The complexity of fuzzy EL under the Łukasiewicz T-norm

Abstract

Fuzzy Description Logics (DLs) are are a family of knowledge representation formalisms designed to represent and reason about vague and imprecise knowledge that is inherent to many application domains. Previous work has shown that the complexity of reasoning in a fuzzy DL using finitely many truth degrees is usually not higher than that of the underlying classical DL. We show that this does not hold for fuzzy extensions of the lightweight DL EL, which is used in many biomedical ontologies, under the finitely valued Łukasiewicz semantics. More precisely, the complexity of reasoning increases from P to ExpTime, even if only one additional truth value is introduced. When adding complex role inclusions and inverse roles, the logic even becomes undecidable. Even more surprisingly, when considering the infinitely valued Łukasiewicz semantics, reasoning in fuzzy EL is undecidable.

Minimalistic fuzzy ontology reasoning: An application to Building Information Modeling

“…In classical ontologies, the OWL 2 language has three sublanguages or profiles with tractable reasoning (i.e., the main reasoning tasks can be solved in a polynomial time), namely OWL 2 EL, OWL 2 QL, and OWL 2 RL [28]. In the fuzzy case, it has been showed that fuzzy extensions of tractable languages are not tractable in general [29], and they can even be undecidable [30]. Despite this fact, some fuzzy extensions of tractable DLs have been investigated, including fuzzy extensions of the logics behind OWL 2 EL [31,32], OWL 2 QL [33], and OWL 2 RL [34].…”

Fuzzy Description Logics – A Survey

“…On the other hand, consistency in Ł-NALC remains undecidable even without ¬ and ∀, and with only crisp axioms [39]. Very recently, it was discovered that even Ł-EL, which extends a logic with polynomial complexity in the classical case, has an undecidable consistency problem [27,28]; however, no such result is known for the variant Π-EL with product semantics. For a detailed discussion of the border between decidability and undecidability in t-norm-based FDLs, we refer the reader to [33].…”

From Fuzzy to Annotated Semantic Web Languages

“…• their reasoning algorithms and computational complexity results [5,6,12,14,15,17,18,19,23,34,37,39,40,42,11,44,45,50,51,54,55,56,57,58,60,59,61,249,49,46,53,62,48,63,72,73,74,114,222,252,255,256,260,261,268,273,275,289,290,315,320].…”