (hence, specially, a moment is an interval), otherwise, f iscalled a point. We also define a derived binary relation MeetsTQTXT as theextension of Meets, so that MeelsT{tut2) denotes that time fi is one of theimmediate predecessors of time £2. The imposed axioms are:

(Tl) Vp e P(p e T)that is, T is the extension of P;

(T2) Vf e T(f e P=> Durit) = Dur{t))that is, Durr is the extension of Dur;

(T3) Vfi,f2 e T(fi,f2 e PAMeets(tht2)=*MeetsT(h,t2))that is, Meetsj is the extension of Meets;

(T4) Vfi,f2 e T(3fi',f2'

that is, two times are identical if and only if they have the same immediatepredecessor and the same immediate successor.

(T5) Vf,,t2eT(Meefsr(i3,t2)=i>3f e TVf',f" e

that is, if two times are separated by a sequence of times, then there is a timewhich connects them. Hence, by axiom (T4), for any two adjacent times, fj andf2, we may denote the adjacent union of fi and f2 as a new time (interval),f = fi©f2. N.B. fi©f2 always implies that Meetsjiti,t2).

(T6) VteTQpi, . . . ,p, ,eP(t=pi,© ... ©p,,))

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Temporal Knowledge in Legal Discourse 203

that is, each element of T is in the form of adjacent union of a sequence of primetimes.

(T7) Vf,,i2 e TÍMeetsjitjM => Durrfh ® h) = DuMU + DurT(t2))

where ' + ' is the conventional arithmetic addition operator. That is, the durationof the combined times fi©Í2 is identical to the sum of duration of fi andduration of ti.

In what follows, without confusion, we shall simply write Durr as Dur, andwrite Meetsr as Meets.

3. A schema for representing temporal knowledge

Events and their effects can be simply expressed as non-temporal assertions,while the causal relationships may be expressed as predicates over the corre-sponding assertion. Given statements about events and their causal relations,what are their corresponding temporal relations in interpretation? Generallyspeaking, temporal references for non-temporal assertions can be made up of aset of primitive time elements related by one or a set of order relations. In fact,it has been shown in Ma & Knight (1994), in terms of the single relation Meets,there are in total 30 temporal relations among time intervals/points can bederively defined. These temporal relations can be classified into the followingfour groups:

• Temporal relations relating intervals to intervals:{Equals, Before, After, Meets, Metjjy, Overlaps, OverlappedJ)y, Starts,Started_by, During, Contains, Finishes, Finished_by).

• Temporal relations relating intervals to intervals:{Equals, Before, After).

• Temporal relations relating points to intervals:{Before, After, Meets, Met_by, Starts, During, Finishes)

• Temporal relations relating intervals to points:{Before, After, Meets, Met_by, Startedjby, Contains, Finished_by).

We use the following schema for representing temporal statements:

1. Causes(e\, c2)—representing that the occurrency of event e\ leads to theoccurrency of event ci, e.g. CflMses(He_has_beaten_her, She_died).

2. Occurs(e, t)—representing that the event e occurs over time t, e.g. Occurs(sign_contract,26_08_1996).

3. Rel(U, t2)—representing that the temporal relation between time fi and time i2

is Rel, where Rel is one of the temporal relations as classified above, e.g.BeforeiiU, f2).

4. Dur(t) < r, Dur(t) = r, Dur(t) > r—representing that the duration of time t isless than r, equal to r, and more than r, where r is a real number (possiblywith some specified measure unit, such as hours, days, and so on).

4. The inference mechanism

Given statements about events occurrences and the corresponding temporalrelations, it is natural to check whether these temporal relations are consistent or

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not. Intuitively, if the temporal relations can be proved as inconsistent, we maydirectly confirm that some statements are untrue. However, if the involvedtemporal relations are consistent, what are the possible scenarios in which thedescribed events might actually happen? In this section, we introduce anintuitive inference mechanism for checking the temporal consistency of anygiven set of legal statements.

