Topological completeness for higher-order logic
نویسندگان
چکیده
منابع مشابه
Topological Completeness for Higher-Order Logic
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces—so-called “topological semantics”. The first is classical higherorder logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over a...
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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 ...
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We present several results concerning deductive completeness of the simply typed λcalculus with constants and equational axioms. First, we prove deductive completeness of the calculus with respect to standard semantics for axioms containing neither free nor bound occurrences of higher-order variables. Using this result, we analyze some fundamental deductive and semantic properties of axiomatic ...
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A classical result on topological semantics of modal logic due to McKinsey and Tarski (often called Tarski theorem) states that the logic S4 is complete with respect to interpretations in R for each n. Recently several authors have considered dynamic topological logics, which are interpreted in dynamic spaces (abstract dynamic systems). A dynamic space is a topological space together with a con...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2000
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2586693