Journal of Logic, Language and Information

, Volume 12, Issue 2, pp 213-225

First online:

A Cut-Free Gentzen Formulation of Basic Propositional Calculus

  • Kentaro KikuchiAffiliated withDepartment of Mathematics and Informatics, Chiba University
  • , Katsumi SasakiAffiliated withDepartment of Mathematical Sciences, Nanzan University

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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.

Basic Propositional Calculus cut-elimination dual-context system Gentzen system Kripke model