Abstract
We introduce a Gentzen style formulation of Basic Propositional Calculus (BPC), the logic that is interpreted in Kripke models similarly to intuitionistic logic except that the accessibility relation of each model is not necessarily reflexive. The formulation is presented as a dual-context style system, in which the left hand side of a sequent is divided into two parts. Giving an interpretation of the sequents in Kripke models, we show the soundness and completeness of the system with respect to the class of Kripke models. The cut-elimination theorem is proved in a syntactic way by modifying Gentzen's method. This dual-context style system exemplifies the effectiveness of dual-context formulation in formalizing various non-classical logics.
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