Abstract In a previous paper, we have shown that clause sets belonging to the Horn Bernays-Schönfinkel fragment over simple linear real arithmetic (HBS(SLR)) can be translated into HBS clause sets over a finite set of first-order constants. The translation preserves validity and satisfiability and it is still applicable if we extend our input with positive universally or existentially quantified verification conditions (conjectures). We call this translation a Datalog hammer. The combination of its implementation in SPASS-SPL with the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. We verify supervisor code for two examples: a lane change assistant in a car and an electronic control unit of a supercharged combustion engine. In this paper, we improve our Datalog hammer in several ways: we generalize it to mixed real-integer arithmetic and finite first-order sorts; we extend the class of acceptable inequalities beyond variable bounds and positively grounded inequalities; and we significantly reduce the size of the hammer output by a soft typing discipline. We call the result the sorted Datalog hammer. It not only allows us to handle more complex supervisor code and to model already considered supervisor code more concisely, but it also improves our performance on real world benchmark examples. Finally, we replace the before file-based interface between SPASS-SPL and VLog by a close coupling resulting in a single executable binary.

Ontology-based access to large data-sets has recently gained a lot of attention. To access data efficiently, one approach is to rewrite the ontology into Datalog, and then use powerful Datalog engines to compute implicit entailments. Existing rewriting techniques support Description Logics (DLs) from ELH to Horn-SHIQ. We go one step further and present one such data-independent rewriting technique for Horn-SRIQ⊓, the extension of Horn-SHIQ that supports role chain axioms, an expressive feature prominently used in many real-world ontologies. We evaluated our rewriting technique on a large known corpus of ontologies. Our experiments show that the resulting rewritings are of moderate size, and that our approach is more efficient than state-of-the-art DL reasoners when reasoning with data-intensive ontologies.

In this paper, we propose a novel data-driven schema for large-scale heterogeneous knowledge graphs inspired by Formal Concept Analysis (FCA). We first extract the sets of properties associated with individual entities; these property sets (aka. characteristic sets) are annotated with cardinalities and used to induce a lattice based on set-containment relations, forming a natural hierarchical structure describing the knowledge graph. We then propose an algebra over such schema lattices, which allows to compute diffs between lattices (for example, to summarise the changes from one version of a knowledge graph to another), to add lattices (for example, to project future changes), and so forth. While we argue that this lattice structure (and associated algebra) may have various applications, we currently focus on the use-case of modelling and predicting the dynamic behaviour of knowledge graphs. Along those lines, we instantiate and evaluate our methods for analysing how versions of the Wikidata knowledge graph have changed over a period of 11 weeks. We propose algorithms for constructing the lattice-based schema from Wikidata, and evaluate their efficiency and scalability. We then evaluate use of the resulting schema(ta) for predicting how the knowledge graph will evolve in future versions.