Analytic Calculi for Monoidal T-norm Based Logic

Authors:
Matthias Baaz;Agata Ciabattoni;Franco Montagna
Affiliations:
Institut für Diskrete Mathematik und Geometrie, Wiedner Hauptstr. 8, A-1040 Vienna, Austria;Institut für Diskrete Mathematik und Geometrie, Wiedner Hauptstr. 8, A-1040 Vienna, Austria;Dipartimento di Matematica, University of Siena, Italy
Venue:
Fundamenta Informaticae
Year:
2004

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Abstract

Monoidal t-norm based logic MTL is the logic of left continuous t-norms. We introduce two analytic calculi for first-order MTL. These are obtained by lifting two sequent calculi for different fragments of this logic to the hypersequent level with subsequent addition of Avron's communication rule. Our calculi enable to prove the mid(hyper)sequent theorem. As corollaries follow Herbrand's theorem for first-order MTL, the decidability of its ∀∃-fragment and admissibility of Skolemization.