Representability in DL-Lite_R Knowledge Base Exchange

Knowledge base exchange can be considered as a generalization of data exchange in which the aim is to exchange between a source and a target connected through mappings, not only explicit knowledge, i.e., data, but also implicit knowledge in the form of axioms. Such problem has been investigated recently using Description Logics (DLs) as representation formalism, 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. In this paper we are interested in the problem of representing a given source TBox by means of a target TBox that captures at best the intensional information in the source. In previous work, results on representability have been obtained for DL-LiteRDFS , a DL corresponding to the FOL fragment of RDFS. We extend these results to the positive fragment of DLLiteR, in which, differently from DL-LiteRDFS , the assertions in the TBox and the mappings may introduce existentially implied individuals. For this we need to overcome the challenge that the chase, a key notion in data and knowledge base exchange, is not guaranteed anymore to be finite.