Time flies like an arrow.… Fruit flies like a banana.—Oettinger (1966)

Many languages have grammatical means to indicate the time when anaction or event occurs, or when a state or process holds. Thisphenomenon is calledtense. In English, for example, addingthe morpheme-ed to the verbwalk, to formwalked, indicates that the event denoted by the verb occurredbefore the present time. What is calledaspect, on the otherhand, deals with the internal constituency of actions, events, states,processes or situations. For instance, it may indicate that an actionis completed or still ongoing. English typically uses the-ing form of verbs to indicate ongoing processes, as inHe is building a house.

After a short introduction to basic notions of tense and aspect webriefly discuss temporal logic, and then Reichenbach’s famousdistinction between speech time, event time and reference time.Event-based semantic theories treat events as ontological primitives,so in the following section we show how time can be constructed fromevent structures, as exemplified by the Russell-Kamp construction.These sections are followed by a discussion of the most importantobservations concerning lexical and grammatical aspect, including thefamous imperfective paradox. Next we introduce two widely discussedtheories of temporality and show how they cope with the imperfectiveparadox. This section is followed by one that shows how temporalinformation is expressed in Artificial Intelligence (AI). We use theevent calculus from AI to present a solution of the imperfectiveparadox, by viewing it as an instance of the frame problem. Thefollowing section is devoted to gathering psycholinguisticevidence showing that at least some of the philosophical and semanticconcepts discussed in this article may be cognitively real. The lastsection discusses some aspects concerning theinterrelationsship between temporal interpretation and thelarger discourse structure.

• 1. Introduction
• 2. Temporal Logic
• 3. Speech Time, Event Time and Reference Time
• 4. From Events to Time
• 5. Lexical and Grammatical Aspect
• 6. Intensionality versus Events
  • 6.1 Nominal Reference and Temporal Constitution
  • 6.2 Compositionality
• 7. Event Calculus
  • 7.1 The Yale Shooting Scenario
  • 7.2 The Completion of a Program
  • 7.3 Introducing Tense Information
  • 7.4 The Imperfective Paradox reconsidered
• 8. Cognitive Aspects
  • 8.1 Lexical Aspect
  • 8.2 Grammatical Aspect
• 9. Tense and Aspect meet Discourse Structure
• 10. Conclusion
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Introduction

Tense roughly means reference to the time at which eventstake place, or at which processes or states hold. English, forexample, clearly distinguishes between past and non-past tense as in(1a) and (1b) and (1c).

1.

(a)

John promised to pay ten pounds.

(b)

I promise to pay you ten pounds.

(c)

The student will work on his thesis.

In English,verb forms are typically used to signal the timewhen an action or event occurs or a state holds. Thus in (1a),John’s promise was given before the present time, in (1b) thepromising is simultaneous with the present time and (1c) says that thestudent’s work on his thesis will occur at some time after thepresent. It should be noted that the verb forms used to expresstemporal information may also be used to signal information that isnot purely temporal. For instance, the present tense form inJohnwalks characterizes a certain habit of John. And in the statementThe train departs at five o’clock tomorrow, the presentverb form clearly has a futurate meaning. So English distinguishesbetween past and non-past but not between future and non-future.Moreover, many linguists exclude future as a pure tense, because theauxiliarywill may be used to express volition as inHewill go swimming in dangerous water.^[1]

Apart fromabsolute tense—exemplified by(1a)–(1c)—where the reference point from which thelocation in time is evaluated is the present, there is alsorelative tense where the reference point is not necessarilythe present but may be given by context. Thus in a sentence likeThe student had worked on his thesis the student’s worktook place at a time before a reference point in the past, in contrastto (1c) where the reference point is the present. Other instances ofrelative tense in English are the present perfect and the futureperfect in (2a) respectively (2b).

2.

(a)

I have lost my watch.

(b)

The student will have finished his thesis next month.

The notion ofaspect according to Comrie refers to“[the] different ways of viewing the internal temporalconstituency of a situation” (1976: 3). It is customary todistinguish betweenlexical andgrammatical aspect.The following are examples concerning lexical aspect. Since Vendler(1967) linguists distinguish at least four aspectual classes. Theseare states likeknow, activities likerun,accomplishments likecross the street and achievementsexemplified by a verb likerecognize. Accomplishmentsdescribe the internal temporal constituency of a situation in a moredetailed way than (say) activities.Crossing the street, forexample, includes the starting of a crossing activity which goes onfor some time and involves a result state that is characterized bybeing on the other side of the street. No such elaborate descriptionsare necessary for activities or achievements. There are grammaticalmeans of distinguishing between these aspectual classes. For example,states and achievements cannot occur with the progressive whileactivities and accomplishments can; more about this below inSection 5. These differences are customarily considered to be lexicaldifferences and this area is therefore dubbedlexicalaspect.

A further crucial aspectual difference is that between perfective andimperfective aspect. Comrie characterizes these notions asfollows.

…perfectivity indicates the view of the situation as a singlewhole, without distinction of the various separate phases that make upthat situation, while the imperfective pays essential attention to theinternal structure of the situation. (Comrie 1976: 16)

In English this difference is often expressed bygrammaticalmeans, for instance by past tense versus past progressive. This is aninstance of grammatical aspect. Slavic language often have anelaborate grammatical system to signal the difference betweenimperfectivity (ipv) and perfectivity (pv). Here is an example fromRussian.

3.

(a)

Petr
Peterpisal\(_{ipv}\)/*napisal\(_{pv}\)
was-writing/*wrotepis’mo,
letter,kogda
whenon
hebyl
wasprervan
interruptedtelefonnym
by-telephonezvonkom.
call.

(b)

Petr
Peter*pisal\(_{ipv}\)/napisal\(_{pv}\)
*was-writing/wrote pis’mo
letteri
andotnes
broughtego
itna
topočtu.
post-office.

Sentence (3b) presents the writing of a letter as a single whole andit is clear that this activity was finished when the letter wasbrought to the post office. By contrast, (3a) focuses on an ongoingactivity of letter writing in the past which is not completed becauseof the interruption. In fact it is consistent with the truth of (3a)that the letter was never completely written.

The natural language categoriestense andaspectembody the linguistic encoding of time. From a typological point ofview these categories are typical verbal categories.^[2] This means that if these categories are morphologically realized in alanguage then these morphemes attach to the verb. Verbs usuallyexpress events, processes, actions or states^[3] and the temporal morphemes locate these eventualities in time. Ofcourse this does not mean that languages that lack such morphemes arenot able to express temporal relations. They just have to choose othermeans for this purpose. One famous example of a language notcontaining temporal morphology is Mandarin Chinese. Often tense andaspect cannot be clearly separated. For example the Quichéprefix \(x-\) denotes a completed (aspect) action in the past (tense).^[4]

Typologists also observed an asymmetry between past and future. Mostlanguages that possess temporal morphology use these means todifferentiate between past and non-past. There are, however, a fewlanguages which use temporal morphology to distinguish between futureand non-future.

We will not go into further details concerning the linguisticrealization of tense and aspect, but present a brief and necessarilyincomplete review of major philosophical and semantic theories ofthese notions.

2. Temporal Logic

Temporal logic was introduced by Arthur Prior (see for instance Prior1967). Here we will sketch only propositional temporal logic (for amore thorough introduction the reader is advised to consult Gamut1991: chapters 2 and 3) and the entry ontemporal logic. Temporal logic introduces operators \(\bG\), \(\bH\), \(\bF\) and\(\bP\), which are similar to the modal operators \(\Box\) and\(\Diamond\). We summarize the intuitive meaning of these operators inTable 1.

By adding the above operators to propositional logic we extendpropositional logic to propositional temporal logic. Let \(q\)abbreviate the sentenceSam is working, then we are able toexpress the following verb tenses in temporal logic:

4.

(a)

\(q\)   Sam is working

(b)

\(\textbf{F}q\)   Sam will work.

(c)

\(\textbf{P}q\)   Sam worked.

(d)

\(\textbf{PP}q\)   Sam had worked.

(e)

\(\textbf{FP}q\)   Sam will have worked.

(f)

\(\textbf{PF}q\)   Sam would work.

A model \(\sM\) for propositional temporal logic consists of anonempty set \(T\) of moments of time, an earlier than relation\(\prec\) and a valuation function \(I\) which for each moment of timeand each proposition letter \(q\) assigns a truth value \(I_{\sM,t}(q)\). The following definition characterizes \(I_{\sM ,t}(\phi)\)for the temporal operators.

These clauses are analogous to the clauses which define the modaloperators \(\Box\) and \(\Diamond\)—with \(\bG\) and \(\bH\)corresponding to \(\Box\), and \(\bF\) and \(\bP\) to\(\Diamond\)—but instead of possible worlds the valuationfunction takes moments of time as arguments. Therefore principle (5)is valid in any model, since the modal analogue is valid for \(\Box\)independently of the accessibility relation.

5.

\(~\bG(\phi\rightarrow \psi) \rightarrow(\bG\phi \rightarrow \bG\psi)\) (andanalogously for \(\bH)\).

However, principle (6), which is often considered as valid for\(\Box\), is presumably not valid for \(\bG\).

6.

\(~\bG\phi \rightarrow \phi\)

Formula (6) is equivalent to \(\phi \rightarrow \bF\phi\). The latterformula says that if \(\phi\) is the case then \(\phi\) will be thecase, which is intuitively incorrect. Suppose that \(\prec\) isirreflexive; this assumption makes sense since it means that no timepoint is earlier than itself. But under this assumption, Principle (6)is obviously wrong. For extensions of temporal logic and more examplesconcerning the correspondence between properties of models and thevalidity or invalidity of formulas see Gamut 1991: chapter 2.

This concludes our brief remarks about temporal logic. We now turn toan alternative approach due to the philosopher Hans Reichenbach.

3. Speech Time, Event Time and Reference Time

The notionsspeech time,event time, andreference time were introduced by Reichenbach (1947) in orderto distinguish simple past and present perfect or, more generally,absolute and relative tense. According to Comrie (1985), who refinedReichenbach’s system (in Chapter 6 of his book on tense) speechtime and event time are sufficient for the analysis ofabsolutetime; i.e., present, (simple) past and future. But forrelative tense—of which the present perfect is but oneexample—reference time is required. Let us explain these notionsby applying them to distinguish between past and present perfect.

Consider the following examples from Steedman (1997).

7.

(a)

I have lost my watch.

(b)

Yesterday, I lost my watch.

It has often been observed that the present perfect in English haspresent relevance. For instance the continuation of (7a) withbutI have found it again is infelicitous in English; the Germantranslation of this sequence is acceptable, showing that the Germanperfect is more like a past tense (but see Kamp et al. 2015 for anextensive discussion, in Other Internet Resources). The samecontinuation is fine for sentence (7b). In this sense the perfect is arelative tense and the past an absolute tense in English. Let \(E\) beshort for event time and let \(S, R\) stand for speech time andreference time respectively.

