A Tense and Aspect Calculus

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A T E N S E A N D A S P E C T C A L C U L U S

D I A N A S A N T O S I N E S C , R. A l v e s R e d o l , 9,

P - 1 0 0 0 L i s b o n , P o r t u g a l d m s ¢ i n e s c , inesc .pt

m a y be used for further reasoning, by assuming it in the absence of contradictory information. Fur- ther investigation should be done to connect these non-monotonic reasoning aspects.

There m a y be more true statements than those t h a t can be proved. However, t h i s seems to be a correct p r o p e r t y for a s y s t e m m o d e l l i n g n a t u - ral language: O r d i n a r i l y , we only express r e l e v a n t facts - - n o t all t r u e facts.

2

T h e m e t h o d

The d e p a r t i n g p o i n t s are a s p e c t u a l classes (stored in the lexicon) and m o r p h o - s y n t a c t i c i n f o r m a t i o n (tenses, aspectualizers, adverbs, p a r t i c l e s , sub- b o r d i n a t e d clauses, etc., which we p r e s u m e are given by former s y n t a c t i c processing).

A s p e c t u a l classes will be t r a n s l a t e d by s i m p l e formulas t a l k i n g a b o u t t i m e s ( i n t e r v a l s , p o i n t s or unspecified w i t h r e g a r d to t h i s d i s t i n c t i o n ) or con- j u n c t i o n s or d i s j u n c t i o n s of these.

The o t h e r m e c h a n i s m s will be d e s c r i b e d by implications. T h e f o r m u l a s on b o t h sides refer di- rectly to t h e a s p e c t u a l classes i n s t e a d of t h e i r re- spective t r a n s l a t i o n s , e n a b l i n g us to e x p r e s s significant generalizations.

Let us m a k e some r e m a r k s on t h e i n t e n d e d m e a n i n g of t h e logical connectives. O R (V) links different p r o p e r t i e s of an object. T h a t is, t a k e n in isolation, t h a t NL f r a g m e n t or device h a s all those properties, irrespective of t h e fact t h a t i t m a y never e x h i b i t t h e m t o g e t h e r in a c t u a l use. It will be the role of o t h e r c o n s t i t u e n t s in t h e t e x t to select the i n t e n d e d reading. However, t h a t se- lection is n o t compulsive, which m e a n s t h a t O R represents l i n g u i s t i c vagueness.

Example: An acquisition (see below) like r e m e m - ber may be used in an inehoative reading (-~ come to my mind~ "After some time, I remembered it"), or in a stative reading (= be in my mind, "~I still remember it"}. But none is enforced in UDead men do not remember ~.

A N D (A) connects a set of p r o p e r t i e s of a single occurrence, even if some do not occur ( b u t they

A b s t r a c t

This paper focuses on a theory of tense and aspect (the representation of time in natural language) that attempts a formM representation of the relevant lilt- guistic devices as implication rules in first order logic. It presents a rich ontology as far as verb aspect is concerned, distinguishing between complex patterns and vagueness.

Examples and conclusions are drawn from tile comparison between English and Portuguese, pinpointing the importance of contrastive studies both for the un- derstanding and for the evaluation of a general theory of tense and aspect.

In the paper, we present the actual translations of a wide range of phenomena, and a short example.

1

Introduction

T h e method w e propose to represent and reason with tense and aspect ( T & A ) in natural language has several distinguished features:

It is both used in the building of the seman- tic representation of natural language text, and in the inferences allowed from what was actually said. There is therefore no conceptual separation between parsing and reasoning.

It is based on a two-step translation into first- order predicate calculus, that allows us to use standard logic while preserving certain generalizations, i.e., some (sets of) patterns of temporal r e l a t i o n s are identified as lexicalizing a n aspec- t u a l class, a n d T & A m e c h a n i s m s are expressed in t e r m s of t h e latter.

