Tense and Aspect: A Mereological Approach

1 Introduction

In this work we address the task of providing a unified ac­ count to phenomena in the domain of tense and aspect (Aktionsarten). Our strategy will be the following: verbal morphology plays a crucial role, specifying the basic units upon which the temporal and aspectual meaning of the sen­ tence is built. Furthermore, syntax combines these mor­ phemes in a maximally regular way, i.e. the syntactic struc­ ture of the verbal system is almost invariant across the lan­ guages we consider here. Although we won't be able to give much detail about syntax and syntactic processing (but, see

* The present work has been partially supported by the Italian National Research Council (CNR), project "Sistemi lnformatici e Calcolo Parallelo", and by the Irst Maia project. We gratefully acknowledge the comments by Achille Varzi on an earlier version of this paper. All the remaining errors are, of course, our own.

t Current address: Deparunent. of Modern Philology, Uni­ versity of Catania, Italy.

[Giorgi and Pianesi, 1991; Giorgi and Pianesi, 1992a; Giorgi and Pianesi,1992b]), a central feature is the integra­ tion of levels of description that have been traditionally set apart, i.e. syntax and morphosyntax. Here, our attention will focus on semantic descriptions and on the domain for seman­ tic interpretation, with a particular emphasis on the role of the part-of relation.

In Section 2, a number of phenomena will be considered in Romance and Germanic languages, which induce contrast· ing grouping. We will analyse the present tense, often con­ sidered to be one of the less controversial ones. The kind of solutions we will propose, will also play a role in explain­ ing the behaviour of the present perfect and can be shown to be generalizable to other tenses. In Section 3 we will con­ sider the question of how to structure the domains for tense and aspect interpretation and we will introduce an non-exten· sional mereological framework as the basis of our account This theory has been independently developed and applied within the framework of terminological logic, where a calcu­ lus has been provided [Allgayer and Franconi, 1992a; Allgayer and Franconi, 1992b; Franconi, 1993]. In Section 4, we extend the mereological theory to the event domain, discussing the examples of Section 2. Finally, in Section 5 we will briefly discuss how these representations can be computed.

2 The present and the present perfect

In previous work [Giorgi and Pianesi, 1991; Giorgi and Pianesi, 1992a; Giorgi and Pianesi, 1992b] we adopted a neo-Reichenbachian framework [Reichenbach, 1947] to ac­ count for the temporal systems of several Romance and Germanic languages. Our aim was to connect temporal se­ mantics to morphosyntax, under the assumption that it is the verbal morphology, 'which, once associated to a peculiar verb (i.e. combined with a specific Aktionsart) determines the array of the possible interpretations.

We start with the present tense. In this respect, English differs from all other Germanic and Romance languages; Italian, on the contrary, can be taken as a representative of the latter (examples are given in English and in Italian). With accomplishment and activity predicates, English does not allow the 'continuous' (or 'imperfective') reading, con­ trasting with all the other languages (we do not consider, here, the progressive present tense, which in English conveys imperfective meaning, and the so called reportive pre­ sent):1

1. a. John eats a chicken
2. John runs
3. a. Gianni mangia un pollo
4. Gianni corre

(l)a cannot mean that "John is presently involved in an act of eating a chicken" and analogously (1)b does not mean that "John is presently involved in an act of running". On the contrary, these readings are available in the other languages.

The possibility of imperfective readings, disappears, even in Italian, with achievement predicates:

1. John finds a book
2. Gianni trova un libro

The only available interpretation is, in fact, the reportive one.

Both in English and in Italian, present tense can express habituality, for instance John eats chickens can mean that John is a chicken-eater and John runs that John is a runner.

Finally, the present tense in all Germanic and Romance languages does not allow for perfective readings, i.e. it is not possible for a sentence like (l)a. or b. to mean that at the speech time an act of eating an apple was performed by the subject.

