Knowledge graphs (KGs) model facts about the world; they consist of nodes (entities such as companies and people) that are connected by edges (relations such as founderOf ). Facts encoded in KGs are frequently used by search applications to augment result pages. When presenting a KG fact to the user, providing other facts that are pertinent to that main fact can enrich the user experience and support exploratory information needs. \em KG fact contextualization is the task of augmenting a given KG fact with additional and useful KG facts. The task is challenging because of the large size of KGs; discovering other relevant facts even in a small neighborhood of the given fact results in an enormous amount of candidates. We introduce a neural fact contextualization method (\em NFCM ) to address the KG fact contextualization task. NFCM first generates a set of candidate facts in the neighborhood of a given fact and then ranks the candidate facts using a supervised learning to rank model. The ranking model combines features that we automatically learn from data and that represent the query-candidate facts with a set of hand-crafted features we devised or adjusted for this task. In order to obtain the annotations required to train the learning to rank model at scale, we generate training data automatically using distant supervision on a large entity-tagged text corpus. We show that ranking functions learned on this data are effective at contextualizing KG facts. Evaluation using human assessors shows that it significantly outperforms several competitive baselines.

Estimating the cardinality (i.e., the number of answers) of conjunctive queries is particularly difficult in RDF systems: queries over RDF data are navigational and thus tend to involve many joins. We present a new, principled cardinality estimation technique based on graph summarisation. We interpret a summary of an RDF graph using a possible world semantics and formalise the estimation problem as computing the expected cardinality over all RDF graphs represented by the summary, and we present a closed-form formula for computing the expectation of arbitrary queries. We also discuss approaches to RDF graph summarisation. Finally, we show empirically that our cardinality technique is more accurate and more consistent, often by orders of magnitude, than the state of the art.

Answering conjunctive queries (CQs) over EL knowledge bases (KBs) with complex role inclusions is PSPACE-hard and in PSPACE in certain cases; however, if complex role inclusions are restricted to role transitivity, a tight upper complexity bound has so far been unknown. Furthermore, the existing algorithms cannot handle reflexive roles, and they are not practicable. Finally, the problem is tractable for acyclic CQs and ELH, and NP-complete for unrestricted CQs and ELHO KBs. In this paper we complete the complexity landscape of CQ answering for several important cases. In particular, we present a practicable NP algorithm for answering CQs over ELHOs KBs—a logic containing all of OWL 2 EL, but with complex role inclusions restricted to role transitivity. Our preliminary evaluation suggests that the algorithm can be suitable for practical use. Moreover, we show that, even for a restricted class of so-called arborescent acyclic queries, CQ answering over EL KBs becomes NP-hard in the presence of either transitive or reflexive roles. Finally, we show that answering arborescent CQs over ELHO KBs is tractable, whereas answering acyclic CQs is NP-hard.

OWL 2 EL is a popular ontology language that supports role inclusions---that is, axioms that capture compositional properties of roles. Role inclusions closely correspond to context-free grammars, which was used to show that answering conjunctive queries (CQs) over OWL 2 EL knowledge bases with unrestricted role inclusions is undecidable. However, OWL 2 EL inherits from OWL 2 DL the syntactic regularity restriction on role inclusions, which ensures that role chains implying a particular role can be described using a finite automaton (FA). This is sufficient to ensure decidability of CQ answering; however, the FAs can be worst-case exponential in size so the known approaches do not provide a tight upper complexity bound. In this paper, we solve this open problem and show that answering CQs over OWL 2 EL knowledge bases is PSPACE-complete in combined complexity (i.e., the complexity measured in the total size of the input). To this end, we use a novel encoding of regular role inclusions using bounded-stack pushdown automata---that is, FAs extended with a stack of bounded size. Apart from theoretical interest, our encoding can be used in practical tableau algorithms to avoid the exponential blowup due to role inclusions. In addition, we sharpen the lower complexity bound and show that the problem is PSPACE-hard even if we consider only role inclusions as part of the input (i.e., the query and all other parts of the knowledge base are fixed). Finally, we turn our attention to navigational queries over OWL 2 EL knowledge bases, and we show that answering positive, converse-free conjunctive graph XPath queries is PSPACE-complete as well; this is interesting since allowing the converse operator in queries is known to make the problem EXPTIME-hard. Thus, in this paper we present several important contributions to the landscape of the complexity of answering expressive queries over description logic knowledge bases.

So-called combined approaches answer a conjunctive query over a description logic ontology in three steps: first, they materialise certain consequences of the ontology and the data; second, they evaluate the query over the data; and third, they filter the result of the second phase to eliminate unsound answers. Such approaches were developed for various members of the DL-Lite and the EL families of languages, but none of them can handle ontologies containing nominals. In our work, we bridge this gap and present a combined query answering approach for ELHO--a logic that contains all features of the OWL 2 EL standard apart from transitive roles and complex role inclusions. This extension is nontrivial because nominals require equality reasoning, which introduces complexity into the first and the third step. Our empirical evaluation suggests that our technique is suitable for practical application, and so it provides a practical basis for conjunctive query answering in a large fragment of OWL 2 EL.

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations.