A Higher-order Fine-grained Logic for Intensional Semantics

This paper describes a higher-order logic with fine-grained intensionality (FIL). Unlike traditional Montogovian type theory, intensionality is treated as basic, rather than derived through possible worlds. This allows for fine-grained intensionality without impossible worlds. Possible worlds and modalities are defined algebraically. The proof theory for FIL is given as a set of tableau rules, and an algebraic model theory is specified. The proof theory is shown to be sound relative to this model theory. FIL avoids many of the problems created by classical course-grained intensional logics that have been used in formal and computational semantics.1