Dual systems of sequents and tableaux for many-valued logics

Workshop on Tableau-based Deduction, Marseille, 1993. Bulletin of the EATCS 51 (1993) 192–197 (with Matthias Baaz and Christian G. Fermüller)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, it is shown that for both of these systems there are always two dual proof systems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and the exclusion of the opposite truth value describe the same situation.)

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