Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics

We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FL ew (i.e. IMALLW) that have a cut-free hypersequent proof calculus. Specifically: every analytic structural rule extension of HFL ew . Decidability for the corresponding exten...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13
Main Authors: Balasubramanian, A. R., Lang, Timo, Ramanayake, Revantha
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Calculus
Computational complexity
Computer science
Fuzzy logic
Upper bound
Online Access:Get full text
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Summary:We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FL ew (i.e. IMALLW) that have a cut-free hypersequent proof calculus. Specifically: every analytic structural rule extension of HFL ew . Decidability for the corresponding extensions of its contraction counterpart FL ec was established recently but their computational complexity was left unanswered. In the second part of this paper, we introduce just enough on length functions for well-quasi-orderings and the fast-growing complexity classes to obtain complexity upper bounds for both the weakening and contraction extensions. A specific instance of this result yields the first complexity bound for the prominent fuzzy logic MTL (monoidal t-norm based logic) providing an answer to a longstanding open problem.
DOI:10.1109/LICS52264.2021.9470733