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TOPOLOGY AND MODALITY: THE TOPOLOGICAL INTERPRETATION OF FIRST-ORDER MODAL LOGIC

Published online by Cambridge University Press:  01 August 2008

STEVE AWODEY*
Affiliation:
Carnegie Mellon University
KOHEI KISHIDA*
Affiliation:
University of Pittsburgh
*
*PHILOSOPHY DEPARTMENT, CARNEGIE MELLON UNIVERSITY E-mail:awodey@cmu.edu
PHILOSOPHY DEPARTMENT, UNIVERSITY OF PITTSBURGH E-mail:kok6@pitt.edu

Abstract

As McKinsey and 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. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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