In most cases of legal statements, temporal knowledge may only be describedin some incomplete ways: it is not necessary or impossible to address thestructure of neither a whole fundamental time line, nor the correspondingcomplete temporal system. In what follows, we shall use (K, Meets, Dur) todenote the temporal reference map with respect to some given involved statements.Here, K is a collection of time elements, expressing the knowledge of whatintervals and points are involved with respect to the corresponding statements;Meets expresses the knowledge (possibly incomplete) as to how the time ele-ments of K are related by means of the immediate predecessor relationship; andDur is a function from K' to Ro+, where K' is a subset of K. That is, Durexpresses the duration assignment knowledge (possibly incomplete) about timeelements in K.

We say a temporal reference map (K, Meets, Dur), is consistent if we can finda fundamental time line (P, Meets, Dur), such that (K, Meets, Dur) can subsumedby means of forming the corresponding closure of (P, Meets, Dur). That is, (K,Meets, Dur) expresses a portion of the complete temporal structure with respectto some fundamental time line.

An intuitive graphical representation of a given temporal reference map, (K,Meets, Dur), has been introduced by Knight and Ma (1992) in terms of a directedand partially weighted graph. In this representation, time elements are denotedas arcs of the graph, and the immediate predecessor relationship over times canbe graphically shown by the node structure in the directed graph, where Meets(t¡,t¡) is represented by t¡ being in-arc and t¡ bring out-arc to a common node. Fortime elements with known duration, the corresponding arcs are weighted bytheir durations, respectively.

The necessary and sufficient condition for the consistency of a temporalreference map with duration constraints, (K, Meets, Dur), can be given asfollowing:

(1) there is a duration assignment over K agreeing upon Dur, such that: for eachsimple circuit in the graph of (K, Meets, Dur), the directed sum of weights iszero;

(2) and for any two adjacent time elements, the directed sum of weights isbigger than zero.

Here, condition (1) guarantees that the known duration assignment to the timeelements obeys axioms (T2) and (T7); and condition (2) ensures that no two timepoints meet each other, that is axiom (P) is preserved.

The consistency checking for a temporal reference map with duration con-straints involves a search for simple circuits, and the construction of a numericalconstraint for each circuit. The existence of a solution to this set of constraintsimplies the consistency of the system, and each such a solution gives a possiblescenarios which can subsume the addressed temporal reference map. Hence, theconsistency checker for a random temporal reference map is in fact a linearprogramming problem.

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Temporal Knowledge in Legal Discourse 205

As an example, consider a temporal map (K, Meets, Dur), where

K = {ti, t2, t3, U, ts, t6, t7, ts, t9);

Meets(h, t2), Meets{th t3), Meets{tz, t5), Meefs(t2, U), Meets(t3, t4),Meeís(t4, t7), Meefs(t5, t8), Meets(t6, t7), Meefs(t7, t8);

and

Dwr(t2) = 1, Dur(U) = 0.5, Dwr(té) = 0, Dur(i8) = 0.3.

The graphical representation of such a temporal map is shown in Figure 1below:

t8 (0.3)

Figure 1.

In the above graph, there are two simple circuits (Figure 2):

j4(0.5)te(O)y

tad)Figure 2.

Setting the directed sum of weights in each of these as 0, we get 2 independentconstraints:

Dur(t2) + DuriXe) = Dwr(t3) + Dwr(t4)Dur{ts) = Dwr(t6) + Dwr(t7)

We can easily find a solution, for instance: Dur(t3) = 0.5, Durits) = Dur(t7) = 1.5.(In fact, the duration assignment to t5 and t7 can be any positive real number,provided that Dwr(t5) = Dwr(t7)).

However, in some special cases where only relative temporal knowledge areaddressed, that is there is no duration constraint involved, the consistencychecking can be reformulated in a more convenient form—(K, Meets) is consist-ent if and only if:

(1) there are no nodes with at least one point in-arc and at least one pointout-arc;

(2) the associated reduced graph is acyclic, where the associated reduced graphis formed by means of removing every point arc in the graph of (K, Meets)and merging any two nodes connected by the point arc.

Here, again, condition (1)' preserves that no two time points meet each other,

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Figure 3.

while condition (2)' preserves that time points are not decomposable, andexcludes any circular time structure.

Consider a temporal map without duration constraints. (K, Meets), where

K=(t , , t2, t3/ U, t5)and

MeetsiU, t2), MeetsiU, t3), Meets(t2, t5), Meets(t3, U), Meets(U, t5)

If t2 is not known to be a time point, then the corresponding graph shown inFigure 3 is acyclic, and hence the network is consistent.

