Algebraic tableau reasoning for the description logic SHOQ

Jocelyne Faddoul, Volker Haarslev
2010 Journal of Applied Logic  
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
more » ... 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. This article extends our work in [10] on ALCOQ to include GCIs, transitive roles and role hierarchies and demonstrates how a standard tableau reasoning algorithm for DLs can be extended with an arithmetic component while maintaining soundness, completeness and termination. The result is a hybrid reasoning algorithm which is more informed about arithmetic constraints imposed by concept descriptions. In particular, a better handling of numerical restrictions implied by 1 The disjointness of the nominals is not even needed to make EU_MemberState unsatisfiable. 2
doi:10.1016/j.jal.2010.08.009 fatcat:bstowqg3qjgrfankxq6s4xqb3i