Involutive Commutative Residuated Lattice without Unit: Logics and Decidability

2023/03/10 by Yiheng Wang, Wang, Yiheng, Hao Zhan +5
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Rough Sets and Fuzzy Logic #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2303.05672

openalex publication_date 2023/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate involutive commutative residuated lattices without unit, which are commutative residuated lattice-ordered semigroups enriched with a unary involutive negation operator. The logic of this structure is discussed and the Genzten-style sequent calculus of it is presented. Moreover, we prove the decidability of this logic.

Related

• Densification in classes of involutive commutative residuated lattices
• The structure of finite commutative idempotent involutive residuated\n lattices
• The Hahn embedding theorem for a class of residuated semigroups
• Families of local involutive integral residuated lattice-ordered commutative monoids admitting Boolean term
• Amalgamation in classes of involutive commutative residuated lattices