Involutive Commutative Residuated Lattice without Unit: Logics and Decidability

Published 10 Mar 2023 in math.LO | (2303.05672v1)

Abstract: We investigate involutive commutative residuated lattices without unit, which are commutative residuated lattice-ordered semigroups enriched with a unary involutive negation operator. The logic of this structure is discussed and the Genzten-style sequent calculus of it is presented. Moreover, we prove the decidability of this logic.

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