Under a perfective reading, an event is seen as a single, complete whole [Smith, 1991]. This does not mean that it may not have subparts; rather, if subparts exist. they are not ~ ~or.referential purpo~. When an accomplishment pred­ tcate IS mterpreted perfecuvely, the realization of the telos (culmi~tion) is impli~; e.g .. the sentence John ate an ap­ ple. entails that the eaung event went on until the apple was ~mtshed. On. the other hand, imperfective readings do not tmply the extstence of the whole and/or of the culmination pennitting access to the substructure of events. '

In [Giorgi and Pianesi, 1992b], the characteristic be­ haviour of the English present tense with accomplishment and activity predicates was connected with the peculiar statllS of the English verbal stem (in X-bar theoretic terms, it is an X0, i.e. a full word, whereas it is an x-1, i.e. a bound mor­ pheme, in the other languages; cf [Roberts, 1991]). On the semantic side, this entails that the English verbal stem (of eventive predicate) is always associated with a perfective event.

Consider now the present perfect. In this case, Romance ~d �~rmanic languages are grouped differently, i.e. English ts not tsolated but patterns with Mainland Scandinavian (i.e. ~ish, Swedish and Norwegian). In the other group we find Ital~ and Romance, but also Icelandic, German and Dutch. Agam, Italian and English are taken as representatives. The contrast we are interested in concerns the possibility of adding a specific temporal reference to the present perfect:

1. a. John left at four

. 1 H~re, we adopt th~ so called Aristotele-Dowty-Yendler clas­ slficauon of aspectualny; see [Dowty, 1979]. Furthermore, we do not consider the present tense of statives.

1. John has left
2. *John has left at four
3. Gianni e' partito aile quattro

As Comrie in [Comrie, 1976; Comrie, 1985] shows, a locating time adverbial like at four is incompatible with a ve~al form l!ke h~ left, but not with the corresponding Italtan forme partlto; furthermore, this phenomenon does not generalise to other kind of temporal adverbials (e.g. re­ cently) whose reference may include the speech time.

~e role of morphemes is once more crucial in the expla­ Jll_lUOD ~f these facts [Giorgi and Pianesi, 1992a; Giorgi and Pianest, 1992b]. The English and Mainland Scandinavian morphemes that combine with the verb to give present tense for.ms (i.e :s) have a temporal meaning (S=R, in Retchenbachtan terms; these morphemes are said to be of category AGR!f) that the corresponding morphemes of the other languages lack (their category is AGR). In Section 4 we will use this asymmetry to explain the different be­ haviour of the present perfect

3 Event domains

In order to account for the phenomena discussed in the pre­ vious section, we need a formalism to make statements about collections of events and their parts. According to a recent influential proposal [Bach, 1986], events form an atomic boolean algebra under an (individual) part-of relation (with the relative join operation). A subset of the atoms (the set of processes) is structured by another, different relation i.e. the process part-of relation (with the relative join), form~ ing a join semi-lattice. The whole system is connected to this subsystem by an homomorphism mapping events into processes. Bach also introduces a temporal part-of (oc) and an overlapping (0) relation, the former being a strict partial or­ der (i.e. transitive, irreflexive and symmetric) and the latter reflexive and symmetric (cf. [Kamp, 1979]).

For the purposes of this work, we will borrow from Bach the temporal part-of and the overlapping relations and will llSe a mereological [Simons, 1987] approach, independently developed for the objectual domain [Allgayer and Franconi, 1992a; Franconi, 1993]. The features of this approach rele­ vant to our work are: a) the possibility of defining plural operators and quantifiers and b) the fact that the theory has already been applied within the framework of terminological logics [Allgayer and Franconi, 1992a; Franconi, 1993]. where a calculus has been proposed. The importance of ter­ minological logics to represent the logical form of a sen­ tence has been often emphasised (e.g., see [Lavelli et al. 1992]). '

3.1 A Mereological Approach

We cons!der, now, collective entities, or collections [Sowa, 1991; Lmk, 1983], adopting a form of non-extensional Mereology, in the sense of [Simons, 1987]. A collection is formed by assembling certain objects, called parts of the col­ lection. Within this framework, both objects and collections of objects are seen as entities of the domain, i.e. they are re~nted by m~ of terms. A part-whole partial ordering relauon on the domam > (to be read has-part) is introduced, to relate collective entities with their parts. For example,

>(beatles, paul) means that the entity paul is part of the collective entity named Beatles.

