Optimizing Algebraic Tableau Reasoning for SHOQ: First Experimental Results

Jocelyne Faddoul, Volker Haarslev
2010 International Workshop on Description Logics  
In this paper we outline an algebraic tableau algorithm for the DL SHOQ, which supports more informed reasoning due to the use of semantic partitioning and integer programming. We introduce novel and adapt known optimization techniques and show their effectiveness on the basis of a prototype reasoner implementing the optimization techniques for the algebraic approach. Our first set of benchmarks clearly indicates the effectiveness of our approach and a comparison with the DL reasoners Pellet
more » ... HermiT demonstrates a runtime improvement of several orders of magnitude. Motivation Nominals play an important role in Description Logics (DLs) as they allow one to express the notion of identity and enumeration; nominals must be interpreted as singleton sets. An example for the use of nominals in SHOQ would be Eye Color ≡ Green ⊔ Blue ⊔ Brown ⊔ Black ⊔ Hazel where each color is represented as a nominal. The cardinality of Eye Color is restricted to have at most 5 instances, i.e., the abovementioned nominals. Qualified cardinality restrictions (QCRs) allow one to specify lower (≥ n R.C) and upper (≤ n R.C) bounds on the number of elements related via a certain role with additionally specifying qualities on the related elements. Due to the interaction between nominals and QCRs the SHOQ concept ≥ 6 has color.Eye Color is unsatisfiable. Each nominal must be interpreted as a set with the cardinality 1 (and thus can be used to enumerate domain elements), whereas an atomic concept is interpreted as a set with an unbounded cardinality. Moreover, the quasi-tree model property, which has always been advantageous for DL tableau methods, does not hold for SHOQ. Resolution-based reasoning procedures were proposed in [8] and were proven to be weak in dealing with QCRs containing large numbers. Hypertableaux [9] were recently studied to minimize non-determinism in DL reasoning with no special treatment for QCRs. These approaches and standard tableau techniques suffer from the low level of information about the cardinalities of concepts and the number of role successors implied by nominals and QCRs (e.g., see the example above) because these algorithms treat these cardinalities in a blind and uninformed way. Our early work on performance improvements for reasoning with QCRs for the DL SHQ was based on a so-called signature calculus [5] and, alternatively, on algebraic reasoning [6] (not applicable to Aboxes). Our algebraic approach represents the knowledge about implied cardinalities as linear inequations. The advantages of such
dblp:conf/dlog/FaddoulH10 fatcat:gu6j4oukzbdodds3fay3lxzlte