Section:
Research Program
Type theory and typed -calculus
Among the various possible logics
that may be used, Church's simply typed
-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
-calculus, and so is our syntax-semantics interface model.
On the other hand, as shown by Gallin [43] ,
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).