A note on bases of admissible rules of proper axiomatic extensions of Lukasiewicz logic

TL;DR

This paper proves that for any proper axiomatic extension of infinite-valued Lukasiewicz logic, the set of single-conclusion admissible rules can be characterized by a finite basis, simplifying their analysis.

Contribution

It establishes that all single-conclusion admissible rules in these extensions are finitely based, providing a significant simplification in understanding their rule structure.

Findings

Single-conclusion admissible rules are finitely based in these logics.

The result applies to all proper axiomatic extensions of Lukasiewicz logic.

This simplifies the study of admissible rules in fuzzy logic systems.

Abstract

In this note we prove that single-conclusion admissible rules of any proper axiomatic extension of the infnite valued Lukasiewicz logic are finitely based.