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Logic Journal of IGPL 2001 9(6):793-812; doi:10.1093/jigpal/9.6.793
© 2001 by Oxford University Press
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Intuitionistic sequent calculi for finitely many-valued logics

E ReznikA1 and P CurminA2

A1 Institut Supérieur d'Electronique de Paris, 21 rue d'Assas, 75006 Paris, France E-mail: eugenia.reznik@isep.fr A2 Trusted Logic, 5 rue du Bailliage, 78000 Versailles, France E-mail: curmin@logique.jussieu.fr

We present an intuitionistic sequent calculus for arbitrary finitely many-valued logics which has a positive semantics given by a natural extension of Kripke models. Our calculus has two types of rules: introduction rules and pseudo-cut rules. The introduction rules introduce formulas at all places on the left or on the right hand side of a sequent. They generalize the introduction rules of 2-places sequent calculus. The pseudo-cut rules allow to introduce formulas in the middle of a sequent. They may not exist in a 2-places sequent calculus. We show the soundness and completeness of our system and we study in detail the cut elimination procedure for these calculi.

Key Words: finitely many-valued logics, sequent calculus, Kripke models, cut elimination


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