Involutive uninorm logic with fixed point enjoys finite strong standard completeness

TL;DR

This paper proves finite strong standard completeness for involutive uninorm logic with fixed point, advancing understanding of its foundational properties and potentially resolving an open problem in substructural fuzzy logics.

Contribution

It provides the first algebraic proof of finite strong standard completeness for this logic, addressing an open problem in the field.

Findings

Finite strong standard completeness established.

Algebraic proof method introduced.

Progress towards solving an open completeness problem.

Abstract

An algebraic proof is presented for the finite strong standard completeness of involutive uninorm logic with fixed point. The result may provide a first step towards settling the open standard completeness problem for involutive uninorm logic posed in [G. Metcalfe, F. Montagna: Substructural fuzzy logics, J. Symb. Logic, 72, 834-864 (2007)].