However, if t2 is known to be a point, that is Durit-d = 0, then we have thereduced graph in Figure 4, which is cyclic, and hence the network is inconsist-ent.

We can see intuitively why this is so, by noting that in Figure 3 we have:t2 = t3 © t4. This is consistent until we add the constraint that t2 is non-decom-posable. However, if Dwr(t2) — 0, that is, t2 is a (prime) point and hence non-decomposable, equation t2 = t3 © U would become impossible. Therefore, wereach the conclusion that in this case, the temporal map is inconsistent.

5. An example

Let us exemplify the representation formalism and inference mechanism pre-sented above. Consider for instance a scenario where two persons, Peter andJack, are suspected of committing a murder during the daytime. In court, Jackand Peter gave the following statements, respectively:

Peter's statements:

I got home with Jack before 1 p.m. We had our lunch, and when Jackleft I put on a video. The video lasts 2 hours. Before it finished, Robertarrived. When the video finished we went to the train station andwaited until Jack came at 4 p.m.

Jack's statements:

Reduced to:

Figure 4.

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Temporal Knowledge in Legal Discourse 207

Peter and me went to his home and arrived there before 1 p.m. Whenwe finished our lunch there, Peter put on a video, and I left and wentto the supermarket. I stayed there for between 1 and 2 hours. Then Idrove to my home to collect some mail. It takes between 1.5 and 2hours to reach my home, and about the same to the train station. Iarrived at the train station at 4 p.m.

In addition, being a witness, Robert made this statement:

I left home at 2 p.m. and went to Peter's house. He was playing a video,and we waited till it finished. Then we went together to the train stationand wailed for Jack. Jack got to the train station at 4 p.m.

Using the graphical representation introduced in Section 4, we can express thescenario with respect to the above statements the graph of Figure 5, where:

ii: the time (interval) over which Peter and Jack went to Peter'shome;

1 p.m.: the reference time (point) before which they arrived at Peter'shome;

¡2". the time (interval) over which Peter and Jack had lunch;Í3: the time (interval) over which Peter played the video (ddi) — 2);¡4: the time (interval) over which Jack went to the supermarket-pi: the time (point) w h e n Robert arrived at Peter 's house;is: the time (interval) over which Peter and Robert went to the train

station;i6: the time (interval) over which Peter and Robert waited for Jack

at the train station;4 p.m.: the t ime (point) w h e n Jack arrived at the train station;Í7: the time (interval) over which Jack stayed in the supermarket

(l<Dwr(z7)<2);is: the time (interval) over which Jack drove to his home

Í9: the t ime (interval) over which Jack collected some post from hishome;

iJ0: the time (interval) over which Jack drove to the train station(1.5<Dwr(i io<2);

2 p.m.: the time (point) w h e n Robert left home;in: the time (interval) over which Robert went to Peter's house;ii2: the time (interval) over which Peter and Robert watched the

video together;ii3/ Í14, •••/ Í27: some extra relative time elements which are used for expressing

the correspondingly relative durat ion knowledge, e.g. with Í19,Í20/ Í21/ Í22, and Durdw) = 1.5 and Durfci) = 2, w e can express that1 .5<D«r ( i 8 )<2 (see Figure 5).

Here, arcs with thin bars represent time intervals (i.e. ii, Í2, ..., Í27), and arcswith thick bold bars represent t ime points (i.e. 1 p.m., 2 p.m., 4 p.m. and pi).Arcs with weights represent intervals that have known absolute durat ions (e.g.Dur(Í3) = 2). Arcs without weights express intervals with u n k n o w n or relativedurations, where relative durat ion knowledge can be represented by means of

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2pm

i25

Figure 5.

adding some correspondingly relative time elements with (e.g. Í19), or without(e.g. Í20) known absolute durations.

Now, we consider whether the above temporal reference map is consistent ornot.

