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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Vydáno v:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 13
Hlavní autoři: Balasubramanian, A. R., Lang, Timo, Ramanayake, Revantha
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 29.06.2021
Témata:
Calculus
Computational complexity
Computer science
Fuzzy logic
Upper bound
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Abstract 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.
AbstractList 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.
Author Balasubramanian, A. R.
Lang, Timo
Ramanayake, Revantha
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  givenname: A. R.
  surname: Balasubramanian
  fullname: Balasubramanian, A. R.
  email: bala.ayikudi@tum.de
  organization: Technische Universität München,Institut für Informatik (I7),München,Germany
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  givenname: Timo
  surname: Lang
  fullname: Lang, Timo
  email: timo@logic.at
  organization: Technische Universität Wien,Institute of Logic and Computation,Vienna,Austria,A-1040
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  givenname: Revantha
  surname: Ramanayake
  fullname: Ramanayake, Revantha
  email: d.r.s.ramanayake@rug.nl
  organization: Computer Science and Artificial Intelligence University of Groningen,Bernoulli Institute for Mathematics,Groningen,Netherlands,NL-9747 AG
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Snippet 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...
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SubjectTerms Calculus
Computational complexity
Computer science
Fuzzy logic
Upper bound
Title Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics
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