Rational fuzzy attribute logic

TL;DR

This paper introduces a rational fuzzy attribute logic that handles if-then formulas with rational truth degrees, providing completeness and decidability results, and characterizing entailment through least models.

Contribution

It develops a new rational fuzzy logic with graded entailment, completeness proofs, and a characterization of entailment based on least models, extending Pavelka-style logic.

Findings

The logic is complete in Pavelka style.

Depending on the structure of truth degrees, the logic is decidable.

Entailment can be characterized via least models.

Abstract

We present a logic for reasoning with if-then formulas which involve constants for rational truth degrees from the unit interval. We introduce graded semantic and syntactic entailment of formulas. We prove the logic is complete in Pavelka style and depending on the choice of structure of truth degrees, the logic is a decidable fragment of the Rational Pavelka logic (RPL) or the Rational Product Logic (R{\Pi}L). We also present a characterization of the entailment based on least models and study related closure structures.