A Model-Theoretic Reconstruction of Type-Theoretic Semantics for Anaphora

Abstract

I present an analysis of the interpretation of anaphora that takes concepts from type-theoretic semantics, in particular the use of the Σ and Π dependent type constructors, and incorporates them into a model-theoretic framework. The analysis makes use of (parametrically) polymorphic lexical entries. The key ideas are that, in the simplest case, eventualities can play the role that proof objects do in type-theoretic semantics; that more complex, compositionally-defined, structures can play that role in other cases; and that pronouns can be modelled by contextdependent functions from proof objects of the preceding discourse (in this sense) to entities.

Quantificational Subordination as Anaphora to a Function

“…In [11], an implementation of the ideas behind TTS is given in simple type theory with polymorphism, once again treating the language of terms as the meaning representation language. Taking the perspective outlined in [11], equivalents for (7) and (8) are shown in (9) and (10), respectively.…”

“…In [11], an implementation of the ideas behind TTS is given in simple type theory with polymorphism, once again treating the language of terms as the meaning representation language. Taking the perspective outlined in [11], equivalents for (7) and (8) are shown in (9) and (10), respectively. The reader can verify that these represent the same meanings as given in (7) and (8) according to the glosses provided, on the understanding that, following a suggestion by [25,Sect.…”

“…where τ := e → e × v Like TTS, the system described in [11] does not straightforwardly have the means to account for the examples (5)- (6). In this section an extension is described that does so, on the basis of the lexicon shown in Fig.…”

“…The syntactic theory assumed here is a modified version of Combinatory Categorial Grammar (CCG, [27]) according to which syntactic categories are potentially parameterized by types. Lexical entries are pairs M : C of meaning M and category C such that the type of M is Ty(C), where Ty is as defined in (11). The combinatory rules for the fragment are shown in Fig.…”

Variable Handling and Compositionality: Comparing DRT and DTS

“…We will leave a comparison between DTS and DCG for another occasion. See alsoGotham (2018) for a comparison between the version of DTS-based compositional semantics presented inBekki (2014) and its reconstruction in simple type theory.…”