Quantification and Anaphora in Natural Language

Abstract

We study several cases of functional anaphora in natural language, that is, cases in which there is a functional correlation between individuals in the domain, introduced in the form of two nested quantifi ers "For every x there is an y . . ." followed by anaphorical references to any pair instantiating the two quantifi ers. After discussing the impossibility of contemporary dynamic theories to deal with this phenomenon, we review some of the main approaches which have tried to address this problem. We end up with some considerations on the representation of quantifi ers and anaphora and with some prospects for further work. Functional dependence in natural languageThe standard view according to which indefi nites in natural language are to be assimilated to existential quantifi ers functions approximatively well if evidence is restricted to sentences like (1) Every man reads a book.It has been often observed that this sentence is ambiguous between two readingscorresponding to the indefi nite having a "narrow" or "wide scope" with respect to the quantifi ed NP 'every man'. The indefi nites as existential quantifi ers view seem to account for this phenomenon, for it is only of a quantifi er or of an operator that it makes sense to say that it is in the scope of another. Problems appear, however, as soon as anaphorical pronouns are involved. For in this case, on the traditional view which regards the relation Unauthenticated Download Date | 6/24/16 8:15 PM 610 Gabriel Sandu and Justine Jacot between an anaphor and its head as one of coreference, one is enclined to view(2) A man smiles. He is happy . as involving the same semantical scheme as(3) John smiles. He is happy .A uniform account of the two NP's in the subject position would then treat both of them referentially, with coreference indicated, as ususal, by an identity statement between two terms or by the pronoun being represented by a copy of its head. In fact, this is the way in which indefi nites are treated in one of the most popular semantic theories born in the early eighties, in both of its versions: Discourse Representation Theory (Kamp 1981) and File Semantics (Heim 1982). Discourse Representation TheoryDRT fi rst converts each of the two sentences into a Discourse Representation Structure ( DRS ), a syntactic entity consisting of reference markers and conditions. Both the indefi nite "A man" and the proper name "John" introduce a reference marker, that is, a free variable, say x . Later on, when "He" is processed, a new reference marker is introduced, say y , together with an identity statement x = y (a condition) which indicates the resolution of anaphora. The fi nal DRSs corresponding to (2) and (3) are respectively: D 2 : ({x,y}, {man(x), smiles(x), happy(y), x = y}) D 3 : ({x,y}, { John(x) , smiles(x), happy(y), x = y})We have a quasi-referential view of indefi nites: they are free variables, and so are anaphorical pronouns. This view has the advantage, over the indefinites as existential quantifi ers view, that a free variable is in principle ...

Knowledge and Its Game-Theoretical Foundations: The Challenges of the Dialogical Approach to Constructive Type Theory

“…Notice how close this formulation is to the one proposed by Sandu/Jacot (2012): the crucial difference is that in Sundholm's formulation the relevant functions are explicit proof-objects. 57 Sundholm uses the membership sign instead of the colon.…”

“…Hintikka's main idea is that a Skolemization of the strategies yields a correct analysis of the anaphora. Sandu/Jacot (2012) added the further step of introducing the skolemization in the object language level by means of Skolem terms.…”

“…(Walkoe 1970, Enderton 1970. Thus, IF logic captures exactly the expressive power of Henkin's branching quantifiers, though according to A classic example of a natural language sentence that involves branching quantifiers from (Hintikka 1973, p. 344 If we formulate this in the new Skolem-terms-frame proposed by Sandu and Jacot (2012) we obtain:…”

“…(Hintikka, 1997, p. 530) What Hintikka seems to be aiming at is to stress the cases where the relevant meaning-relation between a quantifier and the quantified expression is a relation of dependence rather than a compositional one, and that such dependences should be understood as interaction. This was one of the main motivation for a GTS-approach to anaphora and it was further developed by Sandu and his associates (Sandu 1997, Sandu/Jacot 2012. In other words, the main point of anaphora is dependence, dependence is interaction, and thus a semantics of interaction is required.…”

Problematic pronominal anaphora

“…STI rešenje anafore razvili su detaljnije Sandu(1997) i Sandu, Jacot(2012). Po ovom pristupu, neodređene zamenice su izražene kao Skolemovi termini, što je vrlo zgodno jer oni beleže čitavu istoriju igre.…”