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<Paper uid="C96-1007">
  <Title>Computational Semantics of Time/Negation Interaction</Title>
  <Section position="3" start_page="0" end_page="30" type="metho">
    <SectionTitle>
2 Semantic representation
</SectionTitle>
    <Paragraph position="0"> I)l/~l' halt(lies ('.vents as objects in the la.nguag(;.</Paragraph>
    <Paragraph position="1"> Thus, each simple sentence introduces into the r(,.1)resentation (at least) one discourse referent, either an cv(~Ili; or ;I, stat;(% corresponding to tim (;vent;u&amp;lit;y denoted by l,h('. VP.</Paragraph>
    <Paragraph position="2"> With this in mind, negation can either be seen as an operal;or always having a with' scope, over c.vents/statcs, or &amp;s a kind of t~st)('x;tlta.l opcra.-I;or. According t:o t;he tirst vie.w, ncg~tl;iOll Wollld semanl;i(:ally (;onvcy only n(;gativ(! informatioil (&amp;quot;such an (.wentuality a: didn't oc(:ur&amp;quot;). A(:(:or(1ing to the secon(\[ view, negativ(, SCIl|;(}iic(}s co\[ivcy some kind of posil;ivc information, at; the semantic level: they denoi;e a certMn kind of eventuality.</Paragraph>
    <Paragraph position="3"> We want to address this probh;m here, with a focus on sentontial negation in French.</Paragraph>
    <Paragraph position="4"> 2.1. The problem As we ha.ve already said, the two al)tnoaches t;o senl;entiM negai;ion differ with rt;st)t'ct I;o the scope they assign i;() the negation Ol)(;r~rtor. To help illusl;rate this, we shall use the following exam-ph% where wc assume that (lb) is the (scntential) negro;ion of (la). A &amp;quot;standard&amp;quot; repres(,nl;atitm of (la) is K,., (it) a...h;an s'arr&amp;a.. (,I,a:,, .stop'p(ed.) l)..hum ne s'arrC;t~ pas. (,lea'n, didn't stop.)</Paragraph>
    <Paragraph position="6"> What 1(1, says is that l;her(; is ml x, which is ,)ca.n, an evenl~ e, and ;t locatiol~ time t, such that e is the ev(mt of .h~a.n st;opt)ing , (; is inchlded in 1;he location time t, which is itself located in the past ,,r the,, (11,) ,:,.,.ld t;h,,,, t,,, repr,c~sented either I:,y K ll, or by K'u.</Paragraph>
    <Paragraph position="7"> (2)</Paragraph>
    <Paragraph position="9"> Elb sl;atcs somct;hing like &amp;quot;there is no evcnl; of Jean's stot)ping al l;he time t.&amp;quot; K'lb introduces a.</Paragraph>
    <Paragraph position="10"> &amp;quot;spcc.ia,l&amp;quot; cv(~ll(;, (i which is dctined in term of the ncg&amp;tion of aJl &amp;nol;ho.r event.I</Paragraph>
    <Section position="1" start_page="0" end_page="30" type="sub_section">
      <SectionTitle>
2.2 Discussion
</SectionTitle>
      <Paragraph position="0"> Tim t)osit;ion w(' are going to de\[end here is the. one acc.or(ling to which negation should i1ol; \])o. SCCll &amp;s 'The ontological and semantic I)rot)erties of such special (;vents remain to \])e defined, and tlw. variolls 1)rol)onents of this view propose difl'ere.nt detinitions ;t sot|, of &amp;quot;maximal event&amp;quot; (Kriflca, 1989), or at st,~te (:onsisting of the negation of an event (de Swart mM Mohmdijk, 1994), for instance.</Paragraph>
      <Paragraph position="1">  an aspectual operator, but rather as having wide scope over the eventuality, as exemplified by the DRS Klb. This position is the one defended in (Kmnp and Reyle, 1993).</Paragraph>
      <Paragraph position="2"> We first review the arguments in favour of our view, and then summarize the discussion presented in (Amsili and Le Draoulec, 1996) against the counter-arguments to this view presented in (de Swart and Molendijk, 1994). We summarize our semantic proposal in the section 2.3.</Paragraph>
      <Paragraph position="3"> Simplicity. One of the reasons wily we may prefer the representation Klb tO K~b is that it is simpler, from the technical point of view. Thus, if such a representation is sufficient to account for all the data we want to account for, then there is no need for a more complex representation like tile one exemplified in K~b. Another point worth noting is that, the second proposal is also more complex from the ontological point of view. Adding new types of discourse referents like ~ in the language of DRS requires that we define their ontological properties. And since these new kinds are defined in terms of others kinds of discourse referents, this may well be a non-trivial task.</Paragraph>