It is worth noting that such a mereological relation is not extensional; that is, a collection may not be equal to the sum of its proper parts; in other words, two collections hav­ ing the same parts may not be equal. The > relation cannot be equated to the :2 relation of set theory, since the counter­ part of the extensionality axiom does not hold.

To talk about pluralities, we define the plural operator '*':

The purpose is to allow the construction of plural collective entities having singular objects of a certain type as their parts. More specifically, for any subpart 'x' of the plural en­ tity, either 'x' is a part of the given singular type or the lat­ ter is part of 'x'. In this way we can define, for example, the plural predicate P E 0 P LE from the singular predicate PERSON:

PEOPLE = *PERSON.

An important feature of this theory is the possibility of defining generic predicates applying to collective entities. In [Franconi, 1993] the V, ~and (j operators- called plural quantifiers - were discussed. They introduce the distributive, cumulative and group readings for generic unary predicates having a collection as argument.2 They are qualified in the sense that the elements of actual predications are selected by a qualification predicate C. In this way, representational means are introduced to capture the semantics of the (possibly underdetermined) reading variants of NL expres­ sions. As an example, take the possible "left" readings of the sentence John, Paul, George and Ringo sing Yellow Submarine. For the collective reading all the men together sing the song. In the case where each man sings separately, we speak of the distributive reading; it is expressed by means of the V quantifier which specifies that the relation holds for all the subparts of a certain type C. The cumula­ tive reading can describe the mixed situations in which one sings alone, and separately the others sing together. It will be rendered by means of the ~quantifier saying that the rela­ tion holds for some subparts including all the subpart of a certain type C. Finally, the group reading covers the case in which possibly only some of them sing; it is conveyed by the (j quantifier which specifies that the relation possibly holds for some subpart of a certain type C; i.e. it expresses the group reading [Landman, 1989a; Landman, 1989b] as a sort of weakened collective reading. The plural quantifiers are formally defmed as follows.

Definition 2 (Qualified Plural Quantifiers)

v C.P(a) iff \::/x.(>(a, x) A C(x)) --+ P(x) ~C.P(a) iff \::/x.(>(a, x) A C(x))--+ (3s. >(s, x) A P(s)) (j C.P(a) iff 3x.>(a, x) A C(x) A P(x)

2 For the purposes of this work, binary predicates will be used instead of unary ones.

It follows from the defmition that cumulative plural quanti­ fied expressions are more general than non-quantified (i.e. collective) expressions and distributive plural quantified ones:

In this way ambiguities in the readings can be preserved by using the cumulative operator.

3.2 ~ore on the theory of events

Consider, now, an action, e.g. eating. Despite the fact that in this theory it can be (almost indefinitely) decomposed into smaller actions, there is a level below which we do not recognize eating events any more but, e.g., particular movements of the jaws or of the tounge, swallowing, etc ... which do not intuitively qualify as actions of eating. Therefore, we assume that the extension of a predicate like eat in the domain of events (Ee) has qualified atoms, i.e. there are eE/(eat) (the denotation of to eat) such that for ev­ ery e' E/(eat), e > e' ~ e=e' . Furthermore, for a given event, all its (qualified) atomic subparts are mutually non­ overlapping and linearly ordered by oc. With this in mind, the denotation of a perfective sentence is an event (or a col­ lection of them) having proper (qualified) subparts. An im­ perfective sentence, instead, can be taken to refer to a collec­ tion of qualified atoms. This differs from many current pro­ posals (e.g. [Kamp and Reyle, 1993]) where imperfective sentences are taken to denote states. However, it can bear­ gued that imperfectives and statives only share some of their properties (e.g. the possibility of taking for- adverbials) but not others (e.g., states are homogeneous with respect to time, whereas irnperfectives need not be so: e.g., the truth of John loved Mary at an interval, t, entails the truth of the same sentence at every sub-interval oft. On the contrary, the truth of John was running at an interval does entail that it was running at every sub-interval oft) and therefore must be kept conceptually distinct [Smith, 1991].