G r a m m a t i c a l m e c h a n i s m s are t r a n s l a t e d i n t o s i m p l e i m p l i c a t i o n s . On one hand, they r e s t r i c t / identify the set of s i t u a t i o n s they can a p p l y to, w h i l e they m a y also i n t r o d u c e lexical i n f o r m a t i o n of t h e i r own. T h i s second p r o p e r t y allows for an e l e g a n t t r e a t m e n t of redundancy, in a d d i t i o n to a n o b v i o u s e x p l a n a t i o n for t h e i r s t a n d - a l o n e oc- c u r r e n c e (cf. begin or just).

Being proof-theoretical, the m e a n i n g of a sentence or t e x t is w h a t can be proved. If other in- f o r m a t i o n is b r o u g h t to focus b u t n o t proved, it

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may). The several properties conjoined are related for each actual occurrence; they are several faces of the same situation; and no vagueness is at stake. AND links the several ways people may choose to present a given s i t u a t i o n (called view- point aspect in [12[).

Example: A n accomplishment like build may be used in a durative description ("He was building it slowly"), or in a resultative description ("He built it in two years')~ referring nevertheless to the same event. Or, in an a c h i e v e m e n t like leave, the period when a person is leaving surrounds the m o m e n t o f leaving.

The lefthand side of an implication represents the conditions which are required to the felicitous use of the mechanism. In case not all information is available, it may provide the sort of defeasible information t h a t can be seen as the type coercion proposed in [81 .

A sentence has a meaning iff there is at lea~t one derivation including all components. If there is more than one, the alternatives will stand in an OR relation, and one will probably be selected by the following co-text.

Example: "He was attending a course on seman. tics" could mean ~he would" at a future time point relative to the past in question, or that he was ac- tually attending it.

Syntax defines w h a t are the possible arguments to the operators, thus driving inference and disal- lowing certain combinations. One way to model this fact is to allow syntactic structure itself to introduce axioms or metaaxioms, restricting inference order. We stick to compositionality, but assign a non-trivial meaning to syntactic structure, contrarily to e.g. [1].

The method thus reduces to applying simple resolution to get all possible derived information, and possibly get rid of different interpretations. The set of all asserted formulas in the system is w h a t it can understand.

We will now argue for this method's adequacy to handle n a t u r a l language tense and aspect sys- tems by presenting linguistic motivation from two different languages (English and Portuguese), see [10] for more detail. At the same time, we give novel t r e a t m e n t s of well-known phenomena. These two points, we think, should be considered independently. T h a t is, one can accept the general calculus yet proposing totally different trans-

lations, or on the contrary, import our linguistic solutions into a distinct framework.

2.1

A s p e c t u a l c l a s s e s

Aspectual classes indicate the temporal con- stituency of the situation they describe. They range from states (without any restrictions what- soever, or better, with no internal temporal di- mension) to accomplishments or achievements that include a complex temporal pattern in their lexical

ITleaning.

They can~ moreover, represent vague concepts that materialize in different temporal patterns, with some c o m m o n core meaning, as was described above.

Our ontology is based solely in temporal properties, thus cause or agentivity are considered separate information, contrary to the overwhelm- ing majority of aspectual classifications (cf. the

overview in [14]).

In the figure next page, T represents an unspecified temporal object, which can denote either an interval, I, or a time point, t. We define three 'basic' classes, corresponding to three irreducible temporal patterns, and then five others in terms of the former, with some additional "low-level" conditions, linking the temporal variables among the elementary intervening aspectual class definitions. The sole reason why we did not define other combinations is t h a t we did not find, in the languages studied, examples of lexical items t h a t covered such complex patterns.

For a more detailed exposition of the classes and objective criteria for distinguishing between them in Portuguese, see [11]. Still, some remarks are in order here:

1. We distinguish

between changes and achievements since el- ements of the first class cannot be amplified in time, t h a t is, they have to be punctual, like notice or discover, while the others also involve some encompassing time connected to them: leave, die, open. This shows in the acceptance of the progressive by the latter. 2. We distinguish act-states from states, on one hand, for its well-formedness with the progressive, and from activities, on the other, because their present tense implies the progressive.

Example: He lives there, it hangs f r o m there =,~ he is living there, it is hanging there. 1

~They were mentioned as problematic in [4] and ela~ed together in {3].

