Semilinear substructural logics with the finite embeddability property

TL;DR

This paper introduces three semilinear substructural logics, proves their completeness with respect to finite algebra classes, and establishes their status as substructural fuzzy logics.

Contribution

It constructs new semilinear substructural logics and proves their completeness and finite embeddability properties, advancing the understanding of substructural fuzzy logics.

Findings

Completeness of ULw and IULw with respect to finite UL and IUL-algebras.

Finite embeddability property for non-integral ULw and IULw-algebras.

Standard completeness of ULw, IULw, and HpsUL*w.

Abstract

In this paper, three semilinear substructural logics ULw, IULw and HpsUL*w are constructed. Then the completeness of ULw and IULw with respect to classes of finite UL and IUL-algebras, respectively, is proved. Algebraically, non-integral ULw and IULw-algebras have the finite embeddability property, which gives a characterization for finite UL and IUL-algebras. Furthermore, the standard completeness of ULw, IULw and HpsUL*w is proved, which shows that they are substructural fuzzy logics.