The logic of pseudo-uninorms and their residua

TL;DR

This paper extends density elimination to non-commutative substructural logic GpsUL*, proving its completeness and establishing it as the logic of pseudo-uninorms and their residua, thus answering a key open question.

Contribution

It generalizes density elimination to GpsUL* and proves its completeness, identifying it as the logic of pseudo-uninorms and their residua.

Findings

GpsUL* is complete via density elimination.

Established GpsUL* as the logic of pseudo-uninorms.

Answered an open question in substructural logic.

Abstract

Our method of density elimination is generalized to the non-commutative substructural logic GpsUL*. Then the standard completeness of GpsUL* follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that GpsUL* is the logic of pseudo-uninorms and their residua and answered the question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis.