Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a key problem in knowledge representation and databases. This problem can be solved using the chase (aka materialisation) algorithm; however, CQ answering is undecidable for general existential rules, so the chase is not guaranteed to terminate. Several acyclicity conditions provide sufficient conditions for chase termination. In this paper, we present two novel such conditions—model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA)—that generalise many of the acyclicity conditions known so far in the literature. Materialisation provides the basis for several widely-used OWL 2 DL reasoners. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2 DL; furthermore, some systems go beyond OWL 2 RL, but they provide no termination guarantees. In this paper we investigate whether various acyclicity conditions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 DL ontologies are MSA, and that the facts obtained via materialisation are not too large. Thus, our results suggest that principled extensions to materialisationbased OWL 2 DL reasoners may be practically feasible.

While query answering in the presence of description logic (DL) ontologies is a well-studied problem, questions of static analysis such as query containment and query optimization have received less attention. In this paper, we study a rather general version of query containment that, unlike the classical version, cannot be reduced to query answering. First, we allow a restriction to be placed on the vocabulary used in the instance data, which can result in shorter equivalent queries; and second, we allow each query its own ontology rather than assuming a single ontology for both queries, which is crucial in applications to versioning and modularity. We also study global minimization of queries in the presence of DL ontologies, which is more subtle than for classical databases as minimal queries need not be isomorphic.

The dynamic nature of ontology development has motivated the formal study of ontology evolution problems. This paper presents a logical framework that enables fine-grained investigation of evolution problems at a deductive level. In our framework, the optimal evolutions of an ontology O are those ontologies O′ that maximally preserve both the structure of O and its entailments in a given preservation language. We show that our framework is compatible with the postulates of Belief Revision, and we investigate the existence of optimal evolutions in various settings. In particular, we present first results on TBox-level revision and contraction in the EL and FL0 families of Description Logics.

Answering queries in information systems that allow for ex- pressive inferencing is currently a field of intense research. This problem is often referred to as ontology-based data ac- cess (OBDA). We focus on conjunctive query entailment un- der logical rules known as tuple-generating dependencies, existential rules or Datalog+/-. One of the most expressive decidable classes of existential rules known today is that of greedy bounded treewidth sets (gbts). We propose an algo- rithm for this class, which is worst-case optimal for data and combined complexities, with or without bound on the pred- icate arity. A beneficial feature of this algorithm is that it allows for separation between offline and online processing steps: the knowledge base can be compiled independently from queries, which are evaluated against the compiled form. Moreover, very simple adaptations of the algorithm lead to worst-case-optimal complexities for specific subclasses of gbts which have lower complexities, such as guarded rules.

Datalog ∃ is the extension of Datalog, allowing existentially quantified variables in rule heads. This language is highly expressive and enables easy and powerful knowledge-modeling, but the presence of existentially quantified variables makes reasoning over Datalog^E undecidable, in the general case. The results in this paper enable powerful, yet decidable and efficient reasoning (query answering) on top of Datalog ∃ programs. On the theoretical side, we define the class of parsimonious Datalog ∃ programs, and show that it allows of decidable and efficiently-computable reasoning. Unfortunately, we can demonstrate that recognizing parsimony is undecidable. However, we single out Shy, an easily recognizable fragment of parsimonious programs, that significantly extends both Datalog and Linear-Datalog ∃ , while preserving the same (data and combined) complexity of query answering over Datalog, although the addition of existential quantifiers. On the practical side, we implement a bottom-up evaluation strategy for Shy programs inside the DLV system, enhancing the computation by a number of optimization techniques to result in DLV ∃ — a powerful system for answering conjunctive queries over Shy programs, which is profitably applicable to ontology-based query answering. Moreover, we carry out an experimental analysis, comparing DLV ∃ against a number of state-of-the-art systems for ontology-based query answering. The results confirm the effectiveness of DLV ∃ , which outperforms all other systems in the benchmark domain.

A counterexample, inconsistency tolerant query answering methods, known now as the Yale Shooting Scenario, showed and mechanisms supporting update operations that early attempts to make the idea of commonsense expressed over the ontology.

