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

  • STEVE AWODEY (a1) and KOHEI KISHIDA (a2)
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.

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Corresponding author
*PHILOSOPHY DEPARTMENT, CARNEGIE MELLON UNIVERSITY E-mail:awodey@cmu.edu
PHILOSOPHY DEPARTMENT, UNIVERSITY OF PITTSBURGH E-mail:kok6@pitt.edu
References
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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