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2010•Advances in Modal LogicRequires access

A Remark on Propositional Kripke Frames Sound for Intuitionistic Logic.

D. P. Skvortsov

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Abstract

Usually, in the Kripke semantics for intuitionistic propositional logic (or for superintuitionistic logics) partially ordered frames are used. Why? In this paper we propose an intrinsically intuitionistic motivation for that. Namely, we show that every Kripke frame (with an arbitrary accessibility relation), whose set of valid formulas is a superintuitionistic logic, is logically equivalent to a partially ordered Kripke frame.

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What this paper is about

Usually, in the Kripke semantics for intuitionistic propositional logic (or for superintuitionistic logics) partially ordered frames are used. Why? In this paper we propose an intrinsically intuitionistic motivation for that. Namely, we show that every Kripke frame (with an arbitrary accessibility relation), whose set of valid formulas is a superintuitionistic logic, is logically equivalent to a partially ordered Kripke frame.

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Available abstract

Usually, in the Kripke semantics for intuitionistic propositional logic (or for superintuitionistic logics) partially ordered frames are used. Why? In this paper we propose an intrinsically intuitionistic motivation for that. Namely, we show that every Kripke frame (with an arbitrary accessibility relation), whose set of valid formulas is a superintuitionistic logic, is logically equivalent to a partially ordered Kripke frame.

Key concepts: Kripke semantics, Intuitionistic logic, Kripke structure, Intermediate logic, Modal logic, Propositional variable, Well-formed formula, Zeroth-order logic

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