      <Paragraph position="4"> Negation in discourse. The ideas developed in this paragraph are based on a study of negation in discourse currently in progress. The aim of this study is to see how negation interferes with so-called discourse relations (continuation, elaboration, explanation...). To do this, we are using a large corpus taken from French contemporary literature. We shall not describe this study in detail here; nevertheless, one of its findings is relevant to our discussion.</Paragraph>
      <Paragraph position="5"> We have looked at examples involving French passg simple (PS, simple past). This tense typically introduces an event rather than a state. We have a set of 1399 examples of sentential negation, in which one find only 46 occurrences of PS. Among these examples, a majority are of the form exemplified in (3).</Paragraph>
      <Paragraph position="6">  (3) a. Je ne lui rfipondis pas.</Paragraph>
      <Paragraph position="7"> I didn't answer him.</Paragraph>
      <Paragraph position="8"> b. ~ Elle ne sursauta pas.</Paragraph>
      <Paragraph position="9">  She didn't startle.</Paragraph>
      <Paragraph position="10"> Thus, in a majority of cases, PS+negation seems to be used to assert, the absence of an event, and it is very difficult in those cases to find a &amp;quot;real event&amp;quot; which could be seen as denoted by the sentence. null  3 cases in the corpus seem however to suggest that negated event sentences may denote events: (4) a. Elle ne le voulut pas.</Paragraph>
      <Paragraph position="11"> She didn't want it.</Paragraph>
      <Paragraph position="12"> b. L'autre ne prit pas de d~tour.</Paragraph>
      <Paragraph position="13">  The other didn't mince words.</Paragraph>
      <Paragraph position="14"> c. Elle ne se laissa pas faire.</Paragraph>
      <Paragraph position="15"> She didn't let things flow.</Paragraph>
      <Paragraph position="16"> Thus, one can easily imagine that (4a) &amp;quot;refers to&amp;quot; a gesture, or some kind of behaviour that could be interpreted as a refusal. Here, of course, this reflmal could probably be associated with ~.</Paragraph>
      <Paragraph position="17"> But these examples are rare; moreover, the two last sentences of (4) involve more or less idiomatic expressions, so that it seems quite reasonable to see negation here as part of a conventionalised expression (&amp;quot;he passe laisser faire&amp;quot; denoting an event, just like the verb to refuse does).</Paragraph>
      <Paragraph position="18"> Events can be defined as a change of state.</Paragraph>
      <Paragraph position="19"> With this definition in mind, we think that, at least in the case of PS, negation over events is used mostly to convey something like &amp;quot;nothing changed&amp;quot;, or &amp;quot;the expected event didn't occur&amp;quot;, and there is in this case no event denoted by tile sentence. There remain some cases (very few) where such sentences seem to denote some real change of the background, but then we claim that negation is lexically incorporated, and no longer sentential.</Paragraph>
      <Paragraph position="20"> The classical example. We come now to the &amp;quot;classical&amp;quot; example of (Kamp and Reyle, 1993). It involves tile following discourses:  (5) a. Mary looked at Bill. He smiled.</Paragraph>
      <Paragraph position="21"> b. Mary looked at Bill. He was smiling.</Paragraph>
      <Paragraph position="22"> c. Mary looked at Bill. He didn't smile.</Paragraph>
      <Paragraph position="23"> d. Mary looked at Bill. He wasn't smiling.</Paragraph>
      <Paragraph position="24">  The pair (5a-5b) exemplify the contrast between simple past and progressive past in narrative discourse. In the second sentence of (5a), the simple past introduces a new event,, which is localised after tile event introduced in the previous sentence. In constrast, the second sentence of (5b) introduces a state, which overlaps with the event of the previous sentence. This analysis gives tile correct prediction for the contrast: in (5a), Bi{l's smiling is interpreted as a reaction to Mary's looking at Bill, thus following it, whereas in (5b), Bill was already smiling when Mary looked at him.</Paragraph>
