We present a framework for intensional reasoning in typed -calculus. In this family of calculi, called Modal Pure Type Systems (MPTSs), a propositions-as-types-interpretation can be given for normal modal logics. MPTSs are an extension of the Pure Type Systems (PTSs) of Barendregt (1992). We show that they retain the desirable meta-theoretical properties of PTSs, and briefly discuss applications in the area of knowledge representation.
Within the community of researchers applying type theory to natural language there have been proposals to use contexts from type theory to model information states and to use context extension to model information updates. Examples of this are Ranta (1994) and research conducted in the DenK project (e.g. Ahn, 1995, Ahn and Borghuis, 1998).