Anaphora and the Logic of Change

This paper shows how the dynamic interpretation of natural language introduced in work by Hans Kamp and Irene Heim can be modeled in classical type logic. This provides a synthesis between Richard Montague's theory of natural language semantics and the work by Kamp and Heim

Feature-based and Model-based Semantics for English, French and German Verb Phrases

This paper considers the relative merits of using features and formal event models to characterise the semantics of English, French and German verb phrases, and con- siders the application of such semantics in machine translation. The feature-based ap- proach represents the semantics in terms of feature systems, which have been widely used in computational linguistics for representing complex syntactic structures. The paper shows how a simple intuitive semantics of verb phrases may be encoded as a feature system, and how this can be used to support modular construction of au- tomatic translation systems through feature look-up tables. This is illustrated by automated translation of English into either French or German. The paper contin- ues to formalise the feature-based approach via a model-based, Montague semantics, which extends previous work on the semantics of English verb phrases. In so doing, repercussions of and to this framework in conducting a contrastive semantic study are considered. The model-based approach also promises to provide support for a more sophisticated approach to translation through logical proof; the paper indicates further work required for the fulfilment of this promise

Semantic Ambiguity and Perceived Ambiguity

I explore some of the issues that arise when trying to establish a connection between the underspecification hypothesis pursued in the NLP literature and work on ambiguity in semantics and in the psychological literature. A theory of underspecification is developed `from the first principles', i.e., starting from a definition of what it means for a sentence to be semantically ambiguous and from what we know about the way humans deal with ambiguity. An underspecified language is specified as the translation language of a grammar covering sentences that display three classes of semantic ambiguity: lexical ambiguity, scopal ambiguity, and referential ambiguity. The expressions of this language denote sets of senses. A formalization of defeasible reasoning with underspecified representations is presented, based on Default Logic. Some issues to be confronted by such a formalization are discussed.Comment: Latex, 47 pages. Uses tree-dvips.sty, lingmacros.sty, fullname.st

A Compositional Treatment of Polysemous Arguments in Categorial Grammar

We discuss an extension of the standard logical rules (functional application and abstraction) in Categorial Grammar (CG), in order to deal with some specific cases of polysemy. We borrow from Generative Lexicon theory which proposes the mechanism of {\em coercion}, next to a rich nominal lexical semantic structure called {\em qualia structure}. In a previous paper we introduced coercion into the framework of {\em sign-based} Categorial Grammar and investigated its impact on traditional Fregean compositionality. In this paper we will elaborate on this idea, mostly working towards the introduction of a new semantic dimension. Where in current versions of sign-based Categorial Grammar only two representations are derived: a prosodic one (form) and a logical one (modelling), here we introduce also a more detaled representation of the lexical semantics. This extra knowledge will serve to account for linguistic phenomena like {\em metonymy\/}.Comment: LaTeX file, 19 pages, uses pubsmacs, pubsbib, pubsarticle, leqn

Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most

This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical semantics. The meanings are viewed as logical formulae that can thereafter be interpreted in your favourite models. To do so, we depart significantly from the dominant Fregean view with a single untyped universe. Indeed, our proposal adopts type theory with some hints from Hilbert \epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et al. 2010; Moot, Pr\'evot and Retor\'e 2011). Our model also applies to classical examples involving a class, or a generic element of this class, which is not uttered but provided by the context. An outcome of this study is that, in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type theoretical view, terms encode the purely semantic meaning component while their typing is pragmatically determined

Tense and the Logic of Change

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic