On the Undecidability of Fuzzy Description Logics with GCIs with Lukasiewicz t-norm

TL;DR

This paper proves that the problem of determining satisfiability of knowledge bases in fuzzy description logics with GCIs under Lukasiewicz t-norm is undecidable, extending previous results for other fuzzy logics.

Contribution

It establishes the undecidability of knowledge base satisfiability in Fuzzy Description Logics with GCIs under Lukasiewicz Logic, completing the theoretical analysis.

Findings

Knowledge base satisfiability is undecidable under Lukasiewicz Logic.

Undecidability also holds for Product Logic, previously known.

Contrasts classical DL properties with fuzzy extensions.

Abstract

Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic and, specifically, knowledge base satisfiability is an undecidable problem for Product Logic. We complete here the analysis by showing that knowledge base satisfiability is also an undecidable problem for Lukasiewicz Logic.