Exchanging Description Logic Knowledge Bases

mappings are sets of DL inclusions. In such a setting, in order to minimize the exchange (and hence transfer and materialization) of explicit (i. e., ABox) information, we are interested in computing translations, from now on referred to as solutions, that contain as much implicit knowledge as possible. This leads us to define the novel notion of representability, which helps us in understanding the capacity of solutions to transfer implicit knowledge. Checking representability and computing a representation of a source TBox under a mapping turn out to be crucial problems in the context of knowledge base exchange. Furthermore, we argue that the right notion of solution, on which to base our investigations, should not be the standard one based on the correspondence between models of source and target KBs. Indeed, we show that such solutions present severe limitations since, on the one hand, they do not allow for the use of implicit target information to represent implicit source information, and on the other hand, they may lead to exponentially large target ABoxes. To overcome these drawbacks, we introduce the weaker notion of Q-solution, for a query language Q, which is based on the correspondence between answers to queries in Q over source and target KBs. Notice that such a notion, though weaker, is in line with the objective of (data and) knowledge base exchange of providing in the target sufficient information to answer queries in Q that could also be posed over the source. We then develop results and techniques for KB exchange and for the Q-representability problem in the case where Q are unions of conjunctive queries (UCQs), and where KBs are expressed in DL-LiteRDFS, a member of the DL-Lite family (Calvanese et al. 2007) that corresponds to the FOL fragment of RDFS (Brickley and Guha 2004), the widely adopted standard Semantic Web language. In this paper, we 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 study the problem of translating the knowledge in the source KB according to these mappings. We define a general framework of KB exchange, and address the problems of representing implicit source information in the target, and of computing different kinds of solutions, i. e., target KBs with specified properties, given a source KB and a mapping. We develop first results and study the complexity of KB exchange for DL-LiteRDFS, a DL corresponding to the FOL fragment of RDFS, and for DL-LiteR.

Authors

• Marcelo Arenas
• Elena Botoeva
• Diego Calvanese
• Vladislav Ryzhikov
• Evgeny Sherkhonov

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