First-Order, Curry-Typed Logic for Natural Language Semantics

Abstract
The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. The paper sketches a system of tableau rules that implement the theory. Some extensions to the type theory are discussed, including type polymorphism, which provides a useful analysis of conjunctive terms. Such terms can be given a single polymorphic type that expresses the fact that they can conjoin phrases of any one type, yielding an expression of the same type.
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