TY - JOUR
T1 - Topology and Modality
T2 - The topological interpretation of first-order modal logic
AU - Awodey, Steve
AU - Kishida, Kohei
N1 - Publisher Copyright:
© 2008 Association for Symbolic Logic.
PY - 2008/8/1
Y1 - 2008/8/1
N2 - 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.
AB - 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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U2 - 10.1017/S1755020308080143
DO - 10.1017/S1755020308080143
M3 - Article
AN - SCOPUS:84989195875
SN - 1755-0203
VL - 1
SP - 146
EP - 166
JO - Review of Symbolic Logic
JF - Review of Symbolic Logic
IS - 2
ER -