Simple Past	Present Perfect
I saw John	I have seen John

For the simple past, both event time and reference time are situatedon the time line before speech time. In case of the perfect, R and Sare simultaneous and E is earlier than both R and S. Intuitively,reference time represents the perspective from which an eventuality isperceived on the time line. This is not a purely semantic theory oftense like temporal logic, rather it is a pragmatic theory of tense.In particular, reference time (in contrast to event time) has to bemutually known by communication partners. When using the presentperfect, reference time is known since it coincides with speech time.However, reference time is not necessarily known when the past tenseis used, since it is just required to be earlier than speech time andto coincide with event time. This may explain why sentences in thepast sound strange when uttered out of the blue. Steedman (1997)presents the following examples:

8.

(a)

*Chapman breathed a sigh of relief.

(b)

When Nixon was elected, Chapman breathed a sigh of relief.>

The past-tensed sentence (8a) uttered out of the blue is infelicitous,while sentence (8b) is fine, since in this case thewhen-clause introduces the reference time.

This is by no means the complete story of the perfect. For example,Comrie (1976) distinguishes four typical uses of the perfect: theperfect of result, the experiential perfect, the perfect of persistentsituation and the perfect of recent past. For an extensive recentdiscussion the reader is advised to consult Kamp et al. 2015 (in OtherInternet Resources).

The following table summarizes the positions of event time, referencetime and speech time for other tenses:

Comrie (1985) and Gamut (1991) point out that this cannot be acomplete account for temporal constructions that occur in naturallanguages. For instance the temporal profile of the sentenceSamwould have worked cannot be analyzed by using a single referencetime. This is one reason for the extended requirements for a formaltheory of tense proposed by Comrie (1985: chapter 6). Furthermore,Blackburn and Jørgensen (2016) combine the key insights ofPrior and Reichenbach in the framework of hybrid tense logicsuggesting that the two approaches are fully compatible with eachother.

4. From Events to Time

In event semantics following Davidson (1967) events are commonly takenas ontological primitives. This raises the philosophical question howevents and times relate to each other. A construction, due to Russell,Wiener and Kamp, shows that the time line can be constructed fromevents. We will briefly sketch this construction before we move on tolexical and grammatical aspect.

Russell remarked:

Even if there be a physical world such as the mathematical theory ofmotion presupposes, impressions on our sense-organs produce sensationswhich are not merely and strictly instantaneous, and therefore theobjects of sense of which we are immediately conscious are notstrictly instantaneous. Instants, therefore, are not among the data ofexperience and must be either inferred or constructed. It is difficultto see how they can be validly inferred; thus we are left with thealternative that they must be constructed. (Russell 1914: lectureIV)

Kamp (1979) took up Russell’s ideas and slightly modified them.The construction takes event structures as primitives from which thestructure of time, i.e., a total order, can be derived.

An event structure \(\langle E, P, O\rangle\) simply consists of a setof events \(E\) and the relations \(P\) (precedes) and \(O\)(overlaps) and is characterized by axioms A1–7.

Given an event structure satisfying these axioms, the set of instantsand their strict linear ordering can be constructed according todefinition 2. The idea is to identify an instant with the maximal setof pairwise overlapping events. Instants are thus conceived of asabstractions over events that happen (or go on) simultaneously. Eventslinked by the precedence relation will give rise to distinctinstants.

We will first illustrate the Russell-Kamp construction by way of anexample and then show that \(\langle I,\lt \rangle\) has theproperties specified in Theorem 1: it is a strict linear orderingwhich gives rise to an interval structure.

Example 1.Let \(E = \{a, b, c, d, e\}\) and\(P\) be the set of ordered pairs \(\{(a, c), (a, d), (a, e), (b, e),(c, e)\}\). Given A7, the relation \(O\) consists of the set of pairs\(\{(a, b), (b, c), (b, d), (c, d), (d, e)\}\). \(E\) contains threemaximal subsets of pairwise overlapping events, that is, instants\(i_1 = \{a, b\}\), \(i_2 = \{b, c, d\}\) and \(i_3 = \{d, e\}\).Furthermore, \(i_1\), \(i_2\) and \(i_3\) are linearly ordered as\(i_1 \lt i_2 \lt i_3\) because \(a \in i_1\), \(c \in i_2\) and\(P(a, c)\) hence \(i_1 \lt i_2\), and \(c \in i_2\), \(e \in i_3\)and \(P(c, e)\) hence \(i_2 \lt i_3\), and similarly for \(i_1 \lti_3.\)

A proof of the following theorem can be found in (Kamp 1979: 379).

Once having constructed the set \(I\) it is possible to define timeintervals and these, in turn, can be used to measure the temporalextent of an event. In Example 1, for example, \(a\)goes onin the interval [\(i_1], b\) in [\(i_1, i_2], c\) in [\(i_2], d\) in[\(i_2, i_3\)] and \(e\) in [\(i_3\)]. Corollary 1 guarantees thatthese intervals can be constructed (Kamp 1979: 379).

Proof: If \(i_1, i_2 \in e'\) and \(i_1 \lt i \lt i_2\), it has to beshown that \(e \in i\), too. Suppose it is not. Then there is \(d \ini\) such that \(\neg O(d, e)\), hence \(P(d, e)\) or \(P(e, d)\). Inthe first case \(i \lt i_1\) and in the second case \(i_2 \lt i\).Both yield a contradiction.\(\Box\)

We cannot give further details here, but refer the interested readerto Thomason (1986) who discusses how to construct time as acontinuum—isomorphic to the real numbers—and uses adifferent construction originally proposed by Walker (1947). Empiricalevidence for events being ontological primitives will be presented insection 8 where we review psychological studies on event perception. We willnow move to lexical and grammatical aspect, that is the expression ofevent types and how a given event is conceptualized, which form basicconcepts in linguistic theory.

5. Lexical and Grammatical Aspect

Linguists distinguish four or five lexical aspectual classes orAktionsarten. The following four were introduced by thephilosopher Zeno Vendler (1967: chapter four) on the basis of earlierwork by philosophers such as Kenny, Ryle and Aristotle (see also theentry onevents). For a formal definition ofAktionsart the reader is referredto van Lambalgen and Hamm (2005: 85 ff).

In addition, linguists often assume that verbs likeflash,spot andblink form an extra class—the classof semelfactives or points (see Smith 1991).

A useful notion for distinguishingAktionarten is theevent nucleus introduced by Moens and Steedman (1988). Theevent nucleus is constructed from a preparatory phase, a culminatingevent and a consequent phase. Activities only refer to the preparatoryphase, states only to the consequent phase, achievements to theculminating event and to the consequent phase and finallyaccomplishments to all three parts of the event nucleus.

Vendler proposed several linguistic tests for distinguishing theseverb classes. We will present only the most important ones here; for amuch more comprehensive list the reader is referred to Dowty (1979:60). The first test separates non-statives from statives. Onlynon-statives occur in the progressive.

9.

(a)

*Sam is knowing the answer.

(b)

Sam is running.

(c)

Sam is writing a letter.

Accomplishment verbs prefer \(in\)-adverbials as temporal modifiers,whereas activity verbs allow onlyfor-adverbials.

10.

(a)

?Sam wrote a letter for an hour.

(b)

Sam wrote a letter in an hour.

(c)

Sam swam for an hour

(d)

*Sam swam in an hour

Achievement verbs are usually infelicitous withfor-adverbials but allow the combination with\(in\)-adverbials.

11.

(a)

Sam reached the summit in five hours.

(b)

Sam reached the summit for five hours.

The last test we mention here concerns the different entailmentpatterns of activities and accomplishments in the progressive.Activities in the past progressive entail their past reading butaccomplishments in the past progressive don’t.

12.

(a)

Sam was pushing a cart \(\Rightarrow\)

(b)

Sam pushed a cart.

13.

(a)

Sam was building a house \(\not\Rightarrow\)

(b)

Sam built a house.

This is an instance of the famous imperfective paradox. Of course,taken literally this is not a paradox. Nevertheless the entailmentpatterns (12) and (13) pose a significant problem for any formaltheory of tense and aspect. For instance, the first formal proposalfor truth conditions of sentences in the past progressive stated thata sentence S in the past progressive is true if and only if thereexists an open interval before the speech time at which the sentencewithout the progressive is true. According to definition 1.4 thisimmediately validates pattern (12) but without qualifications thistruth definition does not account for pattern (13). Sections6 and7 contain extensive discussion of the imperfective paradox.

Vendler thought of theAktionarten as lexical properties ofverbs. That this position is dubious was pointed out by manylinguists, in particular by Dowty (1979) and Verkuyl (1993). For asimple case, consider the verbdrink. If we assume that beingan activity is a lexical property of this verb, then surely bycombining it with the nounwine this property is preservedfor the complex phrasedrink wine. However, if we combine theverbdrink with the noun phrasea bottle of wine weturn an activity into an accomplishment. The converse problem arisesif we assume that being an accomplishment is a lexical property ofdrink. This phenomenon of aspectual reinterpretation wasdubbedcoercion in Moens and Steedman (1988). InSection 6.1 we will sketch a systematic solution for these types of coercion inmereological semantics (Krifka 1989, 1992).

Aktionsart is not even definitely fixed at the VP-level. Theverbarrive in

14.

(a)

Chapman arrived.

(b)

*Chapman arrived all night.

is an achievement, as demonstrated by the ungrammaticality of (14-b).But if we choose a bare plural as subject it is turned into anactivity and sentence (15) is grammatical.

15.

Visitors arrivedall night.

Therefore a final decision about aspectual class cannot be reachedbelow the sentence level. Steedman’s famous sentence (16)

16.

It took me twoyears to play the “Minute Waltz” in less than sixtyseconds for one hour without stopping.

shows that coercion can be iterated and that aspectual class canswitch back and forth in this iteration process. We close this sectionwith two further examples of aspectual coercion. In the first one astative verb is transformed into an activity.

The verbresemble is a stative verb and therefore (17a) isunacceptable but (17b) is fine.

17.

(a)

*She is resembling her mother.

(b)

She resembles her mother.

However, if we addmore and more every day to (17a) thusforming

18.

She is resemblingher mother more and more every day.

we get an acceptable result. This is due to the phrasemore andmore every day which coerces a state into an activity. Our lastexample is about temporal modification withfor-adverbials.As pointed out above accomplishments are usually rather bad withfor-adverbials. They require \(in\)-adverbials. But considersentence (19) from van Lambalgen and Hamm (2005).

19.

Pollini playedOpus 111 for two weeks.

