Introduction to higher order categorical logic
Introduction to higher order categorical logic
Categorial Grammar and Discourse Representation Theory
COLING '94 Proceedings of the 15th conference on Computational linguistics - Volume 1
Towards abstract categorial grammars
ACL '01 Proceedings of the 39th Annual Meeting on Association for Computational Linguistics
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Journal of Logic and Computation
Hyperintensional dynamic semantics: analyzing definiteness with enriched contexts
FG'10/FG'11 Proceedings of the 15th and 16th international conference on Formal Grammar
Are (linguists') propositions (topos) propositions?
LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics
Weak familiarity and anaphoric accessibility in dynamic semantics
FG'10/FG'11 Proceedings of the 15th and 16th international conference on Formal Grammar
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So-called `dynamic' semantic theories such as Kamp's discourse representation theory and Heim's file change semantics account for such phenomena as crosssentential anaphora, donkey anaphora, and the novelty condition on indefinites, but compare unfavorably with Montague semantics in some important respects (clarity and simplicity of mathematical foundations, compositionality, handling of quantification and coordination). Preliminary efforts have been made by Muskens and by de Groote to revise and extend Montague semantics to cover dynamic phenomena. We present a new higher-order theory of discourse semantics which improves on their accounts by incorporating a more articulated notion of context inspired by ideas due to David Lewis and to Craige Roberts.On our account, a context consists of a common ground of mutually accepted propositions together with a set of discourse referents preordered by relative salience. Employing a richer notion of contexts enables us to extend our coverage beyond pronominal anaphora to a wider range of presuppositional phenomena, such as the factivity of certain sententialcomplement verbs, resolution of anaphora associated with arbitrarily complex definite descriptions, presupposition `holes' such as negation, and the independence condition on the antecedents of conditionals.Formally, our theory is expressed within a higher-order logic with natural number type, separation-style subtyping, and dependent coproducts parameterized by the natural numbers. The system of semantic types builds on proposals due to Thomason and to Pollard in which the type of propositions (static meanings of sentential utterances) is taken as basic and worlds are constructed from propositions (rather than the other way around as in standard Montague semantics).