      <Paragraph position="25"> The contrast in (5c-5d) is clearly parallel to that in (5a-5b). Since the second sentence of (5d) call reasonably be thought of as introducing a state, also introducing a state for the second (negative) sentence of (5c) would lead us to lose the contrast, since this would suggest, for both sentences that Bill was not smiling when Mary looked at him.</Paragraph>
      <Paragraph position="26"> Counter-arguments. We summarize here the discussion given in (Amsili and Le Draoulec, 1996) against some of tile arguments given in favour of the idea,that negative sentences denote an eventuality. There are two main arguments. One is based on the fact that negated event sentences accept durative complements (whereas their positive counterpart do not), this fact being taken as an argument in favour of the aspectual role of negation. Our answers are: first, some French data suggest that durative complements with negation should  not always be seen as demonstrating the din'alive' ity of the predicate; second, Kamp and Reyl. s (1993) representation provides a satisfying way to account tbr such data. The second argument is based on examples ill which an anaphoric reference see, ms to be made to the denotation of negative sentences, therefore suggesting that they have one. But these data are rather constrained, in such a way that it seems that tile discourse referent at stake is an abstract one, nmnely a fact, and not an event/state.</Paragraph>
    </Section>
    <Section position="2" start_page="30" end_page="30" type="sub_section">
      <SectionTitle>
2.3 Proposal
</SectionTitle>
      <Paragraph position="0"> We can now state 1;he t)rol)osal, ill the ternls of (Kamp and Reyle, 1993, p. 548). Roughly, the interpretation of a negated sentence induces the following steps ill tile construction of a DRS: * introduction of a location time t; * introduction of a condition relating t with the speech time n; * introduction of a con(lition saying that there is no event or state of a certain l;yl)e which stands in the relation 'C' or '0' /.o t.</Paragraph>
      <Paragraph position="1"> As an example, the diseom'se (5c) will receive the represenl;atioil (6), the most relevant points of which being, first, that a temporal constant (t) is systematically introduced into the representation, and second, that negation has wide scope over event/state discourse referents, t remaining outside negation.</Paragraph>
      <Paragraph position="3"/>
    </Section>
  </Section>
  <Section position="4" start_page="30" end_page="31" type="metho">
    <SectionTitle>
3 Syntactic Aspects
</SectionTitle>
    <Paragraph position="0"> We now briefly address l;he syntactic aspects of French sentential negation. We adopt the representations envisioned by classical Govermnent and Binding Theory (hereafter GB, Chomsky (1981; 1986)). Several sl;udies on the structure of I,~'ench clauses, and ill t)articular, negative sentences, have been carried out recently ill this framework by Pollock (1989; 1993), Hirshbiihler and Labelle (1993; 1994a) and Pearce (1994) among others. In this section, we adopt some of their most relevant results.</Paragraph>
    <Paragraph position="1"> We are mainly concerned with two of the four levels of representation of GB, namely D-Structure and S-Structure. Tile representations of tiles(; two levels are trees. D-structures represent basic lexical properties such as thematic relations. S-structures represent more superficial properties such as case, binding, etc. S-structures derive fi'om D-structures via Move-a: they are the result of movements that take place in tile latter.</Paragraph>
    <Paragraph position="2"> In this section, we attempt to answer the following two questions: (1) what is the D-structure of French negative clauses? (2) which move.ments take place between D-Structure and S-Structure?</Paragraph>
    <Section position="1" start_page="30" end_page="30" type="sub_section">
      <SectionTitle>
3.1 Split Inflexion Hypothesis
</SectionTitle>