This sentence seems to be fine. However it is not interpreted as anaccomplishment any more but is reinterpreted as an iterated activity.To get this reading, a lot of non-linguistic knowledge is required.First, one has to guess that Opus 111 refers to Beethoven’s lastpiano sonata and moreover one has to be aware that this piece lastsabout 25 minutes. Under these assumptions, sentence (19) says thatPollini played Opus 111 repeatedly within a time span of two weeks.Formal accounts of coercion phenomena are contained in Egg (2005), vanLambalgen and Hamm (2005) and Steedman (1997) among others. The readeris also advised to consult Steedman’s updated manuscript,The Productions of Time (see the Other Internet Resources).Processing studies of coercion are reviewed in Bott (2010); see alsoSection 8.

6. Intensionality versus Events

The most influential approach to solving the imperfective paradox isdue to Dowty (1979). The basic idea is to treat the progressive as amodal operator \((\Box)\) but restrict its domain to inertia worlds.The notion of aninertia world is characterized informally.An inertia world is exactly like the real world up to the time ofevaluation; after this it may differ from the real world but isassumed to be as similar to the real world as possible. Given thisnotion, the following definition introduces truth conditions forsentences in the progressive.

Definition 3 does not yet account for the different entailmentpatterns of activities and accomplishments. Two additional assumptionsare required. The first concerns activities; the second,accomplishments.

20.

If \(\phi\) is anactivity that is true with respect to interval \(I\), then \(\phi\) istrue with respect to any sufficiently large subinterval of \(I\).

Accomplishments likeMary draw a circle are split up into twoparts, an activity partMary draw that satisfies principle(20) and a result part which is characterized by the existence of acircle. Both parts are connected by a causality relationCAUSE.

21.

CAUSE[Mary draw, A circle comes into existence]

Thus an accomplishment has a richer internal structure than anactivity.

With these additional requirements, the inference patterns foractivities and accomplishments follow. Let us first show thatMarywas pushing a cart impliesMary pushed a cart. Assumethat the first sentence is true in \(w\) with respect to speech time\(S\). ThenMary be pushing a cart is true in \(w\) withrespect to an interval \(I\) before \(S\). According to Definition 3,Mary push a cart is then true in every inertia world \(w' \inIE(w)\) with respect to an interval \(I' \supseteq I\). Because ofpostulate (20),Mary push a cart is true in every \(w' \inIE(w)\) with respect to interval \(I \ (I\) is a subinterval of\(I')\). Now, the definition of inertia worlds implies thatMarypush a cart is true in \(w\) with respect to interval \(I\). Thismeans thatMary pushed a cart is true in \(w\) with respectto speech time \(S\).

A completely analogous argument shows thatMary was drawing acircle impliesMary drew. But postulate (20) only holdsfor the first part of accomplishments; the result part is onlyrequired to hold in every inertia world \(w'\) with respect to alarger interval \(I'\), normally one after speech time. Since theinertia worlds after \(S\) may differ from \(w\) and since thesubinterval property (20) is not required to hold for the result partsof accomplishments, the stronger conclusion thatMary drew acircle does not follow.

Many researchers assume that inertia worlds introduce a notion ofnormality for the semantic analysis of the progressive. Thethunderbolt in example (22) from Landman (1992) seems to break thenormal development of the real world. Dowty’s analysis seems tobe tailored for cases like this one.

22.

Mary was crossingthe street, when a thunderbolt from heaven struck her down.

However, objections have been raised to the normality interpretationof inertia. The first one is attributed to Frank Vlach in Ogihara(1990). Consider sentence (23)

23.

John was crossingthe street, when he was hit by a truck.

and a situation in which the truck is only a few centimeters away fromJohn. Moreover the truck’s speed is such that it is impossiblefor it to stop before hitting John. In this situation, the normalcourse of events is such that John will never reach the other side ofthe street. Therefore, given definition 3, sentence (23) should befalse under these circumstances. This is intuitively incorrect. Asimilar objection was raised by Bonomi (1997).

On the other hand, the normality interpretation seems to be at leastquestionable. Consider the following example from Naumann andPiñón (1997).

24.

Rebecca wasrunning across the minefield.

This does presumably not mean that when you are running across aminefield, you normally will eventually get to the other side.

Note that these objections all make use of a particular informalinterpretation of the notioninertia. Judging the validity ofthese objections to Dowty’s theory in a precise way thereforerequires an explicit theory of this notion with exact empiricalpredictions.

Dowty analyzes the progressive as an intensional construction. Doesthe progressive satisfy the standard philosophical tests forintensional constructions, that is, the invalidity of substitution ofco-designative proper names and the impossibility of pulling theexistential quantifier out of the context created by the intensionalconstruction (see Bealer and Mönnich (1989) for a more detaileddiscussion)? Let us consider accomplishments, for example sentence(25).

25.

Jackson Pollockwas painting Ruth Rendel.

Given that Ruth Rendel and Barbara Vine are co-designative propernames, sentence (25) implies thatJackson Pollock was paintingBarbara Vine. Therefore the first test fails. Co-designativeproper names are substitutablesalva veritate in progressiveconstructions. The second one, however, applies, since

26.

Carlos wasbuilding a house.

does not imply that there is a house that Carlos was building. Thesetests therefore don’t provide a clear answer to the questionwhether the progressive is an intensional construction. Even if theanswer is yes, the progressive is certainly a different type ofintensional construction than, for example, propositional attitudeslikebelieve ordoubt.

An extensional alternative was developed by Parsons (1989, 1990).Parsons, like Davidson (1967), assumes that first-order quantificationover events is possible. But unlike Davidson, Parsons assumesquantification over eventualities in the sense of Bach (1986), whichincludes events proper but also states, processes and so on. LikeDowty, Parsons supposes that eventualities are split up into adevelopment phase and a culmination phase. In order to represent thisdifference in first-order logic two new predicates are introduced,Cul\((e, t)\) andHold\((e, t)\). The intuitivemeaning of the first is that eventuality \(e\) culminates at time\(t\). The second one says that \(e\) is either an eventuality in itsdevelopment phase or that \(e\) is a state. Given these assumptions asentence likeMary drew a circle is translated intofirst-order formula (27), \(S\) is again short for speech time.

27.

\(\existsx(Circle(x)\,\wedge\) \(\exists e\exists I[I \lt S \wedge Drawing(e)\\wedge\) \(Subject(e, Mary)\ \wedge\) \(Object(e, x)\ \wedge\)\(Cul(e, I)])\)

The semantic effect of the progressive consists in transforming eventsinto states.

If ‘\(A\)’ is an event verb, then ‘be\(A\)-ing’ is to be treated semantically as a state verb;otherwise, ‘be \(A\)-ing’ is to be treated the same as‘\(A\)’. (Parsons 1989: 222)

With this assumption the logical representation ofMary wasdrawing a circle is (28).

28.

\(\existsx(Circle(x)\,\wedge\) \(\exists e\exists I[I \lt S \wedge Drawing(e)\\wedge\) \(Subject(e, Mary)\ \wedge\) \(Object(e, x)\ \wedge\)\(Hold(e, I)])\)

Obviously (27) does not follow from (28). But (28) does imply thatthere is a circle Mary was drawing. Of course this circle may not becomplete. This means that Parson’s ontology is bound to includeincomplete objects. For a discussion of incomplete objects see forinstance Baggio and van Lambalgen (2007).

According to the quotation above, the progressive doesn’t changeanything in the case of activities. ThereforeMary pushed acart andMary was pushing a cart are predicted to beequivalent.

Parsons’ theory rests on the difference between the predicatesCul andHold. This difference is left to intuition.No axiomatisation of these predicates is given. This is one of theobjections made in Zucchi (1999). Zucchi also notes that under certaincircumstances it is possible to derive a specific version of theimperfective paradox in Parsons’ theory. A careful discussion ofDowty’ and Parsons’ approaches and a combination of thetwo systems is contained in Landman (1992).

Another approach to the imperfective paradox and—moregenerally—non-culminating accomplishments was proposed by Copleyand Harley (2015). They abandon event semantics and propose instead aframework using situations and forces as primitives. Forces lead totransitions between situations. Their theory is motivated by theobservation that across languages, non-culminating accomplishments arecrosslinguistically in fact a very common phenomenon (see also Martin2019). Interestingly, these non-culminating readings are per defaultconveyed by less complex expressions than complete events. Often, itis the perfective and not the imperfective that is markedlinguistically. Prima facie, this is a problem for analyses such asDowty’s which assume that the imperfective paradox in accomplishmentshinges on an additional operator such as PROG. This is where Copleyand Harley’s causal analysis comes into play. Their force-theoreticaccount does not run into this problem because causally efficaciousforces always take effects ceteris paribus, for instance, an effectmay not occur due to the occurrence of a counter force preventingthe effect. They develop a compositional semantic framework linkingforces to the argument structure of the sentence. At the present stageof the theory, however, some of the basic concepts also call foraxiomatisation. For instance, it is crucial to gain a properunderstanding of what it means for a situation to be a ceteribusparibus successor situation for some initial situation. For thispurpose, their semantic framework must be connected to a theory ofcausality connecting linguistic meaning to cognition and causalreasoning via a conceptual level integrating the two.

We will come back to the imperfective paradox inSection 7 where we combine linguistic theory with event theories fromartificial intelligence. This will give us a formalization ofceteris paribus from which a new solution to the imperfectiveparadox will follow.

6.1 Nominal Reference and Temporal Constitution

Let us now show that events are also useful for a systematic accountof certain types of coercion that were mentioned above inSection 5.

Intuitively there is a close link between the nominal predicateswine anda bottle of wine and their verbalcounterparts (29-a), (29-b).

29.

(a)

drink wine

(b)

drink a bottle of wine

Whenever there are two entities to whichwine applies, thispredicate applies to their collection as well. The predicateabottle of wine does not have this property. Whenever there aretwo different entities to whicha bottle of wine applies,this predicate does not apply to their collection. The first predicateiscumulative (see Definition 4) the second isquantized (see Definition 5). A similar argumentation appliesto the difference between the activitydrink wine and theaccomplishmentdrink a bottle of wine. It was observed bymany linguists that the combination of a verb likedrink witha cumulative predicate likewine yields an atelic predicatelike (29-a), whereas its combination with a quantized predicate yieldsa telic predicate like in (29-b).

In order to account for these intuitions in a precise way Krifkaassumes that the parts of the structure \(\mathcal{M} = (\mathfrak{O},\mathfrak{E}, \mathfrak{T})\) consisting of objects \(\mathfrak{O}\),events \(\mathfrak{E}\) and times \(\mathfrak{T}\) are each structuredas complete join semi-lattices without a bottom element (seeGrätzer, 1978). This means that we have a two place relation\(\sqcup\) (join) and relations \(\sqsubseteq\), \(\sqsubset\), and\(\bigcirc\) (part, proper part and overlap) that impose part-wholerelations (mereologies, see the entrymereology) on the sets of objects, events and times. We cannot list all theproperties that must hold for these structures to serve as admissibleinterpretations of natural language but we illustrate these propertiesby giving two examples.

