Conjunctive query inseparability of OWL 2 QL TBoxes

The OWL2 profile OWL 2 QL, based on the DL-Lite family of description logics, is emerging as a major language for developing new ontologies and approximating the existing ones. Its main application is ontology based data access, where ontologies are used to provide background knowledge for answering queries over data. We investigate the corresponding notion of query inseparability (or equivalence) for OWL 2 QL ontologies and show that deciding query inseparability is PSpace-hard and in ExpTime. We give polynomial-time (incomplete) algorithms and demonstrate by experiments that they can be used for practical module extraction

Conjunctive query inseparability in OWL2QL is ExpTime-hard

We settle an open question on the complexity of the following problem: given two OWL2QL TBoxes and a signature, decide whether these TBoxes return the same answers to any conjunctive query over any data formulated in the given signature. It has been known that the complexity of this problem is between PSpace and ExpTime. Here we show that the problem is ExpTime-complete and, in fact, deciding whether two OWL2QL knowledge bases (each with its own data) give the same answers to any conjunctive query is ExpTime-hard

Query inseparability by games

We investigate conjunctive query inseparability of description logic knowledge bases (KBs) with respect to a given signature, a fundamental problem for KB versioning, module extraction, forgetting and knowledge exchange. We develop a game-theoretic technique for checking query inseparability of KBs expressed in fragments of Horn-ALCHI, and show a number of complexity results ranging from P to ExpTime and 2ExpTime. We also employ our results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal UCQ-solutions in knowledge exchange are both ExpTime-complete for combined complexity

Query-based comparison of OBDA specifications

An ontology-based data access (OBDA) system is composed of one or more data sources, an ontology that provides a conceptual view of the data, and declarative mappings that relate the data and ontology schemas. In order to debug and optimize such systems, it is important to be able to analyze and compare OBDA specifications. Recent work in this direction compared specifications using classical notions of equivalence and entailment, but an interesting alternative is to consider query-based notions, in which two specifications are deemed equivalent if they give the same answers to the considered query or class of queries for all possible data sources. In this paper, we define such query-based notions of entailment and equivalence of OBDA specifications and investigate the complexity of the resulting analysis tasks when the ontology is formulated in DL-LiteR

When are description logic knowledge bases indistinguishable?

Deciding inseparability of description logic knowledge bases (KBs) with respect to conjunctive queries is fundamental for many KB engineering and maintenance tasks including versioning, module extraction, knowledge exchange and forgetting. We study the combined and data complexity of this inseparability problem for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL

Games for query inseparability of description logic knowledge bases

We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature---a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved

Conservative Rewritability of Description Logic TBoxes: First Results

We want to understand when a given TBox T in a description logic L can be rewritten into a TBox T' in a weaker description logic L' such that T' is a conservative extension of T. We consider two notions of conservative rewritability: model-conservative rewritability (T' entails T and all models of T can be expanded to models of T') and L-conservative rewritability (T' has the same L-consequences in the signature of T as T) and investigate conservative rewritability from ALCI to ALC, ALCQ to ALC, ALC to EL, and from ALC to DL-Lite_horn. We compare conservative rewritability and equivalent rewritability, give model-theoretic characterizations of conservative rewritability, prove complexity results for the rewritability problem, and provide some rewriting algorithms