Expanding FLew with a Boolean connective

TL;DR

This paper introduces an extension to the FLew logic by adding a unary connective with specific algebraic properties, proving its conservativity, finite model property, and algebraic class characteristics.

Contribution

The paper presents a novel expansion of FLew with a unary connective, establishing its logical and algebraic properties and demonstrating its conservativity and finite model property.

Findings

The expanded logic is conservative.

The logic has the Finite Model Property.

The algebraic expansion forms an equational class.

Abstract

We expand FLew with a unary connective whose algebraic counterpart is the operation that gives the greatest complemented element below a given argument. We prove that the expanded logic is conservative and has the Finite Model Property. We also prove that the corresponding expansion of the class of residuated lattices is an equational class.