Fuzzy Lattice-based Description Logic

TL;DR

This paper introduces LE-FALC, a fuzzy generalization of LE-ALC description logic, with a polynomial-time tableaux algorithm for reasoning in fuzzy formal contexts, extending the capabilities of existing logic frameworks.

Contribution

It presents a novel fuzzy description logic LE-FALC and a complete, sound polynomial-time reasoning algorithm for its knowledge bases, expanding reasoning in fuzzy formal contexts.

Findings

Polynomial-time tableaux algorithm for LE-FALC ABoxes

Complete and sound decision procedure for consistency checking

Extension to acyclic TBoxes with exponential-time algorithm

Abstract

Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes. In this work, we introduce a fuzzy generalization of LE-ALC called LE-FALC which provides a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic. This description logic can be used to represent and reason about knowledge in the formal framework of fuzzy formal contexts and fuzzy formal concepts. We provide a tableaux algorithm that provides a complete and sound polynomial-time decision procedure to check the consistency of LE-FALC ABoxes. As a result, we also obtain an exponential-time decision procedure for checking the consistency of LE-FALC with acyclic TBoxes by unraveling.