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state(P)

~

P(T)

act(P)

~

P(I)

change(P)

~

P(t) A notQ(i) A Q(t) A initial(i, I) A final(t, 1)

ace(P)

~-~ act(P) A change(R) A final(t, I)

=- P(I1) A R(t) A notQ(i) A Q(t) A initial(i, I2) A final(t, I~) A final(t,

I1)

ach(e)

~-~ act(P) A change(P) A inside(t, 1)

--- P ( I 1 ) A P(t) A notQ(i) A Q(t) A initial(i, 1~) A final(t, I~) A inside(Iz, It)

act - state(P) ~

act(P) V state(P) A inside(T, [)

=-- P ( I )

V

P(T) A i n s i d e ( T , I )

acq(P)

~

change(P) V state(P) A initial(t,T)

- - P(t) A notQ(i) A Q(t) A

initial(,', I) A fi.al(t, I) v P(T) A initial(t, T)

series(P)

~

change(P) V act(P) A initial(t, I)

=- e ( t ) A notQ(i) A Q(t) A initial(i, I) A final(t, I) V P ( I ) A initial(t, I)

3. We n a m e a c q u i s i t i o n s those verbs which express b o t h the change t h a t t a k e s place and t h e resulting s t a t e , such as

remember, un-

derstand, know.

T h e y can be o p e r a t i o n a l l y p i n p o i n t e d by the s i m u l t a n e o u s acceptance of p r e s e n t tense and of p o i n t a d v e r b i a l s like

suddenly

in the past. ~

4. Finally, series can m e a n b o t h an i n d i v i d u a l c h a n g e and a set of t h e m . s They accept b o t h frequency a n d d u r a t i o n adverbs in the s i m p l e past:

Example: He coughed all night~once.

T h e t e m p o r a l indices have r o u g h l y the s a m e sta- t u s of those in the s e m a n t i c r e p r e s e n t a t i o n of UCG(15], except t h a t we do n o t impose one (sole) i n d e x per formula. We differ also in t h a t we are n o t c o m m i t t e d to a basic ontological d i s t i n c t i o n b e t w e e n s t a t e s and events, and t h a t i n s t e a d of t h o s e i n d e x e s we use plain t e m p o r a l objects. 2 . 2 G r a m m a t i c a l m e c h a n i s m s

G r a m m a t i c a l m e c h a n i s m s are defined in t e r m s of "simple" a s p e c t u a l classes i n s t e a d of a full trans- l a t i o n into p r e d i c a t e s of time. We further need t w o basic o p e r a t i o n s , n a m e l y s t a t e c r e a t i o n ( S l a t ) a n d a c t i v i t y c r e a t i o n (Act):

S l a t ( P )

= PO

Act(P)

= act(Q)

T h e first a b s t r a c t s from time, to model w h a t we call t e m p o r a l i n t e n s i o n a l i t y (i.e., non-dependence on t e m p o r a l extension). T h e second creates a new a c t i v i t y r a n g i n g over a n interval c o n t a i n i n g 2In Portuguese, where this clals is bigger, there is clearer evidence~ namely the existence of a straightforward difference in meaning between the two "simple pasts", Per- felts and Imperfeito. References to this class (uanmned) can also be found in [4} and [6 I,

aln this last sense, they correspond to the ones in [5]. [9] uses the name "actions" for our series.

more t h a n one i n s t a n c e of P, or, equivalently~ cov- ering an u n h o m o g e n e o u s t e m p o r a l region where P is true. T h e i n t r o d u c t i o n of these two opera- tions corresponds to our belief t h a t t h e r e is m o r e to sentence a s p e c t t h a n verbal aspect, c o n t r a r i l y to w h a t m o s t classifications and calculi have as- s u m e d w i t h o u t questioning. It seems to us t h a t the l a t t e r is a p r o p e r subset of t h e former. T h u s , it m a k e s perfectly sense to let m o r p h o s y n t a c t i c (i.e., non-lexical) m e c h a n i s m s i n t r o d u c e new aspect p r o p e r t i e s t h a t c a n n o t be found a t t h e lexical level.

