Defeasible Inclusions in Low-Complexity DLs

TL;DR

This paper investigates the computational complexity of adding nonmonotonic reasoning, specifically Circumscription, to low-complexity description logics like DL-lite and EL, revealing a range of complexities from P to PSPACE.

Contribution

It provides a detailed complexity analysis of nonmonotonic extensions in low-complexity description logics, identifying fragments with varying computational complexities.

Findings

Complexity ranges from P to the second level of the polynomial hierarchy.

Some fragments reach PSPACE complexity and beyond.

Certain syntactic restrictions influence the computational difficulty.

Abstract

Some of the applications of OWL and RDF (e.g. biomedical knowledge representation and semantic policy formulation) call for extensions of these languages with nonmonotonic constructs such as inheritance with overriding. Nonmonotonic description logics have been studied for many years, however no practical such knowledge representation languages exist, due to a combination of semantic difficulties and high computational complexity. Independently, low-complexity description logics such as DL-lite and EL have been introduced and incorporated in the OWL standard. Therefore, it is interesting to see whether the syntactic restrictions characterizing DL-lite and EL bring computational benefits to their nonmonotonic versions, too. In this paper we extensively investigate the computational complexity of Circumscription when knowledge bases are formulated in DL-lite_R, EL, and fragments thereof. We identify fragments whose complexity ranges from P to the second level of the polynomial hierarchy, as well as fragments whose complexity raises to PSPACE and beyond.