Disjunctive Logic Programs with Inheritance

TL;DR

The paper introduces DLP<, an extension of disjunctive logic programming with inheritance, enhancing knowledge representation and default reasoning capabilities without increasing computational complexity.

Contribution

It presents a new language DLP< with a formal semantics, demonstrates its expressiveness, and shows inheritance does not add computational overhead, supported by an implementation.

Findings

DLP< generalizes answer set semantics for disjunctive logic programs.

Inheritance in DLP< does not increase reasoning complexity.

An efficient translation from DLP< to plain disjunctive logic programming exists.

Abstract

The paper proposes a new knowledge representation language, called DLP<, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language providing a natural representation of default reasoning with exceptions. A declarative model-theoretic semantics of DLP< is provided, which is shown to generalize the Answer Set Semantics of disjunctive logic programs. The knowledge modeling features of the language are illustrated by encoding classical nonmonotonic problems in DLP<. The complexity of DLP< is analyzed, proving that inheritance does not cause any computational overhead, as reasoning in DLP< has exactly the same complexity as reasoning in disjunctive logic programming. This is confirmed by the existence of an efficient translation from DLP< to plain disjunctive logic programming. Using this translation, an advanced KR system supporting the DLP< language has been implemented on top of the DLV system and has subsequently been integrated into DLV.