Type-theoretic logic with an operational account of intensionality

Chris Fox

Shalom Lappin

pp. 563-584

in: Bjørn Jespersen, Marie Duží (eds), Hyperintensionality, Synthese 192 (3), 2015.

Abstract

We formulate a Curry-typed logic with fine-grained intensionality within Turner’s typed predicate logic. This allows for an elegant presentation of a theory that corresponds to Fox and Lappin’s property theory with curry typing, but without the need for a federation of languages. We then consider how the fine-grained intensionality of this theory can be given an operational interpretation. This interpretation suggests itself as expressions in the theory can be viewed as terms in the untyped lambda-calculus, which provides a model of computation.