## Section: Research Program

### Type Theory and Typed $\lambda $-Calculus

Among the various possible logics that may be used, Church's simply typed $\lambda $-calculus and simple theory of types (a.k.a. higher-order logic) play a central part. On the one hand, Montague semantics is based on the simply typed $\lambda $-calculus, and so is our syntax-semantics interface model. On the other hand, as shown by Gallin [41], the target logic used by Montague for expressing meanings (i.e., his intensional logic) is essentially a variant of higher-order logic featuring three atomic types (the third atomic type standing for the set of possible worlds).