We assume that the objectual domain, E0 , has a structure similar to that of Ee. and hypothesise that, in certain cir­ cumstances, a homomorphism h maps elements of E0 into elements of Ee in such a way that the structure of the event domain is determined by the structure of the objectual one [Krifka, 1992]. The existence of such an homomorphism de­ pends on the kind of thematic relations established by the verb; the direct object of an accomplishment verb is such an example [Dowty, 1991] calls it an incremental them~). According to this view, telicity is determined by: a) the exts­ tence of a perfective form; b) the existence of a particular thematic relation and c) the kind of object that enters this re­ lation with the predicate (i.e. mass versus count). With this, the difference between accomplishment and activity sen­ tences reduces to (b) and (c).

Achievements differ from both: crucially, even in lan­ guages like Italian the present tense of achievement predi­ cates can never be imperfective. To account for this be­ haviour, we propose that: a) achievements never have proper

.

(qualified) subparts and b) they are punctual (cf. [Dowty, 1979]).

3.3 States and time

With respect to times, we use an interval domain I whose connection with Ee is explicitly provided by means of a function -r assigning every event a time interval minimally containing it. We assume that the set of relations of [Allen, 1983] can be defmed on I .

Contrary to events, states are not considered here as primi­ tive objects (see [Kamp and Reyle, 1993] for discussion) but as derivative on times. More precisely, a VP like [VP loves Mary] establishes a set of intervals such that A.x,t. love(x, Mary, t) is true; the whole sentence John loves Mary, in turn, requires that the interval S (the speech time) is such that love(John, Mary, S) is true.

4 Applying the theory

In [Giorgi and Pianesi, 1991; Giorgi and Pianesi, 1992a; Giorgi and Pianesi, 1992b] it was proposed that each tense morpheme bears a precise relational temporal meaning. Furthermore, temporal (I) roles were introduced (cf. [�u~ron and Hoekstra, 1989]), in analogy with thematic roles, as a (syntactic) device allowing positions in the thematic grid of a temporal predicate to be fll.led by temporal indices. Hence, a tense morpheme T -marks a VP, this way identifying one of its temporal argument with the temporal index of the VP. For instance, the English present tense morpheme, whose meaning is S=R, behaves like a one (free) place predicate,= (S, T-Arg2). By means ofT-marking, T-Arg2 gets identified with the temporal index of the VP (R)-3

When no tense morpheme is given, as in the Italian pre­ sent tense, the temporal index of the AGR node (S) syntacti­ cally binds the temporal index of the VP; temporal binding entails a weaker relation than (temporal) equivalence, namely containment: S ~ R (cf. [Pianesi, 1992] for an account of how this ideas could be implemented by means of an unifi­ cation based grammar).

