Topology and modality: The topological interpretation of first-order modal logic: Topology and modality

Review of Symbolic Logic 1 (2):146-166 (2008)
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Abstract

As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for 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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10.1017/s1755020308080143

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Steve Awodey
Carnegie Mellon University

Citations of this work

First order S4 and its measure-theoretic semantics.Tamar Lando - 2015 - Annals of Pure and Applied Logic 166 (2):187-218.
Quantified modal logic on the rational line.Philip Kremer - 2014 - Review of Symbolic Logic 7 (3):439-454.
Affine logic for constructive mathematics.Michael Shulman - 2022 - Bulletin of Symbolic Logic 28 (3):327-386.

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References found in this work

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Mathematical Intuitionism. Introduction to Proof Theory.A. G. Dragalin & E. Mendelson - 1990 - Journal of Symbolic Logic 55 (3):1308-1309.
Incompleteness results in Kripke semantics.Silvio Ghilardi - 1991 - Journal of Symbolic Logic 56 (2):517-538.

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