      <Paragraph position="0"> The. lPrench clause representations we use are rather classical. They satisfy X'-theory, which uses well-known syntactic concepts independent of any theoretical Damework. % represent clauses and to build their DRSs, we use a tree structure consisting of a verb phrase VP dominated by tile projection iP of a functional head I bearing the verbal tense and agreement features (I stands for inflezion). IP has the sentence subject NP as its specitier and the. VI' as the complement of its head. The sentence is therefore represented as an &amp;quot;inftcxional phrase.&amp;quot; '\['his m W be illustrated by the S-structure (7b) of sentence (7a);  (7b) Inky also be ret)reseuted as the labelled bracketing giwm ill (7C). 2 (7) a. Julie regarde Marc (indies looks at Marc.)</Paragraph>
      <Paragraph position="2"> \[v, t,\] \[NI' Mm'c\]\]\]\]\] Pollock (1989), starting from this general structure, gives a new insight into the problem, by showing the beuefits of splitting the complex inflexional category I into two distinct flmctional categories, namely tense (T) and verb agreement (Agr). The general structure of French clauses that Pollock (1989) proposes is (8a), so that for instance (7b)becomes (8b):  (8) a. \[Tp NI' rp \[Agrt .... Agr \[VP (AdvP) VP\]\]\] b. \['rl' \[NP Julie\]\[~,., \[7'/ regarde\] \[Ag,-l' \[Agr' \[Agr i t\] \[vp \[v, Iv, t\] \[m' Mare\]\]\]\]\]\]\]</Paragraph>
    </Section>
    <Section position="2" start_page="30" end_page="31" type="sub_section">
      <SectionTitle>
3.2 Negation
</SectionTitle>
      <Paragraph position="0"> (Pollock, 1989) also claims that negation, like tense and verb agreement, is represented as a funcl;ional category, Neg, located between T and Agr.</Paragraph>
      <Paragraph position="1"> 2Note that the morphological decomposition of the verb, shown in (7b), will not be. made explicit in tile following representations.</Paragraph>
      <Paragraph position="2">  In French, this category contains the negative item ne, seen as a weak affix lacking morphological stress. In S-Structure, ne must adjoin to the verb as a clitic. More generally, it must raise to T in finite clauses as well as infinitives.</Paragraph>
      <Paragraph position="3"> This proposal has been accepted by many linguists. However, there is no similar consensus about the position in D-Structure and the possible movements of the second element of French negation, namely one of the adverbs pas, plus, point, guSt'e, etc. Here we adopt the proposal of (Hirschbiihler and Labelle, 1993) which states that pas (or any of the other negative adverbs) is an adjunct to the maximal projection governed by Neg. Since Ncg is located between T and Agr, this projection is AgrP. The general structure of a lq-ench negative clause is therefore: \[TP NP T \[NegP Neg \[agrP Agr \[vl' (AdvP) VP\]\]\]\] a.a The Aspeetual Dimension of Agr The previous clause structure improves significantly the correspondence between syntactic representation and semantic interpretation. In particular, it becomes easier to differentiate the semantic contribution of each element that is relevant at the aspectuo-temporal level. These elements fall into two categories: those below negation (and therefore inside its scope) and those above negation.</Paragraph>
      <Paragraph position="4"> Following (de Preitas, 1994; Borer, 1993; Latca, 1990), we consider Agr to be rather an aspectual category Asp in charge of the aspectual dimension of the semantic representations. This dimension is introduced by discourse referents. Recall that DRT discourse referents do not serve only to account for this aspectual dimension, but do play a fundamental discursive role. Nevertheless, the categorisation into states (s) and events (e) of the utterances to bc represented, and the possible introduction of the discourse referents of one of these aspectual category, may be associated with the Asp head. This association gives us the expeeled result: the discourse referent e or s is in the scope (in the sense of DRS construction) of the possible negation.</Paragraph>
      <Paragraph position="5"> These elements are all illustrated in the cornplete syntactic representation of the sentence (9) given in figure 2. Notice the attachment of the sentential adverb aujourd'hui as adjunct to TP, the highest projection of the representation. Because of space limitation, we cannot develop this point here and refer the reader to (Amsili, 1994).</Paragraph>
