On the relationship between fuzzy logic and four-valued relevance logic

TL;DR

This paper explores how fuzzy logic can reduce to four-valued relevance logic under specific conditions, linking fuzzy truth values with a four-valued logical framework and positioning fuzzy entailment between classical and relevance entailment.

Contribution

It demonstrates the conditions under which fuzzy logic collapses to four-valued relevance logic, establishing a connection between fuzzy truth values and four-valued logic.

Findings

Fuzzy logic collapses to four-valued relevance logic under dual conditions.

Fuzzy entailment is positioned between classical and relevance entailment.

The paper clarifies the relationship between fuzzy truth values and four-valued logic.

Abstract

In fuzzy propositional logic, to a proposition a partial truth in [0,1] is assigned. It is well known that under certain circumstances, fuzzy logic collapses to classical logic. In this paper, we will show that under dual conditions, fuzzy logic collapses to four-valued (relevance) logic, where propositions have truth-value true, false, unknown, or contradiction. As a consequence, fuzzy entailment may be considered as ``in between'' four-valued (relevance) entailment and classical entailment.