Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics

04/20/2021
by   A. R. Balasubramanian, et al.
0

We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus (specifically: every analytic structural rule extension). Decidability for the corresponding extensions of its contraction counterpart FLec 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 long-standing open problem.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

01/07/2022

TOWER-Complete Problems in Contraction-Free Substructural Logics

We investigate the computational complexity of a family of substructural...
03/03/2020

Decision Problems for Propositional Non-associative Linear Logic and Extensions

In our previous work, we proposed the logic obtained from full non-assoc...
01/19/2020

Infinitary Action Logic with Exponentiation

We introduce infinitary action logic with exponentiation—that is, the mu...
02/10/2021

Logics of involutive Stone algebras

An involutive Stone algebra (IS-algebra) is a structure that is simultan...
09/12/2018

A Curry-Howard Correspondence for the Minimal Fragment of Łukasiewicz Logic

In this paper we introduce a term calculus B which adds to the affine λ...
04/15/2019

On the Lambek Calculus with an Exchange Modality

In this paper we introduce Commutative/Non-Commutative Logic (CNC logic)...
11/09/2017

h: A Plank for Higher-order Attribute Contraction Schemes

We present and formalize h, a core (or "plank") calculus that can serve ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.