Steve Awodey: Topology and Modality

Prof. Steve Awodey
Carnegie Mellon University

Povzetek:  As Tarski showed in the 1940s, propositional modal logic is complete with respect to topological semantics, in which the "necessity" operator is interpreted as taking the open interior of an arbitrary subset of a topological space. In this talk, the topological interpretation is extended in a natural way to full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.