4.1 The present tense

First, consider the impossibility for present tense to convey a true perfective meaning (cf. Section 2). It has been sug­ gested that this is so because of the punctual, i.e. duration­ less, nature of the speech time [Dowty, 1979] and the conse­ quent impossibility of accommodating durative events within S. However, this explanation should allow for pre­ sent tense perfective readings with otherwise punctual events (e.g. achievements) and in Section 2 we showed that this is incorrect. We will follow [Kamp, 1979] in defining punctu­ ality directly on the eventive domain in such a way that it does not entail no duration. A qualification (cf. Section 4) will be added, in order to avoid picking up unwanted ele­ ments (i.e. events below qualified atoms). More precisely, an event e is punctual with respect to an event predicate, Q, iff there are no events in the extension of Q that partition e:

3 We do not commit ourselves to the Reichenbachian inter­ pretation of R as the reference time [Reichenbach, 1947], but simply treat it as an argument of a temporal predicate

Let us now assume that the speech event, s, is punctual with respect to whatever predicate is given by the verb of the sentence. If the VP is perfective, it denotes a collection of individual events e having (qualified) atomic processes as subparts which are mutually non overlapping. Considering the way tense morphemes work, we end up with something like S=-r(s)='l'(e) iff s~e and eo (here~ is the relation of temporal containment on events; it can be defined as in [Kamp, 1979]). Therefore, there are eJ and e2, e>eJ, e2 in the extension of the event predicate that overlap s and do not overlap each other, leading to a contradiction. In an imper­ fective sentence, assuming that it denotes a collection of Q­ atomic process eJ, ...· en and choosing one of them, ei, there are no subparts of ei in Q that may conflict with the punctuality of s, hence 'l'(s)='l'(ej) can be asserted.

Both the logical forms of perfective and imperfective sen­ tences are examples of group reading. Consider (1).a and (2).a above. (7).i and .ii give the perfective and imperfective readings:

where Vis the verbal predicate k.3t. (-r(e)=t 1\ eat(e) 1\ t='l'(s)" ·eatfs)) (we neglect the contribution of the Agent argument). Applying it to (7).i we get the collection of events which have a subpart, which is an event of eating a part of a chicken that is itself a chicken. Applying the predi­ cated to (7).ii, we get the collection of events having a (Q­ atomic) subpart that is an event of eating a part of a chicken. Note that: a) the fact that the direct object of to eat (mangiare) is an incremental theme entails that the image of Chicken under the object-to-event homomorphism is taken. b) The semantic contribution of the tense morpheme and of T -marking are embodied into the predicate V. 4 Interpreting (7).i, a collection of events that have subparts is obtained, thereby violating the punctuality of s, and accounting for the general impossibility of perfective present tense events. c) The logical formula for imperfectives (7).ii mentions a pred­ icate Ed. It is contributed by the lexical semantics of the verb and specifies the set of objects that are edible.

In Section 2 it was argued that the English stem of an eventive verb may only refer to perfective events, a property due to morphosyntactic properties of English. In this case, the denotation of t/'Ed. Vreduces to that of t/'Chicken. V, correctly representing the fact that English present tense does not allow imperfective readings. Actually, (7).i per se entails (7).ii in the sense that the latter is more general that the former. Therefore, something like (7).i is the logical form of an English sentence with an eventive verb, whereas (7).ii corresponds to Italian.

It turns out that the contribution of tense morphemes may be crucial in restricting the interpretation to a subset of

4 The Y -predicate for Italian is obtained by substituting t = 'f(s) with 'f(s) r= t in the expression for Y; see above.

(7).ii, e.g. by only allowing the imperfective reading (as in Italian) or by disallowing both (as in English). This ap­ proach can be extended to account for many other phenom­ ena, e.g., the contrast between the simple past tense of lan­ guages like German and Dutch (cf. dutch John at een appel (=John ate an apple)), which can give rise to both perfective and imperfective readings, and the simple past of languages like Italian (Gianni mangio' una me/a(= John ate an apple)) that only permit perfective ones. In the first case, the tense morpheme simply specifies the temporal relation between the speech time and the temporal index of the VP, and the logical form looks like (7).ii. In Italian, the simple past morpheme restricts the range of events provided by the verb, by selecting the perfective ones and giving rise to a logical form close to (7).i.

