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 For AllThere Exists-fragment and admissibility of Skolemization.

M., B., A., C., & Montagna, F. (2004). Analytic Calculi for Monoidal T-norm Based Logic. FUNDAMENTA INFORMATICAE, 59(4), 315-332.

Analytic Calculi for Monoidal T-norm Based Logic

MONTAGNA, FRANCO
2004

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 For AllThere Exists-fragment and admissibility of Skolemization.
M., B., A., C., & Montagna, F. (2004). Analytic Calculi for Monoidal T-norm Based Logic. FUNDAMENTA INFORMATICAE, 59(4), 315-332.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/7147
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