Embedding Description Logic Programs into Default Logic

TL;DR

This paper demonstrates how description logic programs under answer set semantics can be embedded into default logic, providing a unified formalism for integrating rules and ontologies with polynomial and modular translations.

Contribution

It introduces a novel embedding of dl-programs into default logic, covering various semantics and extending to weakly well-supported answer sets, enhancing the formal foundation for ontology-rule integration.

Findings

Embedding is polynomial, faithful, and modular for certain dl-programs.

Two translations effectively eliminate nonmonotonic dl-atoms.

Default logic serves as a promising foundation for ontology-rule integration.

Abstract

Description logic programs (dl-programs) under the answer set semantics formulated by Eiter {\em et al.} have been considered as a prominent formalism for integrating rules and ontology knowledge bases. A question of interest has been whether dl-programs can be captured in a general formalism of nonmonotonic logic. In this paper, we study the possibility of embedding dl-programs into default logic. We show that dl-programs under the strong and weak answer set semantics can be embedded in default logic by combining two translations, one of which eliminates the constraint operator from nonmonotonic dl-atoms and the other translates a dl-program into a default theory. For dl-programs without nonmonotonic dl-atoms but with the negation-as-failure operator, our embedding is polynomial, faithful, and modular. In addition, our default logic encoding can be extended in a simple way to capture recently proposed weakly well-supported answer set semantics, for arbitrary dl-programs. These results reinforce the argument that default logic can serve as a fruitful foundation for query-based approaches to integrating ontology and rules. With its simple syntax and intuitive semantics, plus available computational results, default logic can be considered an attractive approach to integration of ontology and rules.