Seven years on from OWL becoming a W3C recommendation, and two years on from the more recent OWL 2 W3C recommendation, OWL has still experienced only patchy uptake on the Web. Although certain OWL features (like owl:sameAs) are very popular, other features of OWL are largely neglected by publishers in the Linked Data world. This may suggest that despite the promise of easy implementations and the proposal of tractable profiles suggested in OWL's second version, there is still no "right" standard fragment for the Linked Data community. In this paper, we (1) analyse uptake of OWL on the Web of Data, (2) gain insights into the OWL fragment that is actually used/usable on the Web, where we arrive at the conclusion that this fragment is likely to be a simplified profile based on OWL RL, (3) propose and discuss such a new fragment, which we call OWL LD (for Linked Data).

Some of the applications of OWL and RDF (e.g. biomedical knowledge representation and semantic policy formulation) call for extensions of these languages with nonmonotonic constructs such as inheritance with overriding. Nonmonotonic description logics have been studied for many years, however no practical such knowledge representation languages exist, due to a combination of semantic difficulties and high computational complexity. Independently, low-complexity description logics such as DL-lite and EL have been introduced and incorporated in the OWL standard. Therefore, it is interesting to see whether the syntactic restrictions characterizing DL-lite and EL bring computational benefits to their nonmonotonic versions, too. In this paper we extensively investigate the computational complexity of Circumscription when knowledge bases are formulated in DL-lite_R, EL, and fragments thereof. We identify fragments whose complexity ranges from P to the second level of the polynomial hierarchy, as well as fragments whose complexity raises to PSPACE and beyond.

Hybrid MKNF knowledge bases are one of the most prominent tightly integrated combinations of open-world ontology languages with closed-world (non-monotonic) rule paradigms. The definition of Hybrid MKNF is parametric on the description logic (DL) underlying the ontology language, in the sense that non-monotonic rules can extend any decidable DL language. Two related semantics have been defined for Hybrid MKNF: one that is based on the Stable Model Semantics for logic programs and one on the Well-Founded Semantics (WFS). Under WFS, the definition of Hybrid MKNF relies on a bottom-up computation that has polynomial data complexity whenever the DL language is tractable. Here we define a general query-driven procedure for Hybrid MKNF that is sound with respect to the stable model-based semantics, and sound and complete with respect to its WFS variant. This procedure is able to answer a slightly restricted form of conjunctive queries, and is based on tabled rule evaluation extended with an external oracle that captures reasoning within the ontology. Such an (abstract) oracle receives as input a query along with knowledge already derived, and replies with a (possibly empty) set of atoms, defined in the rules, whose truth would suffice to prove the initial query. With appropriate assumptions on the complexity of the abstract oracle, the general procedure maintains the data complexity of the WFS for Hybrid MKNF knowledge bases. To illustrate this approach, we provide a concrete oracle for EL+, a fragment of the light-weight DL EL++. Such an oracle has practical use, as EL++ is the language underlying OWL 2 EL, which is part of the W3C recommendations for the Semantic Web, and is tractable for reasoning tasks such as subsumption. We show that query-driven Hybrid MKNF preserves polynomial data complexity when using the EL+ oracle and WFS.

The size of 3D models used on the web or stored in databases is becoming increasingly high. Then, an efficient method that allows users to find similar 3D objects for a given 3D model query has become necessary. Keywords and the geometry of a 3D model cannot meet the needs of users' retrieval because they do not include the semantic information. In this paper, a new method has been proposed to 3D models retrieval using semantic concepts combined with shape indexes. To obtain these concepts, we use the machine learning methods to label 3D models by k-means algorithm in measures and shape indexes space. Moreover, semantic concepts have been organized and represented by ontology language OWL and spatial relationships are used to disambiguate among models of similar appearance. The SPARQL query language has been used to question the information displayed in this language and to compute the similarity between two 3D models. We interpret our results using the Princeton Shape Benchmark Database and the results show the performance of the proposed new approach to retrieval 3D models. Keywords: 3D Model, 3D retrieval, measures, shape indexes, semantic, ontology