By way of illustration, we report the following sentence together with their logical forms

1. a) John runs Gianni coree ( qT run . V) f1 T run
2. John eats Gianni mangia ( qhEd . V) f1 hEd

Both sentences have an imperfective reading in Italian that is impossible in English. With respect to the previous exam­ ples, note that: with intransitive activity verbs (to run in (8).a), the qualifying predicate is the top of the collection of the events of running (or a similar restriction brought in by the verb). In (8).b, where the intransitive form of a verb hav­ ing an incremental theme is present, the homomorphic im­ age of the set of edible object is taken. This way it is possi­ ble to account for the effects of the intransitivization process in a natural way, by directly resorting to the lexical seman­ tics of the verb and without the introduction of free (orexis­ tentially closed) variables in the argument structure [Pianesi, 1992].

Habituals can be interpreted as stating the existence of an unspecified quantity of events, which apply to an unspecified quantity of objects (when an incremental theme is defined; cf. the SQA- Specified Quantity of A- feature of [Verkuyl, 1987; Verkuyl, 1989]; for habituals, see [Kearns, 1990]). The existence of an unspecified number of events will be rendered by means of the cumulative operator. Here is an ex­ ample

1. i. John eats chickens ii. Gianni mangia polli iii. (.~hchicken . V) f1 h*Chicken

(9).iii denotes the set of events that are the mereological sum of events of eating groups of chickens. Such events are under specified in the sense that it is not required for them to be in the extension of eat. Consider one of them, e, its time, t(e), which is the convex closure of the time intervals asso­ ciated with the single events e is sum of, and the set of in­ tervals that are included in -r(e). (9).i and ii. say that the speech time corresponds to one of these intervals.

Note that no contradictions due to the punctual nature of s arises, since it is not required that S='r(s)='rfei) for any ti which is a part of e; hence, both (9).i and .ii are possible iii English and in Italian, respectively.

4. 2 The present perfect

In Section 2, it was shown that it is not possible to use lo­ cating temporal adverbials with English present perfect sen· tences. To account for these facts we use the notion of con· sequent state [Moens, 1986; Parsons, 1989]. Accordingly, the present perfect is seen as introducing a perfective event and a (consequent) state, holding in a set of intervals ranging from the conclusion (culmination) of the event and including S. The consequent state (and the perfective event) is intro­ duced by the past participle morpheme, English -en and Italian -t- [Giorgi and Pianesi, 1991; Giorgi and Pianesi, 1992a; Giorgi and Pianesi, 1992b]. Italian and English do not differ substantially with respect to the role of the par· ticiple morpheme. We attribute the different behaviour: (a) to the morphosyntactic properties of present tense (on the auxiliary) in the two languages and (b) to the anomalous sta· tus of bounded states. With respect to (a), in English we have an S=R relation, whereas in Italian the syntactic bind· ing gives rise to an inclusion relation. Concerning (b), [Kamp, 1991] points out that when the temporal adverbial locates the event, it establishes an explicit lower temporal bound on the consequent state which, therefore, behaves in a peculiar way. It, in fact, holds only on intervals that are similarly bounded.s Consider now the following examples:

1. (i) John has eaten a chicken
2. (ii) Giovanni ha mangiato un polio
3. (iii) * John has eaten a chicken at five
4. (iv) Giovanni ha mangiato un polio aile cinque

The contribution of the verb plus the past participle mor· pheme is the consequent state of a perfective event:

At. 3e. (meets(t, t(e)) v after(t, t{e))) A P(e)

where P(e) is ( t/'Chicken . EAT) l"l hchicken. This is part of the meaning of all the sentences in (10). Interpreting the present tense of the auxiliary, we obtain:

where we have used the meet and after relation of [Allen, 1983]. {ll}.i and .ii are the logical forms for {lO).i and .ii, respectively. If the contribution of the temporal adverb is taken into account, we first obtain:

S For a different approach to this problem, see [Klein, 1992].