Let us now present some c o n t r a s t i v e analyses:

Progressive act(P) ~ P(t) A inside(t, I)

Progressive P :=¢, Slat(Q) A Q ( T ) A

P(t) A before(T, t) A short(T)

Estar

act(P) -~ P(t) A inside(t, I)

By the first definition 4, progressive a p p l i e s to activities, a c h i e v e m e n t s and acquisitions, a n d is au- t o m a t i c a l l y t r u e of a c t - s t a t e s , or r a t h e r : for t h a t class, the progressive a n d the n o n - p r o g r e s s i v e ver- sions are equivalent.

The second definition e n c o m p a s s e s the f l l t u r a t e reading and s t a t i v e uses such as

He is resem-

bling his father more and more.

W i t h a c c o m p l i s h - rnents, progressive m a y be a m b i g u o u s between tile two.

Estar,

the P o r t u g u e s e progressive, h a s only t h e first English reading.

SirnplePres P =~. S l a t ( P ) A P(now)

Presente

P ~ S l a t ( P )

A P ( T ) A

inside(now, T)

The English definition allows for t h e t i m e l e s s t r u t h s X are Y a n d p r o p e r t y r e a d i n g s such as

She

dances,

while the P o r t u g u e s e one a c c o u n t s for t h e fact t h a t we say

Estou em Lisbon hd £ anos

( " I ' m

4Whenever there are several definitions of tile same op- erator~ an OR is intended.

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in Lisbon (since) two years a g o " - - in English the

present perfect should be used), or

Estou em Lis-

bon atd damingo ("I'm

in Lisbon until Sunday").

l m p e r f e i t o

P :~ state(P)

A P ( T ) A

before(7', now)

Per f e l t s

~ final(t, T) A before(t, now)

S i m p l e P a s t P ~ before(t, now)

P e r f e c t

P ~ f i n a l ( t , T ) A t <. T.~/',Q(T2)

Tim above accounts for the following facts:

I have

run

m e a n s I've finished (and similarly for any

accomplishment/achievement), and t h a t it gets translated by the Portuguese Perfeito in all those

cases. Also,

I had run

means it was finished before

the time I am talking abou, t. Finally,

to have done

definitely m e a n s completion. We can also derive tim meaning of the present and past perfects:

P r e s P e r f

P ~ f i n a l ( t , T ) A t 5~_ T2A

Q(7~) A

Stat(Q) A inside(T2 . . . )

P a s t P e r f

P ~ final(t,7")

A t < 7:~A

Q(T2) A Stat(Q) A before(T2, now)

J u s t

f i n a l ( t , T ) 2, t < 7'.z ~ initial(t, I)

A final(T2, I) A short(I)

This definition allows one to apply

just

only fi~r

perfect tenses, and also to make

just

a function

of measure, thus domain dependent (by the use

of the predicate

short).

Present perfect with

just

is translated in Portuguese by the aspectualizer

aeabar

(syntactically, a verb taking the preposi-

tion

de

before the infinitive verb)

Acabar act(P) A final(t, 11) ~ act(Q)A

final(t, 12) A final(12,

11)

Acabar P(t) ~ initial(t, I) A final(T:, l)A

short(I)

acabar

(see [2]) may either specify the last interval of an activity with definite end, or a short interval after a point event (change). This makes it a m b i g u o u s for accomplishments.

P C act(P) A final(t,

T) -~

before(now, t)A

initial(i, T) A before(i, now)

P C P

:>

Act(P) A final(now, I)

If Perfeito C o m p o s t s (PC) takes an accomplish-

ment, P C rueans the final is not yet over:

Tenho

eonstruido a minha easa

(I have been building my house). If it takes an activity, it means a set of

distinct actual activities up to now:

Tenho cot-

rids

(I have run lately). If it applies to a state, P C may represent a set of distinct states or an

homogeneous up-to-now state:

Tenho estado aqul

todas as quartas / desde as 3,

j u s t like its En- glish present perfect translation ("I've been here every Wednesday / since 3 o'clock"), it should be mentioned that apart from states, the English

translation of PC requires the adverb

lately.

