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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lando, Tamar 2015. First order S4 and its measure-theoretic semantics. Annals of Pure and Applied Logic, Vol. 166, Issue. 2, p. 187.


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    Kishida, Kohei 2011. Neighborhood-Sheaf Semantics for First-Order Modal Logic. Electronic Notes in Theoretical Computer Science, Vol. 278, p. 129.


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

  • STEVE AWODEY (a1) and KOHEI KISHIDA (a2)
  • DOI: http://dx.doi.org/10.1017/S1755020308080143
  • Published online: 01 August 2008
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
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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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