Journal of Logic, Language and Information

, Volume 12, Issue 2, pp 213–225

A Cut-Free Gentzen Formulation of Basic Propositional Calculus

Authors

  • Kentaro Kikuchi
    • Department of Mathematics and InformaticsChiba University
  • Katsumi Sasaki
    • Department of Mathematical SciencesNanzan University
Article

DOI: 10.1023/A:1022363219134

Cite this article as:
Kikuchi, K. & Sasaki, K. Journal of Logic, Language and Information (2003) 12: 213. doi:10.1023/A:1022363219134
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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.

Basic Propositional Calculuscut-eliminationdual-context systemGentzen systemKripke model
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© Kluwer Academic Publishers 2003