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Browsing Arts Research & Publications by Author "Baaz, Matthias"
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Item Open Access Dual systems of sequents and tableaux for many-valued logics(European Association for Theoretical Computer Science, 1993-01) Baaz, Matthias; Fermüller, Christian G.; Zach, RichardThe 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, we show 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.Item Open Access Elimination of cuts in first-order finite-valued logics(Institut für Informatik, 1994-01) Baaz, Matthias; Fermüller, Christian G.; Zach, RichardA uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.Item Open Access Note on calculi for a three-valued logic for logic programming(1992) Baaz, Matthias; Zach, RichardItem Open Access Systematic Construction of Natural Deduction Systems for Many-valued Logics: Extended Report(IEEE, 1993-05-01) Baaz, Matthias; Fermüller, Christian G.; Zach, RichardWe exhibit a construction principle for natural deduction systems for arbitrary finitely-many-valued first order logics. These systems are systematically obtained from sequent calculi, which in turn can be extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness and normal form theorems for the natural deduction systems.