Residuated Basic Logic-Reference-Cited by-同舟云学术

Residuated Basic Logic

Published:2023-10-13 Issue:10 Volume:12 Page:966
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Lin Zhe¹^ORCID,Ma Minghui²^ORCID

Affiliation:

1. Department of Philosophy, Xiamen University, Xiamen 361005, China

2. Department of Philosophy, Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China

Abstract

Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a non-associative binary operator in RBL. The conservativity is shown by relational semantics. A Gentzen-style sequent calculus GRBL, which is an extension of the distributive full non-associative Lambek calculus, is established for residuated basic logic. The calculus GRBL admits the mix-elimination, subformula, and disjunction properties. Moreover, the class of all residuated basic algebras has the finite embeddability property. The consequence relation of GRBL is decidable.

Funder

CENTRAL UNIVERSITY BASIC RESEARCH PROJECT

CHINA FUNDING OF SOCIAL SCIENCES

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/10/966/pdf

Reference32 articles.

1. A closer look at some subintuitionistic logics;Celani;Notre Dame J. Form. Log.,2003

2. Subintuitionistic logics;Restall;Notre Dame J. Form. Log.,1994

3. A propositional logic with explicit fixed points;Visser;Stud. Log.,1981

4. Chagrov, A., and Zakharyaschev, M. (1997). Modal Logic, Clarendon Press.

5. Weak logics with strict implication;Corsi;Zeitschr. F. Math. Logik Grundlagen D. Math.,1987