Reasoning with Forest Logic Programs Using Fully Enriched Automata

Abstract Forest Logic Programs (FoLP) are a decidable fragment of Open Answer Set Programming (OASP) which have the forest model property. OASP extends Answer Set Programming (ASP) with open domains-a feature which makes it possible for FoLPs to simulate reasoning with the expressive description logic SHOQ. At the same time, the fragment retains the attractive rule syntax and the non-monotonicity specific to ASP. In the past, several tableaux algorithms have been devised to reason with FoLPs, the most recent of which established a NEXPTIME upper bound for reasoning with the fragment. While known to be EXPTIME-hard, the exact complexity characterization of reasoning with the fragment was still unknown. In this paper we settle this open question by a reduction of reasoning with FoLPs to emptiness checking of fully enriched automata, a form of automata which run on forests, and which are known to be EXPTIME-complete

Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases

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

On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

Reasoning in systems integrating Description Logics (DL) ontologies and Datalog rules is a very hard task, and previous studies have shown undecidability of reasoning in systems integrating (even very simple) DL ontologies with recursive Datalog. However, the results obtained so far constitute a very partial picture of the computational properties of systems combining DL ontologies and Datalog rules. The aim of this paper is to contribute to complete this picture, extending the computational analysis of reasoning in systems integrating ontologies and Datalog rules. More precisely, we first provide a set of decidability and complexity results for reasoning in systems combining ontologies specified in DLs and rules specified in nonrecursive Datalog (and its extensions with inequality and negation): such results identify, from the viewpoint of the expressive abilities of the two formalisms, minimal combinations of Description Logics and Datalog in which reasoning is undecidable. Then, we present new results on the decidability and complexity of the so-called restricted (or safe) integration of DL ontologies and Datalog rules. Our results show that: (1) the unrestricted interaction between DLs and Datalog is computationally very hard even in the absence of recursion in rules; (2) surprisingly, the various ”safeness” restrictions, which have been defined to regain decidability of reasoning in the interaction between DLs and recursive Datalog, appear as necessary restrictions even when rules are not recursive