The increasing use of Ontologies, formulated using expressive Description Logics, for time sensitive applications necessitates the development of fast (near realtime) reasoning tools. Multicore processors are nowadays widespread across desktop, laptop, server, and even smartphone and tablets devices. The rise of such powerful execution environments calls for new parallel and distributed Description Logics (DLs) reasoning algorithms. Many sophisticated optimizations have been explored and have considerably enhanced DL reasoning with light ontologies. Nondeterminism remains a main source of complexity for implemented systems handling ontologies relying on more expressive logics.In this work, we explore handling non-determinism with DL languages enabling qualified cardinality restrictions. We implement a fork/join parallel framework into our tableau-based algebraic reasoner, which handles qualified cardinality restrictions and nominals using in-equation solving. The preliminary results are encouraging and show that using a parallel framework with algebraic reasoning is worth investigating and more promising than parallelizing standard tableau-based reasoning.

Multicore processors are nowadays widespread across desktop, laptop, server, and even smartphone and tablets devices. The rise of such powerful execution environments calls for new parallel and distributed Description Logics (DLs) reasoning algorithms. Many sophisticated optimizations have been explored and have considerably enhanced DL reasoning with light ontologies. Non-determinism remains a main source of complexity for implemented systems handling ontologies relying on more expressive logics.In this work, we explore handling non-determinism with DL languages enabling qualified cardinality restrictions. We implement a fork/join parallel framework into our hybrid algebraic reasoner, which handles qualified cardinality restrictions and nominals using in-equation solving. Preliminary evaluation shows encouraging results. I. MOTIVATIONApplications of the semantic web are numerous, wide ranging and have tremendous potential for adding value in a vast array of situations which can take advantage of intelligence, i.e., the capacity to reason over knowledge stored in a knowledge base such as an ontology. However, if the application is time sensitive, the time required for reasoning can be prohibitive.Description logics (DL) have gained a lot of attention in the research community as they provide a logical formalism for the codification of medical knowledge, ontologies, and the semantic web. There has been a great deal of research into optimizing DL reasoning strategies and in carving out fragments over which reasoning can proceed at a reasonable pace -but reasoning using these strategies or over these fragments often does not scale to allow the use of large ontologies. Reasoning for time sensitive tasks (e.g., those required in a clinical decision support system) still requires severe restrictions on the expressivity, the complexity and/or the size of the ontology used.Standard DL inference services, e.g., TBox classification, concept satisfiability checking, instance checking, etc., have been extended with query answering in order to extract information and drive applications such as web services and workflow management systems [1]. For many applications (e.g., associated with health services delivery) these services are time sensitive, but require time consuming reasoning over complex and often large ontologies. The expressivity of the domain knowledge is often sacrificed in order to meet practical reasoning performance. For example, the Lipid ontology used in [2] relies heavily on QCRs. It is expressed using the DL ALCHIQ using 715 concepts and 46 properties. The comprehensive classification of Lipids [3] is expressed using the DL SHQ using 729 concepts and 3 properties. Expressions of the form ≥ nR.C and ≤ nR.C (e.g., LC Hexaacylaminosuar ≥ 6 hasProperFat.Primary Acyl Chain ≤ 6 hasProperFat.Primary Acyl Chain) are used heavily, and the full ontology cannot be classified by existing reasoners within hours of CPU time. Hence the recent popularity of lightweight ontologies, i.e., expressed using the extensions of th...

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Semantic web applications based on the web ontology language (OWL) often require the use of numbers in class descriptions for expressing cardinality restrictions on properties or even classes. Some of these cardinalities are specified explicitly but quite a few are entailed and need to be discovered by reasoning procedures. Due to the description logic (DL) foundation of OWL those reasoning services are offered by DL reasoners which employ reasoning procedures that are arithmetically uninformed and substitute arithmetic reasoning by "don't know" non-determinism in order to cover all possible cases. This lack of information about arithmetic problems dramatically degrades the performance of DL reasoners in many cases, especially with ontologies relying on the use of nominals (O) and qualified cardinality restrictions (Q). In this article we present a new algebraic tableau reasoning procedure for the DL SHOQ that combines tableau procedures and algebraic methods, namely linear integer programming, to ensure arithmetically better informed reasoning procedures. SHOQ extends the standard DL ALC (which is equivalent to the multi-modal logic K m ) with transitive roles, role hierarchies, qualified cardinality restrictions, and nominals, and forms an expressive subset of the web ontology language OWL 2. Although the proposed algebraic tableau (in analogy to standard tableau) is still double exponential in the worst case, it deals with cardinalities in a very informed way due to its arithmetic component and can be considered as a novel foundation for informed reasoning procedures addressing cardinality restrictions.