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

被引：18

作者：

Awodey, Steve ^{[1
]}

Kishida, Kohei ^{[2
]}

机构：

[1] Carnegie Mellon Univ, Dept Philosophy, Pittsburgh, PA 15213 USA

[2] Univ Pittsburgh, Dept Philosophy, Pittsburgh, PA 15260 USA

来源：

REVIEW OF SYMBOLIC LOGIC | 2008年 / 1卷 / 02期

关键词：

D O I：

10.1017/S1755020308080143

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：146 / 166

页数：21

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