From Figure 5, there are three time elements (i.e. two intervals, in and in andone point, pi) standing between 2 p.m. and 4 p.m. Since each interval has apositive duration and each point has a non-negative duration, we can infer that:

2 (5.1)

(5.2)

1.5 = 4 (5.3)

in addition, since D«r(i3) = 2, hence

Dur(i3) + Dur(i5) + Dur(i6) < 2 + 2 = 4

However,

Dur(U) + D«r(i7) + Dur(i8) + Dur{\9) + Dur(i]0)>0 + l +

Therefore, for the simple circuit i3, i5, i6/ iio, h, is- h, U, as shown below in Figure6, there does not exist any duration assignment over K agreeing upon d, suchthat

Dur(i3) + Dur(i5) + Dwr(i6) = D«r(i4) + Dwr(i7) + Dur(i8) + Dwr(i9) + Dt<r(iio)

that is,

Dur(i3) + Dur(i5) + D«r(i6) - D«r(i4) - Dur(i7) - Dur(is) - Dur(i9) - Dur(iio) = 0

Hence, the temporal reference map shown in Figure 5 is inconsistent, andtherefore we can directly confirm that some statements are untrue. Suppose thevideo can be checked that it did actually last for two hours, we can confirm thatthere must be some falsity in either Robert's or Jack's statements. If it can be

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Temporal Knowledge in Legal Discourse 209

i6

i7

Figure 6.

proved that Robert did leave home at 2 p.m., then Jack must have lied, whenmaking his statements. Otherwise, to convince us that his statements are true,Jack must prove that Robert left home at some time before 2 o'clock in theafternoon.

6. Conclusions

In this paper, we have introduced a formalism for representing temporalinformation, possibly in the legal domain, which allows an explicit expression oftime and event occurrences. The formalism is based on a fundamental timestructure that is characterized as a well-ordered discrete set of non-decompos-able intervals with positive duration and points with zero duration. An intuitivegraphical representation for a temporal reference map with respect to a given setof legal statements is introduced, where a consistency checker in two differentforms is provided for cases with, and without, duration constraints, respectively.The general consistency checking algorithm, which addresses both absolute andrelative temporal knowledge, turns out to be a linear programming problem (inthe perspective of optimization methods), while in the special case where onlyrelative temporal relations are involved, it becomes a simple question of search-ing for cycles in the graph-theoretic representation of the corresponding legaltext. It is shown that the formalism supports a full representation of differenttypes of temporal information, including: absolute temporal references, which referto points in time; absolute temporal durations, which refer to some certain amountof temporal granularity; relative temporal references, which refer to times that areknown only by their relative temporal relations to other temporal reference(which again, may be absolute or relative); and relative durations, which refer tosome uncertain amount of temporal granularity.

We did not take into account the psychology of time, as opposed to standardclock time. Narrated time, when narrating the Self, is involved in complexphenomena of reconceptualization; cf. Linde (1993). This, in turn, is importantfor the psychology of legal evidence. In court, narratives and the very wordingfit, after all, in deliberate strategies (Drew, 1990).

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Psychology aside, the model proposed here focuses on the temporal structure,but does not attempt to integrate it organically in a theory of action, e.g. of thekinds current in the literature of formal semantics, such as van Voorst's eventsemantics (1993); cf. (Linde, 1987). This stems from our choice to avoid, for thetime being, the treatment of linguistic expression of time. This would have ledus into having to deal with tense and aspect, e.g. with the progressive, for whichsee Landman (1992). Some lexical items may convey a temporal or nontemporalsense, e.g. 'already' versus 'still' (Michaelis, 1996), and then, to disambiguate,reasoning on time alone is not enough. See Song & Cohen (1995) on the temporalanalysis of natural-language narratives. Nakimovsky (1988) proposed an elegantframework for dealing with the temporal structure of narratives. For a represen-tation formalism adequate to support a rich gamut of natural-language con-structs, beyond tense and aspect, we would select Schubert's episodic logic(Hwang & Schubert, 1993); from the same team, see Gerevini & Schubert (1995)and Hwang & Schubert (1994) on temporal reasoning.

In this paper, instead, we presented a basic temporal formalism, elegant inthat it handles both time points and intervals, and also addresses granularity. Itis not specifically tailored for natural-language constructs, and may suit as well,say, tabular information in legal databases. Our general approach can arguablybe incorporated as an ingredient in a variety of treatments within knowledgerepresentation, to suit a panoply of tasks in modelling the legal domain.

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