An Optimized KE-Tableau-Based System for Reasoning in the Description Logic $${\mathcal {DL}}_{{\mathbf {D}}}^{4,\!\times }$$

Abstract

We present a KE-tableau-based procedure for the main TBox and ABox reasoning tasks for the description logic DL 4LQS R,× (D), in short DL 4,× D . The logic DL 4,× D , representable in the decidable multi-sorted quantified set-theoretic fragment 4LQS R , combines the high scalability and efficiency of rule languages such as the Semantic Web Rule Language (SWRL) with the expressivity of description logics. Our algorithm is based on a variant of the KE-tableau system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the γ-rule. The novel system, called KE γ -tableau, turns out to be an improvement of the system introduced in [3] and of standard first-order KE-tableaux [11]. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that the performances of the KE γ -tableau-based reasoner are often up to about 400% better than the ones of the other two systems. This a first step towards the construction of efficient reasoners for expressive OWL ontologies based on fragments of computable set-theory.In this paper, the KE-tableau-based procedure defined in [3] is modified, by eliminating the preprocessing phase for universally quantified formulae and replacing the standard KE-elimination rule with a novel elimination rule, called E γ -rule, incorporating the standard rule for treating universally quantified formulae (γ-rule). The resulting system turns out to be more efficient than the and the First-Order (FO) as shown by suitable benchmarking tests executed on C++ implementations of the three systems. The main reason for such a speed-up relies on the fact that the novel E γ -rule does not need to store the instances of universally quantified formulae on the KE-tableau. DL 4,× D -formula ϕ. A 4LQS R DL 4,× D -interpretation is a pair M = (D, M ), where D is a nonempty collection of objects (called domain or universe of M) and M is an assignment

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“…directions. Finally, representing the ontological stack through the decidable fragments of set-theory as in [20,[24][25][26][27][28][29][30] is one of the future works.…”