• \(\forall x, y \exists z(x \sqcup y = z)\) (completeness)
• \(\forall x, y (x \bigcirc y \leftrightarrow \exists z (z\sqsubseteq x \wedge z \sqsubseteq y))\) (overlap)

Definitions 4 and 5 now allow for a formal descripion of thereferential difference betweenwine anda bottle ofwine.

30.

(a)

\(\textit{wine}\subseteq \mathfrak{O}\wedge \textit{CUM}(\textit{wine}) \)

(b)

\(\textit{a bottle of wine} \subseteq\mathfrak{O}\wedge\mathit{QUA}(\textit{a bottle of wine})\)

For verbal predicates Krifka assumes that they are event denoting andmoreover that thematic relations likeagent,theme,etc are represented as in (31-b). Thematic roles of verbs are crucialsince they determine which verbs give raise to thedrink wineversusdrink a bottle of wine distinction.^[5]

31.

(a)

Mary runs.

(b)

\(\textit{run}(e)\wedge\textit{Agent}(e, \textit{Mary})\)

It is now straightforward to fix the reference of the verbalpredicates in a way that exhibits their simlarity to the respectivenominal predicates.

32.

(a)

\(\textit{drink wine}\subseteq \mathfrak{E}\wedge \textit{CUM}(\textit{drink wine})\)

(b)

\(\textit{drink a botle of wine}\subseteq \mathfrak{E}\wedge \textit{QUA}(\textit{drink a bottle of wine})\)

Cumulativity of nominal predicates corresponds to atelicity in theverbal domain and a quantized nominal predicate corresponds to a telicverbal predicate.

There is still something missing. How can the impact of the referenceof the nominal predicates on the aspectual class be derived formally?We will present only the basic idea of Krifka’s construction here. Let\(w\) be the predicate corresponding towine and let \(e\) bethe event predicate representingdrink wine. The basic ideais that an object is changed by the influence of such an event in agradual manner. Since we know that \(w\) is cumulative thispredicate also applies to proper parts of \(w\), say \(w'\). Thengiven thatdrink wine can be applied to \(e\) it shouldalso be possible to apply it to a proper part of \(e\), say \(e'\).Quantized predicates show a different behaviour. Sincea bottle ofwine is quantized no proper part of it isa bottle ofwine and therefore no proper part of \(e\) can be described asdrink a bottle of wine. To account for this intuitiveexplanation in formal terms it is necessary to specify certainpreservation properties for thematic roles since these roles relatethe algebraic structure of events and the algebraic structure ofobjects. This means that notions likesummativity,uniqueness of objects etc. have to be defined for relationsbetween events and objects; i.e. thematic roles.

Here we will illustrate these concepts with only one example,summativity (SUM).

Summativity says that the sum-operation \(\sqcup\) on events andobjects is preserved under summative relations on events and objects.For instance if we have two distinct events ofdrinking a bottleof wine we get an event ofdrinking two bottles ofwine.

With this formal background it is now possible to state exactly when apredicate of events corresponding to a verb-phrase is cumulative,telic etc.. Again we will just state one result. Let \(\phi = \{ e\mid\exists x(\alpha(e) \wedge \delta(x) \wedge \theta(e, x))\}\) be sucha predicate where \(\alpha\) represents a verb—saydraw—\(\delta\) the nominalpredicate—pictures—and \(\theta\) a thematicrelation—saytheme. It then follows that one set ofconditions for \(\phi\) being cumulative is that \(\delta\) iscumulative and \(\theta\) is summative. An example is the verbphrasedraw pictures. Similar resultscharacterize,iterative,telic,atelic etc.readings.

6.2 Compositionality

A second central linguistic problem concerns the notion ofcompositionality. It has often been claimed that eventsemantics faces serious problems with compositional accounts ofquantification, negation and other logical connectives. Champollion(2015) developed one possibility to reconcile classicalcompositional semantics and event semantics. We will briefly sketchthe basic ideas of this approach here.

It has often been observed that the existential quantifier binding theevent variable always takes narrow scope with respect to otherquantifiers and operators in a given sentence. Therefore the correcttranslation of

33.

John kissed everygirl.

in Parsonian or Neo-Davidsonian event semantics is

34.

\(\forall x(girl(x)\rightarrow \exists e (kiss(e) \wedge Subject(e, John) \wedgeObject(e, x)))\)

and (35) is considered as a problematic reading.

35.

\(\exists e(kiss(e) \wedge Subject(e, John) \wedge \forall x(girl(x) \rightarrowObject(e, x)))\)

36.

(a)

Noboy laughed.

(b)

John didn’tlaugh.

In Champollion (2015) one way to achieve this goal is via typeshifting (see Hendriks 1993). We will now briefly explain the basicsof this strategy. Consider the sentence

37.

It israining.

In Neo-Davidsonian approaches the semantics of the predicaterain is represented as:

38.

\([[ rain]] =\lambda e.rain(e)\)

In Champollion (2015) a variable \(E\) that denotes sets of events isintroduced andrain is represented now as follows:

39.

\([[ rain ]] = \lambda E\exists e( rain(e) \wedge E(e))\)

We assume here that apart from the basic types \(e\) and \(t\) thereis a type \(v\) for events. \(E\) is a variable of type \(\langle v,t\rangle \) and the expression in (39) is of type \(\langle\langlev,t\rangle , t\rangle \).

Intuitively this means that a verb will be true of a set of eventswhen this set contains an event that satisfies the respective verbaldenotation. Thus one may think of (39) as a type shifted version of(38). This has consequences for the rest of the grammar. If verbs aresystematically type shifted according to (39) other grammaticalcategories have to be type shifted as well in order for functionalapplication to work.

Let us now see how (39) allows for compositional interpretations.Under (39) a sentence likeIt is raining is rendered as(\(\lambda e\ true\) is the set of all events; \(true\) could forinstance be \(x = x\)):

40.

\(\lambda E\existse (rain(e) \wedge E(e)) (\lambda e.true)\)

After two application of \(\lambda\)-conversion (40) reduces to

41.

\(\exists e(rain(e)\wedge true)\)

which is equivalent to

42.

\(\existse(rain(e))\)

Since it is assumed that verbs introduce event variables, existentiallowest closure is enforced by applying it at the level of the verb’slexical entry. Sentence (33) here repeated as (43)

43.

John kissed everygirl.

is now interpreted as follows (neglecting tense for simplicity). Weassume the following standard representations ofevery girl(44-b) andJohn (44-c). \(P\) is as usual a variable of type\(\langle e,t\rangle \) and \(j\) a constant of type \(e\).

44.

(a)

\([[\textit{kiss}]]=\lambda E\exists e(\textit{kiss}(e)\wedge E(e))\)

(b)

\([[\textit{every girl}]]=\lambda P\forall x(\textit{girl}(x)\rightarrow P(x))\)

(c)

\([[\textit{John}]] = \lambda P.P(j)\)

Here we will skip the derivation of the combination of NPs withthematic roles. In Champollion (2015)every girl as object ofkiss is derived from (44-b) as

45.

\(\lambda V\lambdaE\ \forall x (girl(x) \rightarrow V(\lambda e(E(e) \wedgeObject(e,x))))\)

where \(V\) is a variable of type \(\langle\langle v,t\rangle,t\rangle\). Expression (45) is therefore of type\(\langle\langle\langle v,t\rangle, t\rangle, \langle\langlev,t\rangle ,t\rangle\rangle\). Functional application of thisexpression with the verbkiss (of type \(\langle\langlev,t\rangle, t\rangle\)) as representated in (44-a) delivers:

46.

\(\lambda E \forallx (girl(x) \rightarrow \exists e (kiss(e) \wedge E(e) \wedgeObject(e,x)))\)

(46) is the interpretation of the VPkissed every girl, againof type \(\langle\langle v,t\rangle , t\rangle \).John asagent is translated in a similar way as the object NPeverygirl.

47.

\(\lambda V\lambdaE\ V(\lambda e(E(e) \wedge Subject(e, john)))\)

When formula (47) of type \(\langle\langle\langle v,t\rangle ,t\rangle, \langle\langle v,t\rangle, t\rangle\rangle\) is applied to therepresentation ofkissed every girl (representation (46)) theresult is:

48.

\(\lambda E \forallx (girl(x) \rightarrow \exists e (kiss(e) \wedge E(e) \wedgeSubject(e, john) \wedge Object(e, x)))\)

Finally computing the closure of this formula with \(\lambda e.true\)one derives (49)

49.

\(\forall x(girl(x) \rightarrow \exists e (kiss(e) \wedge Subject(e, john) \wedgeObject(e,x)))\)

This shows that a tree like (50) can be interpreted in a strictlycompositional way.

50.

[CP [closure] [IP[DP John ] [VP [V kissed ] [DP every girl ]]]]

Based on (40) and combining methods of the previous section with thequantificational approach of this section, Champollion develops abroad range of solutions for observations pertaining to scopeambiguity in sentences like (51),

51.

Every student reada book.

as well as to negation, conjunction and adverbial modification (seeChampollion 2015; and Coppock and Champollion 2022). These resultsclearly demonstrate that there is no conflict between standardcompositional semantics and event semantics.

This concludes our glimpse of events in linguistic semantics; Readersinterested in a more comprehensive treatment of these issues may findChampollion (2014, seeOther Internet Resources) and Champollion (2015) useful sources. For a more philosophicaldiscussion of various forms of compositionality the reader is advisedto consult Pagin and Westerståhl (2010a), Pagin andWesterståhl (2010b), Peters and Westerståhl (2006,especially Chapter 11) and the Encyclopedia’s entry oncompositionality.

We now come back to the imperfective paradox and turn to an eventcalculus that was developed in artificial intelligence.

7. Event Calculus

In the following section we will show that the imperfective paradox isan instance of the frame problem prominent in Artificial Intelligence(AI). To this end we will explain the event calculus, which is anextension of McCarthy’s situation calculus (McCarthy 1977)developed by Kowalski and Sergot (1986). Then we will indicate how theevent calculus leads to a formalization of natural language tense andaspect by analysing the imperfective paradox.

Consider narrative (52).

52.

Yesterday morningVincent loaded the gun. Then he smoked a cigarette. After smoking hepointed the gun at Fred and pulled the trigger.

Assuming that shooting at somebody with a loaded gun will lead to thedeath of that person, we will interpret the discourse in a way thatFred eventually gets killed. Arriving at this inference is, however,not a trivial task. In (33) the frame problem is exemplified in theform of the Yale Shooting Scenario (Hanks and McDermott 1986). Todemonstrate this, we will start with a very simple calculus—avariant of theSimple Event Calculus by Shanahan (1997) whichonly incorporates a very basic notion of instantaneous change. Laterwe will add axioms in order to deal with continuous change and thenreturn to the imperfective paradox. In short, we will argue that theparadox can be viewed as an instance of the frame problem.