      <Paragraph position="6">  (9) Aujourd'hui Pierre ne possbAe pas de voiture.</Paragraph>
      <Paragraph position="7"> ~ibday Pierre doesn't own a ear'.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="31" end_page="32" type="metho">
    <SectionTitle>
4 Bottom-up construction
</SectionTitle>
    <Paragraph position="0"> We now integrate the semantics and the syntax of sentential negation. We show in this last section that both representations fit together in the framework of a bottom-up construction procedure, which allows a satisfactory computational treatment of negation. We use the method proposed in (Asher, 1993), presented in section 4.1, and then show how this nmthod can be applied to the representations discussed earlier.</Paragraph>
    <Section position="1" start_page="31" end_page="31" type="sub_section">
      <SectionTitle>
4.1 Principle
</SectionTitle>
      <Paragraph position="0"> The construction procedure is bottom-up. DRtheoretic expressions are associated with leaves, and then combined to form the final DR,S. The combinatorial method used here is A-conversion, with two kinds of ~-expressions, namely predicative DRSs and partial DRSs. We associate verbs and nouns with 1)redicatiw~ DRSs (for instance, the verb voir (see)) yields Aa:ky voir(x,y)), the role of which is to introduce predicates into the representation. In constrast, discourse ret~rents are only present in the form of DR-variables; they will be introduced by the partial DRSs. The translation of noun phrases (NP) or determiners is quite close to that of the Montagovian tradition. A determiner is associated with a partial DRS, which is, so to speak, what remains of a DRS when one takes away a predicative DRS. As a consequence, there will be variables over predicative DRSs (PDRS-variables) in partial DRSs. A partial DRS can also contain a declared discom'se referent. This discourse referent is meant to serve as an argument of the predicative DRS which will be assigned to one PDRS-wxriable during the conversion. In (10) we give a graphical representation of a simple and general case of A-conversion.</Paragraph>
      <Paragraph position="1"> pm'tial DRS pred. DRS conversion We have i1o room here to elaborate oi1 the details of the construction procedure; we refer the reader to (Asher, 1993), and give in figure 1 a complete example (with a simpliiied syntactic representation), for the sentence (11).</Paragraph>
      <Paragraph position="2"> (11) Un gars voyait Marie A boy was seeing Mary</Paragraph>
    </Section>
    <Section position="2" start_page="31" end_page="32" type="sub_section">
      <SectionTitle>
4.2 Implementation
</SectionTitle>
      <Paragraph position="0"> What remains to be done is to integrate this construction procedure with the proposals we have made in this paper. We cannot, in this short text, review all aspects of this integration, and will therefore mention only the most rele, vant points.</Paragraph>
      <Paragraph position="1"> We have seen that the representation of time in DRT makes us('. of two discourse referents (at least). It is thus necessary to determine in both cases which nod(; will be in charge of introducing the discourse referent. The pure temporal dinmnsion, which is accounted for by the time referent; t, will be introduced at the node T. The aspectual dimension, which is accounted for at the semantic level by the discourse referent e/s, is associ-</Paragraph>
      <Paragraph position="3"> ated with the head Asp. We will therefore ass(lelate with this node a partial I)RS to introduce tim discourse retb, rent. Finally, we have t(/ take into account the possible role of temporal a(tverbials, which predicate over t. We associate thus a predicative DRS with the node Advl ~ adjoined to TP. This leads to the complete treatm(,nt of time sket(:hed her(,:</Paragraph>
      <Paragraph position="5"> What we have said so far should be suificient to mLderstand figure 2 (next page), whi(:h represents the (:onstruction procedure applied to the cxamt)h' (9).</Paragraph>
    </Section>
  </Section>
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