i..L 3e. meets(t, t(e)) A P(e) A t(e)~ 5

i.e. only intervals that have a lower temporal bound comply­ ing with the location time are acceptable (at five is inter­ preted as denoting an interval including 5 o'clock). About the temporal containment relation between events and locat­ ing adverbials, see [Kamp and Reyle, 1993]. Finally:

(12) i. 3e. meets(S, t(e)) A P(e) A t(e)!;; 5 English ii. 3e,L meets(t, t(e)) A P(e) A t(e)s:;; 5 A S !;;; t Italian

which are the logical fonns of (lO).iii and iv., respectively. In the general case, the first fonnula is unsatisfiable, since S is required to meet f( e) which, in turn, is contained in the 5 o'clock interval. 6

5 Computing the Representations

Before concluding, let us briefly see how these representa­ tions could be built during parsing by considering a simple example. We assume a lexicon of stem and affixes. Verbal stems come into three fundamental varieties: statives, activi­ ties (including both the traditional activities and accom­ plishments) and achievements. With respect to thematic rela­ tion, we assume that those inducing an object-to-event ho­ momorphism are stored in a list: Homomorphic­ list= (!ncr-Theme, ... ). The following is (part) of a possible lexical entry:

eal-

Jl'Cd:

aspect

8-relation 1:

8-relation2:

eat

activity

Agent

!ncr-Theme

When the thematic relation is in the Homomorphic-list, the value for the SQA feature of the object is percolated to the VP. Tense morphemes, as we· saw, introduce temporal relations by means of T-marldng (they may also restrict the denotation of the object they combine with; in a system based on, e.g., typed feature structures, this could be ob­ tained by restricting the type of the VP [Sanfilippo, 1991]):

Arg2: < 1 >]

·S Cat: AGR!f Sem: [ pred: Arg1: Subcat: [ Cat: = s VP

Sem: [ T-index: < 1 > ] ]

Interpreting syntactic structures, the application of the qualified plural quantifiers operator may be attempted on the VP (the operator ~ or on the AGRP (the operator {;). Furthennore, there is a condition on ~ to the effect that it only applies to VPs whose SQA value is"-" or undefined.

6-rhe fact that this argument crucially relies on the width of the relevant intervals does not prejudice it, given the variable acceptability (at least for certain informants) of (lO).iii when uttered few minutes after 5, say at 5:04

Now consider sentence (2).a. The VP IVP mang- INP un polio]] inherits the SQA+ specification from the object NP thanks to the fact that the thematic relation is Incr-Theme; therefore, the ~operator cannot apply. The further con­ stituent to be considered is IAGRP -a IVP mang- INP un pollo]J]. Its denotation is: A.e.3t. (f(e)=t A eat( e) A f(s)a A ·eaJ(s)), where the inclusion relation between the speech time ( f( s )) and the time index of the VP is due to syntactic binding (cf Section 4). Finally, applying the g operator, we get the logical fonn (9).i. As before, the perfective variant is impossible, given the punctual nature of s.

6 Conclusions

In this work, we have explored the use of a simple mereo­ logical framework to address several temporal and aspectual phenomena. The choice of a mereological approach is due to the necessity to talk about collections of events and about their parts, in order to accommodate linguistic data. An im­ portant result is that many differences between languages have been shown to reduce to lexical and/or morphosyntacti­ cal peculiarities, whereas syntax and semantics are ruled by the same principles.

Several issues still need to be considered within the mere­ ological approach: the existence of atoms (entities which have no subparts), the possibility of using several different >i relations [Winston eta/., 1987] and the introduction of a mass dissective predicate as in [Link, 1983]. The first two points would be important to allow for more structured do­ mains; this way, the differences between perfective and im­ perfective events could be stated more explicitly than it has been possible here. Dissective predicates, in turn, would pennit to face the general question of homogeneity (a prob­ lem we did not address here) and give a more satisfactory sta­ tus to states.