7.1 The Yale Shooting Scenario

Suppose we have three kinds of actions/events—Load,Smoke andShoot—and three time dependentproperties, the fluentsAlive,Loaded andDead.^[6],[7] Besides actions and fluents we will also need instants of time in ourbasic ontology. The predicates listed in Table 4 are used to expressactions and their effects and to locate them in time.

The predicates are related to each other by a set of four simpleaxioms (53)–(56). In these axioms, all variables are assumed tobe universally quantified with maximal scope. We will come to thesemantics of the implication when we have introduced the completescenario.

53.

\(Initially(f)\rightarrow HoldsAt(f, 0)\)

54.

\(Initially(f)\wedge \neg Clipped(0, f, t) \rightarrow HoldsAt(f, t)\)

55.

\(Happens(a, t_1)\wedge Initiates(a, f, t_1) \wedge t_1 \lt t_2\ \wedge\) \(\negClipped(t_1, f, t_2) \rightarrow HoldsAt(f, t_2)\)

56.

\(Happens(a, t)\wedge t_1 \lt t \lt t_2 \wedge Terminates(a, f, t) \rightarrow\)\(Clipped(t_1, f, t_2)\)

The first three axioms state the conditions under which a fluent canhold at a time \(t\): either it holds right from the start or it isinitiated at a time \(t_1\) before \(t\) without a terminating actionoccurring in between the two. The fourth axiom defines the predicateClipped\((t_1, f, t_2)\) saying that a fluent \(f\) isclipped between times \(t_1\) and \(t_2\) if it is terminated by someaction \(a\) happening between \(t_1\) and \(t_2\). Simplifying awhole lot, the axioms (53)–(56) formalize the notion ofinstantaneous change, such as two balls colliding or somebody dying.Moreover, they embody a notion of inertia: fluents continue to holdunless terminated.

Next, we have to translate the discourse (52) into the Simple EventCalculus. The first set of formulas (57)–(59) states what thementioned actions do. These formulas provide a crude sketch of thelexical meaning ofload,smoke andshoot.The effect of aLoad action is to make the fluentLoaded hold, aShoot action makesDead hold(andAlive not hold) withLoaded being aprecondition. Finally,Smoke is assumed to have no effects(thus, there are no rules involvingSmoke).

57.

\(Initiates(Load,Loaded, t)\)

58.

\(HoldsAt(Loaded,t) \rightarrow Initiates(Shoot, Dead, t)\)

59.

\(HoldsAt(Loaded,t) \rightarrow Terminates(Shoot, Alive, t)\)

(52) comprises aLoad action followed by aSmokeaction followed by aShoot action. Using four arbitrarilychosen time points \(T_1\)–\(T_4\) the discourse can berepresented as follows:

60.

\(Initially(Alive)\)

61.

\(Happens(Load,T_1)\)

62.

\(Happens(Smoke,T_2)\)

63.

\(Happens(Shoot,T_3)\)

64.

\(T_1 \lt T_2 \ltT_3 \lt T_4\)

From this little theory we want to deriveHoldsAt(Dead, \(T_4)\). Unfortunately, this sequentis not valid in the classical sense of being true in all models whichsatisfy the theory. Think for example of a situation in which the gunobscurely becomes unloaded while Vincent is smoking. In such a model,the precondition of the shooting action is clearly not met and thusthe action will lack any effects. Note that nothing rules out such amodel since it is entirely consistent with our theory. We thus have tofurther constrain the models under consideration. Crucially, we haveto find a way to deal with the non-effects of actions; this is thefamousframe problem.

How to proceed? From the fact that no terminating action wasmentioned, we want to conclude that no terminating event occurred. Todo so, we have to strengthen the assumptions of the theory in a waythat only those events are assumed to occur which have been explicitlystated in the discourse. The discourse model should be minimal,linking discourse understanding intimately toclosed worldreasoning. It is important to note that this strategy forcesreasoning to be non-monotonic: adding further premises to a theory canmake inferences invalid that were valid before (see the entry onnon-monotonic logic).

7.2 The Completion of a Program

There are different techniques for formalizing this line of reasoning;one is circumscription (e.g., Shanahan 1997). Here, we will use thecompletion of a logic program technique, adopting theEvent Calculus of van Lambalgen and Hamm (2005). Taking acloser look at the formulas of the theory \(((53) \wedge \ldots \wedge(64))\), an important feature to notice is that formulas come in twovariants: they are eitherfacts consisting of a simplepredicate expression or they expressrules with a conjunctionof potentially negated formulas to the left of the implication signand a single positive atomic expression to its right (in logicprogramming the former is called thebody and the latter iscalled thehead of a clause). We will now illustrate how thecompletion of a simple logic program is computed. Consider thedescription of a situation where the gun gets loaded at time 1 and ashooting event happens at time 10. This situation is stated in thefollowing program:

65.

\(Happens(Load,1)\)

66.

\(Happens(Shoot,10)\)

The uncompleted program does not yet rule out intervening events. Itis, for example, consistent with anUnload event occurring attime instant 9. The completion of the program should tell us that (65)and (66) were the only events. The completion is computed according tothe following procedure.^[8] We start with the facts in (65) and (66). Both of these areHappens formulae. The completion of the program intuitivelycorresponds to an assertion that, given this program,Happens\((e, t)\) can only meanLoad occurring at 1orShoot occurring at 10. We therefore first substitutevariables for the constants and write the following disjunction:

67.

\((e = Load \wedget = 1) \vee(e = Shoot \wedge t = 10)\)

Then, we universally quantify over the variables \(e\) and \(t\) andstrengthen the implication to a bi-implication:

68.

\(\forall e\forall t(Happens(e, t) \leftrightarrow (e = Load \wedge t = 1)\ \vee\)\((e = Shoot \wedge t = 10))\)

From (68) it follows that there were no intervening events.Strengthening the implications to bi-implications makes it impossiblethat a head can be true without the enabling conditions being met.^[9] The uniquely determined model of (68) is the minimal model of thelogic program consisting of (65) and (66).

We can now come back to the Yale Shooting Problem in discourse (52).From the completion of the logic program ((53))\(\wedge \ldots\wedge\)((64)) it follows (non-monotonically) thatHoldsAt(Dead, \(T_4)\). Enriching the program withfurther information and computing the new completion, however, couldclearly lead to cancellation of this inference.

7.3 Introducing Tense Information

If we want to use these ideas to model natural language discourse, weneed to incorporate tense. In van Lambalgen and Hamm (2005) this isdone by adopting the classic tripartition intoreferencetime,event time andspeech time due toReichenbach (seesection 3).

Recall that above, when we translated discourse (52) intoShanahan’s Event Calculus, we arbitrarily chose instants of time\(T_1 ,\ldots ,T_4\) to locate actions in time. This is not how it isdone in natural language discourse. The first sentence (Yesterdaymorning Vincent loaded the gun) states that within some timeinterval \((=\) reference time) before now \((=\) speech time) therewas a time \(t'\) at which a loading event happened \((=\) eventtime). The second sentence (Then he smoked a cigarette) islinked to this event by the connectivethen, stating that atsome later time \(t''\) a smoking event happened with \(t''\) alsobeing temporally located beforenow. Analogously for thethird sentence: there is an event time \(t'''\) at whichShoot happens and \(t'' \lt t''' \lt\)now. Notethat when locating events in time it is always done by existentialstatements of the formthere is a time. So far, however, wehave only been dealing with universally quantified variables. Clearly,a formula like \(\forall t\).Happens(Load, \(t)\wedge t \lt\)now cannot be used to represent tense since itwould state thatLoad happens at all times in the past. Wehave to find a way to introduce existentially quantifiedinformation.

Intuitively, it suffices to introduce new entities into the domain ofdiscourse. This approach lies at the heart of dynamic semantictheories such as Discourse Representation Theory (Kamp and Reyle 1993,and see also the entry onDiscourse Representation Theory) or File Change Semantics (Heim 1982). We will need an updateprocedure that introduces new actions/events into the discourse modelbut is compatible with the non-monotonic semantics introduced so far.Following van Lambalgen and Hamm (2005) we will useintegrityconstraints—a device from database theory (for a morecomplete and formal treatment the reader is referred to Kowalski 1995and van Lambalgen and Hamm 2005: ch. 8)—to implement the notionof a minimal update of a discourse model. Consider discourse (69).

69.

The gun is loaded.Vincent is ready to shoot.

In interpreting the first sentence, we want to update the situationmodel in a way that makes the sentence true. The tense informationwill be interpreted as a goal to minimally update the situation modelwith a fluentLoaded that holds now. In our frameworksemantic interpretation is thus closely linked to planning, in thatfinding an interpretation for a sentences requires coming up with asequence of actions that makes the goal succeed.

70.

Make the query\(?HoldsAt(Loaded, now)\) succeed.

To resolve this integrity constraint we will use the axioms of theSimple Event Calculus plus the world knowledge about the consequencesof a load action stated in (71).

71.

\(Initiates(Load,Loaded, t)\)

In logic programming, the sort of reasoning required to resolve (70)is carried out by a derivation procedure calledresolution.We will use resolution here in a non-standard way, i.e. logicprogramming combined with integrity constraints (for details see vanLambalgen and Hamm 2005). It starts with the formula that has to bemade true in the discourse model. Resolution proceeds by identifyingrules which have the query as their consequent and substituting theconsequent with the antecedent conditions of the rule, making theantecedent formulas new queries themselves. The resolution stops whenthe query cannot be further resolved, that is, when a plan has beencomputed whose preconditions are all fulfilled given an appropriateupdate of the discourse model. To get an impression of how this workswe will illustrate the resolution of (70). First, we have to computethe completion of the program and whenever possible substitute thevariables with constants, in our caseLoaded andnow. In logic programming this substitution is doneautomatically via unification. Here is the completion of theHoldsAt predicate which forms the head of twoaxioms—(54) and (55).

72.

\(HoldsAt(Loaded,now)\,\leftrightarrow\) \((Initially(Loaded) \wedge \neg Clipped(0,Loaded, now))\,\vee\) \((Happens(a, s) \wedge Initiates(a, Loaded, s)\wedge s \lt now \wedge\) \(\neg Clipped(s, Loaded, now))\)

Since the theory doesn’t contain the statementInitially(Loaded), closed world reasoning yieldsthat at time 0 the gun is not loaded\((\neg\)Initially(Loaded)). No matter how we updatethe discourse representation the first disjunct can never succeed. Wethus have to move on to the second disjunct. In this case, thedatabase is searched for an action \(a\) and a time \(s\) such thatInitiates\((a, f, s)\),Happens\((a, s)\) and\(\neg\)Clipped\((s\),Loaded, \(t)\). On the solebasis of the information provided in the discourse the subquery?Happens\((a, s)\) will fail, because in discourse (50) thereis no information about a load action. However, since integrityconstraints are intended to be made true, the database will be updatedwith a clauseHappens(Load, \(s) \wedge s \lt\)now which makes the second disjunct true and the querysucceed.

