Data Complexity of Query Answering in Expressive Description Logics via Tableaux

Abstract

The logical foundations of the standard web ontology languages are provided by expressive Description Logics (DLs), such as SHIQ and SHOIQ. In the Semantic Web and other domains, ontologies are increasingly seen also as a mechanism to access and query data repositories. This novel context poses an original combination of challenges that has not been addressed before: (i) sufficient expressive power of the DL to capture common data modelling constructs; (ii) well established and flexible query mechanisms such as those inspired by database technology; (iii) optimisation of inference techniques with respect to data size, which typically dominates the size of ontologies. This calls for investigating data complexity of query answering in expressive DLs. While the complexity of DLs has been studied extensively, few tight characterisations of data complexity were available, and the problem was still open for most DLs of the SH family and for standard query languages like conjunctive queries and their extensions. We tackle this issue and prove a tight coNP upper bound for positive existential queries without transitive roles in SHOQ, SHIQ, and SHOI. We thus establish that, for a whole range of sublogics of SHOIQ that contain AL, answering such queries has coNP-complete data complexity. We obtain our result by a novel tableaux-based algorithm for checking query entailment, which uses a modified blocking condition in the style of Carin. The algorithm is sound for SHOIQ, and shown to be complete for all considered proper sublogics in the SH family.

Linking Data to Ontologies

“…As for issue 1, an effort has been undertaken to understand which language would be best suited for representing ontologies in a setting where an ontology is used for accessing large quantities of data [7,26,17]. This work has shown that most of the languages proposed so far are not really suited for this task.…”

“…Recent research has shown that OWL, the W3C Web Ontology Language for the Semantic Web 5 , if not restricted, is not suited as a formalism for representing ontologies with large amounts of instance assertions in the ABox [7,26,17], since reasoning in such a logic is inherently exponential (coNP-hard) with respect data complexity, i.e., with respect to the size of the ABox.…”

Hydrowl: A Hybrid Query Answering System for OWL 2 DL Ontologies

“…First, it is trivial to see that in theory query bases always exist. 3 Second, ans is expected to be mostly complete (T usually includes few "problematic" constructors) leaving few queries that need to be evaluated using the fully-fledged OWL 2 DL system. Third, it has been shown [19] that even in cases that Hydrowl needs to use ans , the scalable system can still be exploited in order to speed up the evaluation by ans .…”

“…Unfortunately, query answering over OWL 2 DL ontologies is of very high computational complexity [3,4] and even after modern optimisations and intense implementation efforts [5] OWL 2 DL systems are still not able to cope with datasets containing billions of data.…”

On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

“…The only known studies related to this topic are the work on CARIN [20], which has shown decidability of nonrecursive positive Datalog with the DL ALCN R, and the studies on conjunctive query answering in DLs (see e.g. [7,24,25,14,15]), which are indirectly related to integrating Datalog and DLs (since conjunctive queries can be seen as nonrecursive Datalog programs consisting of a single rule).…”