Journal of Logic, Language and Information
, Volume 12, Issue 2, pp 213225
A CutFree 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 adualcontext 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 cutelimination theorem isproved in a syntactic way by modifying Gentzen's method. Thisdualcontext style system exemplifies the effectiveness of dualcontextformulation in formalizing various nonclassical logics.
 Title
 A CutFree Gentzen Formulation of Basic Propositional Calculus
 Journal

Journal of Logic, Language and Information
Volume 12, Issue 2 , pp 213225
 Cover Date
 200303
 DOI
 10.1023/A:1022363219134
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Basic Propositional Calculus
 cutelimination
 dualcontext system
 Gentzen system
 Kripke model
 Authors

 Kentaro Kikuchi ^{(1)}
 Katsumi Sasaki ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Informatics, Chiba University, 133 Yayoicho, Inageku, Chiba, 2638522, Japan
 2. Department of Mathematical Sciences, Nanzan University, 27 Seireicho, Setosi, Aichi, 4890863, Japan