7.4 The Imperfective Paradox reconsidered

In the following, we will analyze the imperfective paradox as aninstance of the frame problem (cf. Stenning and van Lambalgen 2005;van Lambalgen and Hamm 2005; Stenning and van Lambalgen 2008; Baggioand van Lambalgen 2007; Baggio et al. 2008). Both activities andaccomplishments involve continuous change and we therefore have to addadditional predicates and axioms to properly deal with graduallychanging objects which are under the influence of an external force.Table 5 introduces two new predicates; axioms A1–A5 provide ageneral theory of instantaneous and continuous change (from vanLambalgen and Hamm 2005: 40). As can be easily seen, the axiom systemextends that of Shanahan (1997).

Axioms 4 and 5 define continuous change. Axiom 4 defines theTrajectory predicate. To see what it says, let’sconsider a situation ofrunning a mile where \(f_1\) isinstantiated byrunning and \(f_2\) bydistance\((x)\). Shouldrunning be true during thewhole interval from \(t\) until \(t'\) thendistance\((a +1)\) will be true at \(t'\). The value of \(x\), that is, the actualdistance actually run at each time instant will be determined by thelaw of the process under consideration (here, running speed). Axiom 5defines the predicateClipped\((t, f, t')\) which is true if\(f\) is terminated or released by an event \(e\) which happens in thetime interval between \(t\) and \(t'\). ThusClipped coversboth instantaneous and continuous change. The axioms provide a generaltheory of what can change and what stays constant.

For concrete situations, we also need the specific temporal and causalrelationships. This kind of information is specified in so calledscenarios representing lexical meaning. The lexical meaningof the accomplishmentrun a mile corresponds to scenario(73). Like the axioms, the scenario takes the form of a logic program.All variables are universally quantified.

73.

(a)

\(Initially(distance(a))\)

(b)

\(Initiates(start, run, t)\)

(c)

\(Releases(start, distance(x))\)

(d)

\(Initiates(finish, distance(a + 1), t)\)

(e)

\(Terminates(finish, run, t)\)

(f)

\(HoldsAt(run,t) \wedge HoldsAt(distance(a + 1), t) \rightarrow\) \(Happens(finish,t)\)

(g)

\(HoldsAt(distance(x), t) \rightarrow \) \(Trajectory(run, t,distance(x + g(d)), d)\)

Scenarios formalize the event nucleus of Moens and Steedman (1988).Every accomplishment takes the same form of scenario, the onlydifferences being that the individual scenarios involve differentpreparatory processes (run,build, etc.),incremental themes (distance\((x)\),house\((x)\),etc.) and resultant states. Furthermore, it is obvious that thepreparatory processrun, an activity, is a proper part ofscenario (73). The simpler activity scenario can be easily arrived atif we remove clauses (d)–(f) from (73). We are now in theposition to solve the imperfective paradox avoiding the problemsdiscussed insection 6. Both a past progressive activity sentence as in (74-a) and a pastprogressive accomplishment sentence (74-b) will trigger a discourseupdate as stated in integrity constraint (74-c).

74.

(a)

John was running.

(b)

John was running a mile.

(c)

\(?HoldsAt(run,t) \wedge t \lt now\) succeeds.

The discourse update of the completed program (73) yields that at somepoint after \(t\) John will achieve the culmination and will have runone mile (see van Lambalgen and Hamm 2005: 61ff. for a proof).Obviously, the same integrity constraint in combination with theactivity in (74-a) only licenses the inferences that there was somepast running activity. In the case of an accomplishment the course ofevents dramatically changes if we add information to therepresentation as in (75-b). Now, both (75-a) and (75-b) only allowthe inference that there was a running event but, arguably, Johndidn’t reach his goal in (75-b). Without going into furtherdetails it should be clear how this non-monotonic inference works. Thederivation works analogously to the simpler instances of the frameproblem discussed above.

75.

(a)

John was running, when he was hit by a truck.

(b)

John wasrunning a mile, when he was hit by a truck.

The solution to the imperfective paradox just outlined makes referenceto the intentions of the agent involved in the event; therefore thenotion of a goal or intention is built into the system right from thestart. Note, however, it does not involve possible worlds, orprimitive notions like inertia worlds; instead it is based uponminimal models and non-monotonic reasoning. This yields additionalbenefits. Firstly, the Event Calculus will compute a minimal model incases where an integrity constraint can be satisfied. Moreover, thenumber of construction steps required for this yields a precisecomplexity measure which (for example) allows us to derive predictionsfor cognitive processing. Secondly, the non-monotonic nature of theEvent Calculus can be used to model the incremental construction of atemporal model with inferences which hold locally at a discoursesegment \(s_n\) but which can be undone at some later discourse unit\(s_{n+1}\). This is a necessary prerequisite if we think ofinterpreting sentences like (75-b) from left to right assumingincremental interpretation (see e.g., Baggio and van Lambalgen 2007and Bott 2010 for implementations of the Event Calculus as aprocessing model). In the next section we will review psychologicaland psycholinguistic work on the interpretation of aspect which willprovide empirical motivation for the outlined analysis.

8. Cognitive Aspects

Due to limitations of space, we will not discuss psychological andpsycholinguistic studies of tense but will focus solely on processingstudies of aspect. Moreover, within this topic we limit ourselves to aselection of studies of the adult system. The interested reader isreferred to Dickey (2001) and the references therein forpsycholinguistic work on tense as well as to the entry ontemporal consciousness and the contributions in Grondin (2008) for psychology of time ingeneral.

Psychologists have extensively studied event perception and eventmemory as well as their neural basis (e.g., Zacks and Tversky2001; Zacks, Tversky, and Iyer 2001; Zacks et al. 2006; see Zacks2020 for a review). The underlying question behind this line ofresearch is whether events play a role in how we cognitively structureand remember changing states of affairs and how they are represented.Zacks, Tversky, and Iyer (2001) use an analogy from the domain ofobjects to the domain of events to define an event as a “segmentin time at a given location that is conceived by an observer to have abeginning and an end” (p.30). They claim that “the abilityto identify the parts of events and their relationships constitutes adistinct perceptual process” (p.30) which they calleventstructure perception. Just as an object is an ontologicalprimitive in the spatial domain, so an event is an ontologicalprimitive in the spatio-temporal domain.^[10] Objects are recognized by shape, color etc. and have boundaries inspace. Analogously, events have boundaries in time, but are alsobounded in space. An event of buttering toast, for instance, happensat a particular time, but also in a particular location in space andis therefore spatially bounded. Continuing the analogy, both objectsand events can be identified and categorized using hierarchicalrelations.

In Zacks, Tversky, and Iyer’s experiments, participantssegmented an ongoing activity (likewashing dishes) whilewatching it on film by pressing a key to mark “natural andmeaningful” unit boundaries. The grain at which participantssegmented the activity was manipulated between subjects: one group wasasked to mark the largest meaningful units (coarse grain size), theother group the smallest units (fine grain size) which still could beconsidered to be complete events. The placement of perceived eventboundaries provides information about the psychological status ofevents and their partonomic hierarchy. If the stream of action isperceived as consisting of discrete events, participants should placeevent boundaries consistently and this is what Zacks, Tversky, andIyer (2001) found. Further, if participants make use of partonomichierarchies, coarse event boundaries should be aligned with fineboundaries, since the end of each superordinate event is also the endof its last subevent. Again, this hypothesis was corroborated by astrong hierarchical bias effect. Events thus seem to bepsychologically real and to be hierarchically structured. Theseeffects are not limited to event perception but also affect eventmemory. Furthermore, studies of event perception and event memory showthat comprehenders focus on the goal of actions rather than on theirsuperficial surface structures (see Zacks, 2020, and the referencestherein).

While studies on event perception show that complex events areclearly structured into simpler ones, there is also clear evidenceforevent variability with great interindividualdifferences in event representations (see, e.g., McRae et al.2019). Recent advances in computational modeling show thatprediction-based neural network models can learn these rich and highlyvariable event structures and produce behaviors that reflect humanperformance (Elman and McRae 2019). Prediction-based neuralnetworks have also been successfully applied to event prediction intext comprehension modeling effects in ERP research (Rabovsky etal. 2018; Venhuizen et al. 2019). So far, however, to our knowledgeneither tense nor grammatical aspect have been incorporated intothese models.

8.1 Lexical Aspect

During the last decade psycholinguists have started to investigate thecognitive reality of lexical aspect and how it is processed. Theexisting studies can be sub-classified into studies concerningAktionsart simpliciter and those concerned with shifts fromone aspectual class to an other, i.e.,aspectual coercion. Inthe following, we will provide a brief overview of both areas ofresearch.

McKoon and Macfarland (2002) were among the first to study processingconsequences of decompositional analyses along the lines of Dowty(1979). They provided evidence from reading times and lexical decisiontimes that accomplishments \((\alpha\) CAUSE \(x\) BECOME IN-STATE)are inherently more complex than achievements \((x\) BECOME IN-STATE).Similarly, Gennari and Poeppel (2003) compared eventive predicates(which included accomplishments, achievements and activities) tostatives and found that the former were more complex to process thanthe latter. Brennan and Pylkkänen (2010) extended this line ofresearch to psychological verbs and compared accomplishments (e.g.,scare) with statives (e.g.,cherish) using readingtime methods and magnetoencephalography (MEG). They also included acomparison of the simple psychological statives with modifiedsentences that required coercion (e.g.,within half an hour, thechild cherished the precious kitten). Reading times and MEG dataindicated that accomplishments were more complex to comprehend thanstatives and, moreover, that the enhanced semantic complexity led todifferent MEG components than aspectual coercion. Finally, Coll-Floritand Gennari (2011) compared durative states and punctual eventpredicates (mostly achievements) and observed longer reading times ofstatives than of event predicates. They attributed thiseffect—which runs counter to what would be expected under adecomposition analysis—to the fact that durative situationsoccur in semantically more diverse contexts and elicit more diverseassociations than event predicates which may modulate the requiredprocessing effort. Taken together, the existing studies provideevidence for complexity differences between the aspectual classes,lending support to decompositional analyses. However, not all issuesare entirely solved yet and further research is required.

