|Time:|| 12 - 1:20 p.m.
Department of Philosophy
University of Pittsburgh
Topological Semantics for Modal Logic
|Abstract:||As Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the ``necessity'' operation is modeled by taking the interior of an arbitrary subset of a topological space. This talk will show how to extend this interpretation from propositional to first-order logic by using the topos of all sheaves on a space, or its equivalent notion of local homeomorphisms.|