Topological Completeness of First-order Modal Logic
نویسندگان
چکیده
As McKinsey and Tarski [19] 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. The topological interpretation was extended by Awodey and Kishida [3] in a natural way to arbitrary theories of full first-order logic. This paper proves the resulting system of first-order S4 modal logic to be complete with respect to such topological semantics.
منابع مشابه
Topological Completeness of First-Order Modal Logics
As McKinsey and Tarski [20] 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. This topological interpretation was recently extended in a natural way to arbitrary...
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