In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp . The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.
In this paper we develop the beginnings of a tableau system for natural logic, the logic that is present in ordinary language and that us used in ordinary reasoning. The system is based on certain terms of the typed lambda calculus that can go proxy for linguistic forms and which we call Lambda Logical Forms. It is argued that proof-theoretic methods like… (More)
An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach , which underlies the Description Theory of (Marcus et al. 1983) was integrated with a pure… (More)
Eindhoven. Het is gefinancierd door het Samenwerkingsorgaan Brabantse Univer-siteiten (SOBU), onder projectcode 99-M, Hintikka's revolution in the foundations of mathematics. Preface People compare the process of writing a PhD-thesis with all kinds of things. When I had just decided to undertake this adventure, I was very happy to hear from a recent… (More)
In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this… (More)