Doing Natural Language Semantics in an Expressive First-Order Logic with Flexible Typing

A BSTRACT. We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types.1 We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like most. We use the type system and our treatment of generalized quantifiers in natural language to construct a typetheoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous type-theoretic analyses of this phenomenon.
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Chris Fox & Shalom Lappin (2004). An Expressive First-Order Logic with Flexible Typing for Natural Language Semantics. Logic Journal of the Interest Group in Pure and Applied Logics 12 (2):135--168.
Melvin Fitting (2004). First-Order Intensional Logic. Annals of Pure and Applied Logic 127 (1-3):171-193.

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