Density Elimination for Semilinear Substructural Logics

TL;DR

This paper introduces a uniform density elimination method applicable to various semilinear substructural logics, demonstrating its effectiveness on involutive uninorm logic IUL and establishing its standard completeness.

Contribution

It provides a novel, uniform approach to density elimination in semilinear substructural logics, including a proof for IUL's density elimination and completeness.

Findings

Density elimination method successfully applied to IUL

Standard completeness of IUL established using the method

Unified approach applicable to multiple semilinear substructural logics

Abstract

We present a uniform method of density elimination for several semilinear substructural logics. Especially, the density elimination for the involutive uninorm logic IUL is proved. Then the standard completeness of IUL follows as a lemma by virtue of previous work by Metcalfe and Montagna.