The second line of research concerns aspectual coercion. Here, themain research question has been whether aspectual coercion is a costlyoperation. Existing research has almost exclusively focused on onecoercion type, i.e., coercion of point action verbs into an iterativeinterpretation (but see Brennan and Pylkkänen 2010 and Bott 2010for other types of aspectual coercion). Again, the findings are mixed.The first studies provided evidence for coercion costs employingsecondary tasks such ascross-modal lexical decision orstop making sense judgments (Piñango, Zurif, andJackendoff 1999; Todorova et al. 2000). Pickering et al. (2006) usedthe same materials as in the experiments mentioned above, but tested acoerced meaning during ordinary reading without an additional task. Intwo self-paced reading and two eyetracking experiments, they foundaspectual coercion to be no more difficult than their aspectualcontrol conditions. This lack of effect let them propose the aspectualunderspecification hypothesis, stating that the aspectualrepresentation stays underspecified during normal reading. Brennan andPylkkänen (2008) challenged this view and reported a coercioneffect of coercion sentences like (76-a) as compared to aspectualcontrols (76-b) both in self-paced reading and in MEG; on the basis ofa rating study they had carefully selected clear instances of pointaction verbs. Their MEG study revealed activation in the anteriormidline field, a MEG component that has been observed for othernon-aspectual cases of coercion, too.

76.

(a)

Throughout the day, the studentsneezed inthe back of the classroom.

(b)

After twentyminutes, the studentsneezed in the back of the classroom.

Complicating matters, Bott (2008, 2010) applied the same normingprocedures, but did not find evidence of coercion cost in iterativepoint action verbs in German. With other types of aspectual coercion,however, there were clear indications of processing difficultyindicating that the underlying processes differ between coerciontypes. Furthermore, the study provided evidence that at least in somecases (achievement ⇝ accomplishment) coercion operations are nottriggered by an aspectual mismatch, but can proceed smoothly byenriching the aspectual representation with additional eventualities.This was shown in an event-related potentials (ERP) study in which adouble dissociation of ERP components was elicited by sentences withaspectual coercion as compared to sentences that contained anaspectual mismatch.

Another ERP study by Paczynski et al. (2014) investigatedthe processing of iterative events due to aspectual coercion.The critical condition involved punctual event predicatesmodified by durative adverbials such asfor severalminutes, the cat pounced on the rubber mouse. This condition ledto a sustained negativity relative to conditions with both punctual(after several minutes) and frequentive adverbials(several times) similar to the ones obeserved in previous ERPstudies on aspectual coercion and the imperfective paradox (Baggio etal. 2008, Bott 2010). One difference between Paczynski et al.’s(2014) study and other studies on iterative coercion could be slightbut crucial differences in the semantic properties of thepunctual events: while Paczynski et al. (2014) employed telicpredicates, other studies used atelic point-action verbs.

8.2 Grammatical Aspect

Grammatical aspect has recently received increased interest inpsycholinguistics (for a comprehensive review see Madden and Ferretti2009). One line of studies has investigated (e.g., Ferretti et al.2007) the accessibility of event participants in English progressiveand simple sentences. They provide evidence that, in line with thelinguistic description provided above, the progressive presents anevent from the inside, making participants, instruments and placesfully accessible, whereas the simple forms present events as completeunits and the event participants are less accessible. Using pictureselection/verification, Madden and Zwaan (2003) found thatparticipants were faster and more likely to choose a picture showing acomplete event, rather than a picture depicting an ongoing event,after they had read a sentence with an accomplishment verb in thesimple past. This indicates that English speakers encodeaccomplishments in the simple past as complete events. This findingwas supported by a study by Anderson et al. (2008). They comparedaccomplishments describing a path such asTom jogged/was joggingto the woods and then stretched when he got there. Participantslistened to these sentences while using a computer mouse to drag anddrop a human character in a visual scene. When hearing a sentence inthe past progressive, many drops took place at the beginning and thecenter of the path, whereas in the simple past most drops were at theend of the path. Interestingly, the differences were by no meanscategorical. Even in the simple past condition, the character was insome trials positioned well before the end of the path. This indicatesthat accomplishments in the simple past are consistent with incompleteevents.

Another study relevant for the discussion in the previous sections isan ERP study on the imperfective paradox by Baggio et al. (2008). Theyinvestigated the processing of Dutch imperfective sentences such ashet meisje was een brief aan het schrijven (the girl waswriting a letter) which were either followed by awhen-clause that made the culmination unlikely (when herfriend spilled coffee on the paper) or by a sentence which wascompatible with the attainment of the goal (when her friend spilledcoffee on the tablecloth). The first kind of sentences elicited largersustained anterior negativities compared to sentences that werecompatible with the culmination. Moreover, the amplitude of thenegativity was correlated with the frequency with which participantsresponded that the culmination was not reached. These findingsindicate that a progressive sentence triggers a default inference to acomplete event which can be canceled again, if the context sorequires.

Grammatical aspect is subject to clear crosslinguistic differences.This raises the question of whether the grammatical system has aninfluence on how we process language. In von Stutterheim et al. (2009)the authors reported findings of a production study comparing eventdescriptions of English, German and Dutch speakers that were elicitedwhile they were watching and describing a silent video clip. Theirstudy revealed clear differences between productions from the threelanguages. English speakers used the progressive to start eventdescriptions well before the endpoint was visible (e.g.,A car isgoing down a lane … to a farmhouse). Germans showed adifferent behavior, relating their descriptions to the endpoint of amotion event. It thus seems as if production is constrained by thelanguage in which it is realized. Recently, von Stutterheim et al.(2012) extended this line of research to a sample of seven languagesand showed that the aspectual properties of a language influence howspeakers conceptualize events. It’s not only that speakers ofdifferent languages talked differently about motion events (e.g.,mention of endpoints), their language also had a clear influence ontheir viewing behavior while watching the movies and influenced theirmemory capacity for those parts of the scene corresponding toendpoints.

As for comprehension, Bott and Hamm (2014) investigated how theaspectual system of a language influences processing difficulty. Theycompared coercion of German and English accomplishments which weremodified byfor \(x\) time adverbials. (77) is a sampleitem.

77.

(a)

Der Architekt errichtete das Monument zwei Jahrelang, aber dann wurde ihm der Kredit gekündigt.

(b)

The architectbuilt the monument for two years, but then the bank canceled hiscredit.

In the German experiments, condition (77-a) was read as fast as anon-coercing control condition with anin x time adverbial.This was different in English where the authors found coercion tocause a substantial slowdown of reading speed. They interpret thiscrosslinguistic difference as follows: languages which have thegrammatical means to express an aspectual difference via alternativeforms—the progressive vs. simple forms in English—enforceimmediate aspectual commitment, whereas languages that lack thisgrammatical feature have to leave it underspecified. In other words,German readers will leave it to the context whether an accomplishmentexpresses a complete or incomplete event, whereas English readersimmediately strengthen an accomplishment in the simple form into acomplete event interpretation. They take this strengthening to be apragmatic process that is due to competition between alternativegrammatical forms.

The time course of incremental aspectual interpretation has alsobeen crosslinguistically studied in a visual-world eyetracking studyby Minor et al. (2023) comparing English, Russian and Spanishperfective and imperfective sentences. Participants heard thesesentences while inspecting a display showing one picture withan ongoing accomplishment event and another one showing theaccomplishment’s consequent state. In Russian and Spanish,comprehenders immediately started to fixate on the ongoingevent for imperfective verbs and on the completed event afterperfective verbs providing further evidence for incremental aspectualinterpretation in aspect languages. For English, however, they onlyfound incremental effects for progressive sentences. Sentences withsimple past forms, however, turned out to be compatible withboth ongoing and complete event interpretations. This findingcontrasts with the results reported in Bott and Hamm (2014) andthere seems to be more interpretational leeway for Englishaccomplishments in the simple past than previously assumed.

In an eyetracking during reading study, Bott and Gattnar (2015)followed up on the observed cross-linguistic variation in theprocessing of grammatical aspect comparing an aspect language,Russian, with the non-aspect language German. They investigatedwhether the differences in the aspectual systems of the two languagesaffected the time course of mismatch detection in the case of lexicalaspectual mismatch. All test sentences contained clear instances of(in Russian always perfective) transitive achievement verbs such aswin,find,reach,notice, etc.which were modified by a semantically mismatchingfor-adverbial (e.g.,for three hours) or asemantically fittingago-adverbial (e.g.,three hoursago) in aspectual control conditions. Crucially, both Russian andGerman have relatively free word order making it possible to test foreffects of mismatching vs. matchingadverbials in the word ordersubject verb object adverbial but also in the orderadverbial verb subject object. The results show that Russianreaders immediately detect the aspectual mismatch irrespective ofwhether they have seen the subject or the object argument yet. This isdifferent in German where aspectual mismatch detection only startedafter the verb plus all its obligary arguments had been encountered.This result was modeled by Bott and Sternefeld (2017) in anincremental event semantics drawing on insights from mereologicalsemantics as proposed by Krifka (1989, 1992) and building on thecompositional event semantics of Champollion (2015); see alsosection 6.1 (and the entrymereology). The incremental semantic derivations show that in a non-aspectlanguage like German, lexical aspect really is a property of wholesentences and strongly depends on the compositional interpretation ofthe verb, its arguments, and their thematic roles. In an aspectlanguage like Russian, on the other hand, the grammatical aspectimposes itself strong constraints on lexical aspectual interpretation.These psycholinguistic results thus nicely fit semantic proposals forgrammatical aspect that have been proposed in the framework ofmereological semantics (see, e.g., Filip 2008, a.o.). The results ofBott and Gattnar’s study may, however, be restricted toachievement predicates and perfective aspect since an ERP study byKlimek-Jankowska and Błaszczak (2020) did not reveal anyeffects on Polish accomplishment verbs marked for aspect. Forperfective verbs, mismatch effects were only evident on the followingobject marking the incremental theme while imperfectiveaccomplishments were compatible withbothfor- andin-adverbials.Employing self-paced reading and eyetracking during reading,Klimek-Jankowska et al. (2018) provided further evidence forunderspecification of imperfective aspect marking in Polish. Lastbut not least, Lukassek et al. (2017) investigated adverbialmodification of ambiguous German motion verb phrases such asüber die Nordsee segeln (sail over the NorthSea) with Germanin- andfor-adverbials. Both types of modification turned out to becomparable in processingload suggesting underspecification of motion verbs withrespect to telicity. Additional evidence, however, forthe highly incremental interpretation of aspectual operators inRussian and their relevance for language comprehension comes from acomparison of aspect marking by means of aspect markingvia verbal suffixes vs. prefixes (Minor et al. 2022). Thecomparison involved a visual-world eyetracking study employing thesame methods as in Minor et al. (2023). The study revealed asignificant difference in the onset of looks to the target withearlier looks to the target for aspect marking with a prefix relativeto marking with a suffix. Thus, comprehenders seem in fact tointerpret aspectual operators right away as soon as they areencountered.

To summarize, the existing studies largely lend empirical support tothe aspectual distinctions made in the semantic and philosophicliterature, even though the experimental findings provide us with acomplex picture. While some parts of aspectual interpretationproceed incrementally and automatically, other parts seem to call forunderspecification. Moreover, the grammatical system of alanguage influences the way language is processed and may eveninfluence the way we experience the world.

