DL-Lite and Conjunctive Queries Extended by Optional Matching (Extended Abstract) ?
Shqiponja Ahmetaj, Wolfgang Fischl, Reinhard Pichler, Mantas Šimkus, Sebastian Skritek · 2015
Conjunctive Queries (CQs) constitute the core of most query languages and have been studied intensively in several areas. For querying incomplete data, CQs however suffer one major drawback: they require the complete query to be matched into the data to return answers. One extension of CQs that tries to overcome this problem are well-designed pattern trees (wdPTs) [9]. Developed in the context of the Semantic Web, wdPTs are equivalent to a well-behaved fragment of {AND,OPT}-queries of SPARQL [12], and allow a user to retrieve partial answers to a query. Because of this feature, however, wdPTs are nonmonotone. This is problematic for query answering in the presence of implicit knowledge – expressed e.g. by an ontology specified in some Description Logic (DL) – since the usual certain answer semantics turns out to be unsatisfactory in this setting. We observe that the recently released recommendation of the SPARQL entailment regimes [6] provides a semantics exactly for this case. However, it is defined in a simpler and less expressive way than the certain answers semantics, and does not utilize the full potential of the implicit information. The goal of this work is to introduce an intuitive certain answer semantics for the class of well-designed pattern trees under DL-LiteR (which provides the theoretical underpinning of the OWL 2 QL entailment regime). After introducing wdPTs, we first discuss some of the problems with an adoption of a certain answer semantics for them and propose a suitable modified definition. We then briefly present results on the complexity of typical reasoning tasks. Related Work to our findings includes the work our approaches are based upon [3–6]. There is a huge body of results on CQ answering under different DLs (cf. [4, 5, 11, 13]). For SPARQL recent work [8] presents a stronger semantics, where entire mappings are discarded, whose possible extensions to optional subqueries would imply inconsistencies in the knowledge base. Further related work includes [2, 7, 10] which is discussed in the long version of this paper.