Lately flnal(t,

7")

A t <_ T~ ^ inside(T~, now)

initial(t, I)/~ f i n a l ( n o w , I)/~ short(I)

Tile formula above says that

lately

requires the

present perfect, and implies t < T~. This is jus- tified if we note t h a t even t h o u g h states can be

used with present perfect and

lately

in English,

this use requires t h a t tile state does not extend

til now:

Have you been here latelyf

would other-

wise not m a k e s e n s e .

Andar P(t) ~ Act(Q)

Andar act(P) :~- act(Q) A inside( lz, I1)

Andar

either creates a big activity out of small events, or selects a subactivity inside one. English

renderings of the first meaning are

keep -ing, now

and then

or tim iterative progressive. The second is usually translated by the progressive (check the similarity with our translation of the English progressive).

2 . 3 C o n n e c t o r s

Connectors relate two different tense-aspectual descriptions and are realized ms t e m p o r a l connectives or prepositions.

To clearly indicate their double input, we will use the symbol & to separate the conditions from the first and the second a r g u m e n t s (the second is the one immediately following the connector).

At

P(t)&Q :~ Q(t)

While act(P) v P(t)&act(Q) :> inside(Te, I0)

While the translations above do not explain the different interpretations arising from different po- sitioning of the arguments, we believe t h a t this is precisely the kind of information t h a t should be brought by syntax, though for tile m o m e n t we do not have a precise formulation for it.

3 E x a m p l e

Example: "Many people died yesterday".

die:

act(die) A change(die) A inside(t, ll)

yesterday:

P ~ before(T,,tow) A

d a y ( T ) A 0 <

T - now < 24h A inside(Tp,

7")

simple-past:

P ~ before(T, now)

plural-NP: P =>

Act(P) 5

die-yesterday:

act(die)

A

change(die) A inside(t,I) A before(T, now) A

day(T) A inside(t, T) A inside(I, T)

died-yesterday:

act(die)

A

change(die) A inside(t, I) A befo~e(T,.o,O A

day(T) A inside(t, T) A inside(l, T)

SSince we are dealing only with tente-~pectual phenomena, we ~implify plural noun phrases interpreting them ;~s activity creation.

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many-people-died-yesterday:

Act(act(dle)) A Act(change(die)) A ...

This example deliberately reflects an important issue, namely, the relevance of non-verbal con- stituents to the overall aspect, which is the sub- ject of most calculi (see [13] or [7]). We agree with Krifka [7] on that, as aspect marking on noun phrases in several languages demonstrates, there is no fundamental difference in the import brought by lexical aspect, be it of verbs or other parts of speech. When we postulate a verbal aspect as opposed to sentence one, thus, the stress should be on lexical rather than verbal. What is particular to our approach is the belief that grammatical means (syntax or tense) may pur- port significant aspect properties not available (or not present) at the lexical level.

4

D i s c u s s i o n

From a descriptive point of view, the system pro- vides a liner characterization of verbs, drawing an important distinction: that between the parts of a same situation and a don't care or vagueness associated with a lexical item (the first is related to the perception of an action by a speaker of a language; the second is related to the language system / lexicon).

Second, it is based on a linguistic comparison of two distinct languages, therefore making it ap- plicable at least to more than one. This makes it also of interest for machine translation research.

Third, we expect a system thus formalized to be easy to extend, simply by adding new and sub- tler constraints in the form of implications and/or complex syntax import, and not bothering with the reasoning algorithm, by using standard logic. Finally, we think that this method has significant advantages compared to applicational mod- els in the treatment of redundancy. Redundancy is a pervasive property of natural language, but it is hard to model when one device is required to apply before another, each bringing different information. In this account, on the contrary, simi- lar information brought in twice does nothing but assert it once.

To conclude, we should acknowledge that given the early stage of this investigation, no implemen- tation and thus testing results are yet available.

5

Acknowledgements

I a m indebted to J N I C T w h o granted m e a P h D scholarship, and to I B M Portugal for support of

my studies. Most of the ideas present in this paper arose from stimulating discussions with Lauri Carlson.

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