Resolution in Linguistic Propositional Logic based on Linear Symmetrical Hedge Algebra

TL;DR

This paper develops a propositional linguistic logic based on linear symmetrical hedge algebra, defining logical connectives with G"{o}del's t-norm and t-conorm, and introduces a resolution inference rule with reliability for uncertain reasoning.

Contribution

It introduces a novel linguistic propositional logic system with resolution inference based on hedge algebra and reliability, advancing uncertain reasoning with linguistic information.

Findings

Resolution rule handles contradictory linguistic truth values

Reliability concept captures approximation in inference

Resolution procedure maximizes reliability

Abstract

The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider G\"{o}del's t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.