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Query answering over Description Logic (DL) ontologies has become a vibrant field of research. Efficient realizations often exploit database technology and rewrite a given query to an equivalent SQL or Datalog query over a database associated with the ontology. This approach has been intensively studied for conjunctive query answering in the DL-Lite and EL families, but is much less explored for more expressive DLs and queries. We present a rewriting-based algorithm for conjunctive query answering over Horn-SHIQ ontologies, possibly extended with recursive rules under limited recursion as in DL+log. This setting not only subsumes both DL-Lite and EL, but also yields an algorithm for answering (limited) recursive queries over Horn-SHIQ ontologies (an undecidable problem for full recursive queries). A prototype implementation shows its potential for applications, as experiments exhibit efficient query answering over full Horn-SHIQ ontologies and benign downscaling to DL-Lite, where it is competitive with comparable state of the art systems.

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Abstraction refinement is a recently introduced technique using which reasoning over large ABoxes is reduced to reasoning over small abstract ABoxes. Although the approach is sound for any classical Description Logic such as SROIQ, it is complete only for Horn ALCHOI. In this paper, we propose an extension of this method that is now complete for Horn SHOIF and also handles role- and equality-materialization. To show completeness, we use a tailored set of materialization rules that loosely decouple the ABox from the TBox. An empirical evaluation demonstrates that, despite the new features, the abstractions are still significantly smaller than the original ontologies and the materialization can be computed efficiently.

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Exploring complex structured knowledge graphs (KGs) is challenging for non-experts as it requires knowledge of query languages and the underlying structure of the KGs. Keyword-based exploration is a convenient paradigm, and computing a group Steiner tree (GST) as an answer is a popular implementation. Recent studies suggested improving the cohesiveness of an answer where entities have small semantic distances from each other. However, how to efficiently compute such an answer is open. In this paper, to model cohesiveness in a generalized way, the quadratic group Steiner tree problem (QGSTP) is formulated where the cost function extends GST with quadratic terms representing semantic distances. For QGSTP we design a branch-and-bound best-first (B3F) algorithm where we exploit combinatorial methods to estimate lower bounds for costs. This exact algorithm shows practical performance on medium-sized KGs.