9. Tense and Aspect meet Discourse Structure

We introduced and discussed several important semantic, philosophicaland technical concepts and theories of temporality and at leastindicated how these concepts and theories are related to cognition.However, we did this exclusively from a sentence internal perspective.Tense and aspect are important means for organizing discourse as well(see Kamp, 1991). To conclude our overview, we present a briefintroduction to work addressing the intricate relations anddependencies between tense and aspect and the larger discoursestructure. Let us start with French examples due to Kamp andRohrer (see van Lambalgen and Hamm 2005, ch. 9) and indicate the roletense and aspect play in discourse organization. Consider sentence(78) in which thepassé simple (PS) occurs fourtimes.

78.

Pierre seleva, monta dans sa chambre, ferma la porte et alluma la radio.
Pierre got up, went up to his room, closed the door, and switched onthe radio.

First the PS in (78) provides temporal information; all events arelocated in the past. But the PS conveys aspectual information too. Itsays that the internal constitution of the events is not important andthis means that PS expresses perfectivity. PS imposes a view of theevents “from the outside”. This is then taken to explainwhy multiple uses of the PS imply a succession of the events describedas witnessed in example (78). This means that Pierre getting upprecedes his going up to his room and this event precedes closing thedoor which finally precedes turning the radio on. Thus, the PSstructures the above little discourse in a particular way. Earlydiscourse representation theory explains this effect by assuming thatthe PS introduces a new reference point after a previously introducedone.

The discourse function of the French imparfait is different. Example(79-a) shows that, like the past in English, the imparfait^[11] is not felicitous when uttered out of the blue.

79.

(a)

*Il faisait chaud.
It was hot.

(b)

Il faisaitchaud. Jean ôta sa veste.
It was hot. Jean took off his sweater.

Kamp explains these facts in the following way. The imparfait does notintroduce its own reference time and in (79-a) there is no previousreference point given. Therefore (79-a) is out. In (79-b) the sentencein the passé simpleJean ôta sa veste introducesa reference time that can be used to anchorIf faisait chaud.The imperfective aspect of the imparfait is then explained by the factthat the PS event happens while the sentence in the imparfait holds.Thus passé simple and imparfait not only provide temporalinformation but they also serve as means to structure discourse indifferent ways.

Dynamic semantics views tense as anaphoric. It relates ananaphorically given reference time \(t\) to the utterance time \(n\)and lexical and grammatical aspect determine the relation between\(t\) and the event time \(e\) (see, e.g. Kamp and Reyle 1993). ForEnglish, an event sentence in the past introduces three conditions: 1)that the event time \(e\) is included in the reference time \(t\), 2)that \(t\) follows an anaphorically given reference time \(t'\)resolved to the reference time of the previous sentence and 3) that\(t\) is located before the speech time \(n\). The second conditionguarantees forward movement of the narrative. Thus, a sequence ofevent sentences in the past translates into a sequence of completedevents. For stative sentences, the semantics is different. Here thereference time is resolved to the reference time of the precedingsentence, and furthermore the state includes this reference time,which still lies in the past of \(n\). The following examples (fromAsher and Lascarides 2003, p. 62) illustrate this point. Sentence(80-a) is most naturally interpreted as narrative progression similarto (78), but the state described in the second sentence of (80-b) ismost naturally understood as the narrative background for the event ofMax entering the room.

80.

(a)

Max entered the room. The room became dark.

(b)

Max entered the room. The room was dark.

For (80-a) and (80-b), the interpretations proposed by Kamp and Reyleare well in accordance with our intuitions. However, it has repeatedlybeen noted, for instance, by Asher and Lascarides (Lascarides andAsher 1993; Asher and Lascarides 2003) that the analysis often failsto make the right predictions. The contrast in (81) from Asherand Lascarides (2003) involves sentences with identical forms andaspectual properties. However, their temporal interpretations arerather different. In (81-a) the pushing probably preceded the falling,but in (81-b) the temporal order is different, here falling precedeshelping him up.

81.

(a)

Max fell. John pushed him.

(b)

Max fell. John helped him up.

This difference can easily be explained, once we take the coherencerelations between the discourse units into account. In (81-a) the twosentences stand in an EXPLANATION relation to each other, whereas in(81-b) we are dealing with a NARRATION or RESULT relation. Since causescannot follow their effects, the temporal ordering follows from thesediscourse relations. More generally, many discourse relationsunderlying discourse cohesion impose temporal constraints on theinterpretation of discourse. Asher and Lascarides (2003) amend thesemantics of DRT and extend DRT toSegmented DiscourseRepresentation Theory (SDRT) with individual sentencesrepresented as single discourse representation structures(micro-DRSes) and a macro dicourse representation structure providinghierarchical discourse structures organized by means of discourserelations or rhethorical relations. In SDRT, discourse relations areinferred employing non-monotonic logic. Much of temporalinterpretation follows from the semantic effects of these discourserelations. To give a brief impression of the temporal consequences ofdiscourse relations, (82) shows the temporal consequences ofEXPLANATION (from Asher and Lascarides 1993, p. 160).

82.

(a)

\(\phi_{Explanation(\alpha, \beta)} \Rightarrow \neg (e_{\alpha} \prece_{\beta})\)

(b)

\( \phi_{Explanation(\alpha, \beta)}\Rightarrow (event(e_{\beta}) \Rightarrow e_{\beta} \prece_{\alpha})\)

The temporal consequences of EXPLANATION depend on whetherthe second sentence is eventive or not. For an eventivesentence such as in (81-a) the combination of (82-a/b) make surethat this event (e.g., pushing) precedes the eventuality introduced bythe first sentence (e.g., falling). In the case of a stativecause (e.g.,Max fell. The road was icy.), theinterpretation is slighly different. Here, it is just guaranteed thatthe stative cause does not follow its effect. Let us turn to thespatiotemporal consequences of NARRATION (ibid., p. 163). Here is asomewhat simplified characterisation ignoring for the moment that theprestate of the second eventuality is commonly linked to theconsequent state of the first one by adverbials (e.g.five minuteslater ornear the building).

83.

\(\phi_{Narration(\alpha, \beta)} \Rightarrowoverlap(prestate(e_{\beta}),consequent\state(e_{\alpha}))\)

The spatiotemporal consequences of NARRATION in turn should constrainthe aspectual properties of the verbs appearing in the sentences.Altshuler (2012) observed that imperfective aspect in Russianshould in fact be incompatible with sequences of events in a NARRATIONrelation which make reference to complete events. In fact,aspectual information should in turn have a strong impact on thediscourse relations inferred for discourse in the absence of explicitmarking of relations via discourse connectives. Altshuler (2012; p.61) discusses the following example in Russian.

84.

(a)

Nedeljunazad Marija po-celova-l-a Dudkina.
Week ago Maria PFV-kissed-PST.3S-FEM Dudkin
‘A week ago, Maria kissed Dudkin.’

(b)

On dari-lej cvety
He give.IPF-PST.3S her flowers.
‘He had given her flowers.’

(c)

ipriglasa-l ee v teatr.
and invite.IPF-PST.3S her to theatre
‘and had invited her to the theatre.’

With the sequence of a perfective followed by two imperfectivesentences as in (84), the discourse is interpreted not as a NARRATIONsequence but as involving some other discourse relation, most likelyinvolving an EXPLANATION relation: The fact that Dudkin had givenflowers to Maria and had invited her to the theatre provides anexplanation why he kissed her. Minimally changing the discourse byusing three perfective verb forms instead, has a quite dramaticeffect. Now the discourse is a sequence of NARRATIONs and the kissinghappens before the giving flowers which in turn precedes theinvitation to the theatre. See also Gehrke (2022) for similar claimsmade for Russian and Czech, despite existing functionaldifferences in aspect functions between these languages.

The English example in (85) illustrates a similar effect due to thecontrast between an eventive sentence in the simple past vs. thepast progressive. Depending on tense and aspect the discourse ismost naturally understood as NARRATION in (85-a) or as BACKGROUNDin (85-b).

85.

(a)

Max enteredthe building. He whistled a song.

(b)

Max entered the building. He was whistling asong.

Experimental work looking into the effects of aspect marking ondiscourse coherence is consistent with these claims from thetheoretical literature. Kehler et al. 2008 (see also Ferretti et al.2009 for ERP evidence) conducted story continuation experimentstesting English transfer-of-possession verbs such asMarygave John the book orMary got the book fromJohnwhich they tested both in their simple past form aswell as in the progressive triggering an imperfective interpretation.With these verbs, commonly a so-called goal bias effect is observed,that is, participants tend to continue the discourse about the goalargument and comprehenders expect goal continuations.Forgive this corresponds to the subject, whereasforget this is the prepositional object.Crucially, however, Kehler et al. show that this preference stronglydepends on discourse coherence, here in fact a NARRATION or RESULTrelation. Their experimental studies show that the aspect manipulationhas a predictable effect on coherence relations—imperfectiveaspect leads to less NARRATION or RESULT relations—and this inturn affects referential preferences with weaker corefererence goalbiases for progressive transfer-of-possession predicates than forperfective ones. Their studies thus provide experimental supportfor the intricate relations assumed to exist between discoursestructure and aspectual properties but also referentialinterpretation in discourse processing.

Of course these brief remarks about the discourse function of tenseand aspect barely touch the tip of the iceberg. For more informationon the discourse semantics of temporality and discourseorganization in general, the reader is advised to consult de Swart andCorblin (2002), Asher and Lascarides (2003) and van Lambalgen and Hamm(2005, especially chapter 9).

10. Conclusion

This short note on discourse structure completes our article on tenseand aspect. As noted in various places, this entry could only coversmall parts of the vast literature on tense and aspect in philosophy,linguistics, psychology and computational modeling. In allmentioned fields this still is an active research area with manyquestions still unresolved. Further information the reader isadvised to consult the references as well as the other internetresources listed below.

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Other Internet Resources

• Champollion, L., 2014,Integrating Montague semantics and event semantics, ESSLLI Lecture Notes.
• Kamp, H., U. Reyle, and A. Rossdeutscher, 2015,Perfects as feature shifting operators, unpublished manuscript, Institut für maschinelleSprachverarbeitung, Universität Stuttgart.
• Steedman, Mark, 2005,The Productions of Time, draft tutorial notes about temporal semantics.
• Grammatical Aspect, entry inWikipedia.
• Tense, Mood and Aspect, entry inWikipedia.
• Chapter onTense and Aspect, in the World Atlas of Language Structures Online.
• A Bibliography of Tense, Verbal Aspect, Aktionsart, and Related Areas, by Robert I. Binnick.
• Tenses, Moods and Aspects, Questionnaire by the Max Planck Institute for EvolutionaryAnthropology.
• Special issue “Tense and Aspect across Languages” (special issue oflanguages edited by H. de Swart and B. Le Bruynwith articles dating from 2022 and 2023)

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consciousness: temporal |discourse representation theory |events |logic: non-monotonic |logic: temporal |mereology