19 research outputs found

    Module extraction via query inseparability in OWL 2 QL

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    We show that deciding conjunctive query inseparability for OWL 2 QL ontologies 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

    Query inseparability by games

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    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

    When are description logic knowledge bases indistinguishable?

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    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

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    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

    Query inseparability for ALC ontologies

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    We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable for conjunctive queries (CQs), but 2ExpTime-complete for unions of CQs (UCQs). The same results hold if (U)CQs are replaced by rooted (U)CQs, where every variable is connected to an answer variable. We also show that inseparability by CQs is still undecidable if one KB is given in the lightweight DL EL and if no restrictions are imposed on the signature of the CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query over any ABox in a given signature and show that, for CQs, this problem is undecidable, too. We then develop model-theoretic criteria for HornALC TBoxes and show using tree automata that, in contrast, inseparability becomes decidable and 2ExpTime-complete, even ExpTime-complete when restricted to (unions of) rooted CQs

    Knowledge base exchange: the case of OWL 2 QL

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    In this article, we define and study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We define a general framework of KB exchange, and study the problem of translating the knowledge in the source KB according to the mappings expressed in OWL 2 QL, the profile of the standard Web Ontology Language OWL 2 based on the description logic DL-LiteR. We develop novel game- and automata-theoretic techniques, and we provide complexity results that range from NLogSpace to ExpTim

    Modularity Through Inseparability : Algorithms, Extensions, and Evaluation

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    Module extraction is the task of computing, given a description logic ontology and a signature ∑ of interest, a subset (called a module) such that for certain applications that only concern ∑ the ontology can be equivalently replaced by the module. In most applications of module extraction it is desirable to compute a module which is as small as possible, and where possible a minimal one. In logic-based approaches to module extraction the most popular way to define modules is using inseparability relations, the strongest and most robust notion of this being model ∑-inseparability, where two ontologies are called ∑-inseparable iff the ∑-reducts of their models coincide. Then, a ∑-module is defined as a ∑-inseparable subset of the ontology. Unfortunately deciding if a subset of an ontology is a minimal ∑-module, over ontologies formulated in even moderately expressive logics, is of perpetually high complexity and often undecidable, and for this reason approximation algorithms are required. Instead of computing a minimal ∑-module one computes some ∑-module and the main research task is to minimise the size of these modules --- to compute an approximation of a minimal ∑-module. This thesis considers research surrounding approximations based on the model ∑-inseparability relation including: improving and extending existing approximation algorithms, providing a highly-optimised implementations, and the introduction a new methodology to evaluate just how well approximations approximate minimal modules, all supported by a significant empirical investigation
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