Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases

TL;DR

This paper introduces a new algorithm for reasoning in Forest Logic Programs, a decidable fragment of Open Answer Set Programming, and extends it to a hybrid framework combining ontologies and rules without DL-safety constraints.

Contribution

It provides the first sound, complete, and terminating satisfiability checking algorithm for FoLPs and introduces f-hybrid knowledge bases that integrate ontologies and rules more flexibly.

Findings

Decidability established for FoLPs.

Algorithm is sound, complete, and terminating.

Reasoning with f-hybrid knowledge bases reduces to FoLPs.

Abstract

Open Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this article, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where \SHOQ{} knowledge bases and forest logic programs co-exist, and we show that reasoning with such knowledge bases can be reduced to reasoning with forest logic programs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, providing thus a genuine alternative approach to current integration approaches of ontologies and rules.