On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

Abstract

Abstract. 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.

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“…This is mainly due to undecidability of reasoning in such systems. This is particularly the case for those systems integrating DL ontologies with recursive or hybrid rules [57,58]. So, bridging the discrepancy in these two knowledge representations is a challenging problem.…”

“…So, bridging the discrepancy in these two knowledge representations is a challenging problem. Many studies [57][58][59][60] have shown that to avoid undecidability of reasoning, practically all decidable approaches to integrating ontologies and rules should impose specific conditions which restrict the interaction between the rules and the ontology. In this work, we adopt a similar decidable reasoning approach by adhering to restrictions, such as avoiding recursive and hybrid rules.…”

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“…Additionally, there might be other predicate symbols available, but without loss of generality we assume they cannot coincide with complex concept or role descriptions. Note that we do not impose Datalog safeness or (weakly) DL safeness [28,30,29] for the rule component. Intuitively, the restricted shape of FoLPs suffices to guarantee decidability; FoLPs are in general neither Datalog safe nor weakly DL-safe; we will discuss the relation with weakly DL-safeness in detail in Section 6.…”

“…Furthermore, they serve well as an underlying integration vehicle for ontologies and rules. In order to illustrate this, we define f-hybrid knowledge bases (fKBs), consisting of a SHOQ knowledge base and a rule component that is a FoLP, with a nonmonotonic semantics similar to the semantics of g-hybrid knowledge bases [12], r-hybrid knowledge bases [30], and DL+log [29]. Our approach differs in two points with current other proposals:…”

“…• To ensure effective reasoning, our approach does not rely on a (weakly) DL-safeness condition such as [27,29,30], which restricts the interaction of the rule component with the DL component. Instead, we rely on a translation of the hybrid knowledge to FoLPs.…”