Web ontology representation and reasoning via fragments of set theory

In this paper we use results from Computable Set Theory as a means to represent and reason about description logics and rule languages for the semantic web. Specifically, we introduce the description logic \mathcal{DL}\langle 4LQS^R\rangle(\D)--admitting features such as min/max cardinality constructs on the left-hand/right-hand side of inclusion axioms, role chain axioms, and datatypes--which turns out to be quite expressive if compared with \mathcal{SROIQ}(\D), the description logic underpinning the Web Ontology Language OWL. Then we show that the consistency problem for \mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is decidable by reducing it, through a suitable translation process, to the satisfiability problem of the stratified fragment $4LQS^R$ of set theory, involving variables of four sorts and a restricted form of quantification. We prove also that, under suitable not very restrictive constraints, the consistency problem for \mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is \textbf{NP}-complete. Finally, we provide a $4LQS^R$-translation of rules belonging to the Semantic Web Rule Language (SWRL)

A Novel Approach to Multimedia Ontology Engineering for Automated Reasoning over Audiovisual LOD Datasets

Multimedia reasoning, which is suitable for, among others, multimedia content analysis and high-level video scene interpretation, relies on the formal and comprehensive conceptualization of the represented knowledge domain. However, most multimedia ontologies are not exhaustive in terms of role definitions, and do not incorporate complex role inclusions and role interdependencies. In fact, most multimedia ontologies do not have a role box at all, and implement only a basic subset of the available logical constructors. Consequently, their application in multimedia reasoning is limited. To address the above issues, VidOnt, the very first multimedia ontology with SROIQ(D) expressivity and a DL-safe ruleset has been introduced for next-generation multimedia reasoning. In contrast to the common practice, the formal grounding has been set in one of the most expressive description logics, and the ontology validated with industry-leading reasoners, namely HermiT and FaCT++. This paper also presents best practices for developing multimedia ontologies, based on my ontology engineering approach

Hybrid Rules with Well-Founded Semantics

A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program is a pair of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories, and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized as description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers. Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics, and for completeness of the operational semantics are given

Approximate OWL-Reasoning with Screech

Applications of expressive ontology reasoning for the Semantic Web require scalable algorithms for deducing implicit knowledge from explicitly given knowledge bases. Besides the development of more effi- cient such algorithms, awareness is rising that approximate reasoning solutions will be helpful and needed for certain application domains. In this paper, we present a comprehensive overview of the Screech approach to approximate reasoning with OWL ontologies, which is based on the KAON2 algorithms, facilitating a compilation of OWL DL TBoxes into Datalog, which is tractable in terms of data complexity. We present three different instantiations of the Screech approach, and report on experiments which show that a significant gain in efficiency can be achieved

Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

Ontology-Based Data Access Using Rewriting, OWL 2 RL Systems and Repairing

Abstract. In previous work it has been shown how an OWL 2 DL on-tology O can be `repaired ' for an OWL 2 RL system ans|that is, how we can compute a set of axioms R that is independent from the data and such that ans that is generally incomplete for O becomes complete for all SPARQL queries when used with O [ R. However, the initial implementation and experiments were very preliminary and hence it is currently unclear whether the approach can be applied to large and com-plex ontologies. Moreover, the approach so far can only support instance queries. In the current paper we thoroughly investigate repairing as an approach to scalable (and complete) ontology-based data access. First, we present several non-trivial optimisations to the rst prototype. Sec-ond, we show how (arbitrary) conjunctive queries can be supported by integrating well-known query rewriting techniques with OWL 2 RL sys-tems via repairing. Third, we perform an extensive experimental evalua-tion obtaining encouraging results. In more detail, our results show that we can compute repairs even for very large real-world ontologies in a rea-sonable amount of time, that the performance overhead introduced by repairing is negligible in small to medium sized ontologies and noticeable but manageable in large and complex one, and that the hybrid reasoning approach can very eciently compute the correct answers for real-world challenging scenarios.

Structure-based classification and ontology in chemistry

<p>Abstract</p> <p>Background</p> <p>Recent years have seen an explosion in the availability of data in the chemistry domain. With this information explosion, however, retrieving <it>relevant </it>results from the available information, and <it>organising </it>those results, become even harder problems. Computational processing is essential to filter and organise the available resources so as to better facilitate the work of scientists. Ontologies encode expert domain knowledge in a hierarchically organised machine-processable format. One such ontology for the chemical domain is ChEBI. ChEBI provides a classification of chemicals based on their structural features and a role or activity-based classification. An example of a structure-based class is 'pentacyclic compound' (compounds containing five-ring structures), while an example of a role-based class is 'analgesic', since many different chemicals can act as analgesics without sharing structural features. Structure-based classification in chemistry exploits elegant regularities and symmetries in the underlying chemical domain. As yet, there has been neither a systematic analysis of the types of structural classification in use in chemistry nor a comparison to the capabilities of available technologies.</p> <p>Results</p> <p>We analyze the different categories of structural classes in chemistry, presenting a list of patterns for features found in class definitions. We compare these patterns of class definition to tools which allow for automation of hierarchy construction within cheminformatics and within logic-based ontology technology, going into detail in the latter case with respect to the expressive capabilities of the Web Ontology Language and recent extensions for modelling structured objects. Finally we discuss the relationships and interactions between cheminformatics approaches and logic-based approaches.</p> <p>Conclusion</p> <p>Systems that perform intelligent reasoning tasks on chemistry data require a diverse set of underlying computational utilities including algorithmic, statistical and logic-based tools. For the task of automatic structure-based classification of chemical entities, essential to managing the vast swathes of chemical data being brought online, systems which are capable of hybrid reasoning combining several different approaches are crucial. We provide a thorough review of the available tools and methodologies, and identify areas of open research.</p