A cut-free Gentzen formulation of basic propositional calculus

Abstract
We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved in a syntactic way by modifying Gentzen's method. Thisdual-context style system exemplifies the effectiveness of dual-contextformulation in formalizing various non-classical logics.
Keywords Basic Propositional Calculus  cut-elimination  dual-context system  Gentzen system  Kripke model
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Reprint years 2004
DOI 10.1023/A:1022363219134
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