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We establish decidability for the infinitely many axiomatic extensions of thecommutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have acut-free hypersequent proof calculus (specifically: every analytic structuralrule extension). Decidability for the corresponding extensions of itscontraction counterpart FLec was established recently but their computationalcomplexity was left unanswered. In the second part of this paper, we introducejust enough on length functions for well-quasi-orderings and the fast-growingcomplexity classes to obtain complexity upper bounds for both the weakening andcontraction extensions. A specific instance of this result yields the firstcomplexity bound for the prominent fuzzy logic MTL (monoidal t-norm basedlogic) providing an answer to a long-standing open problem.

Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics