We present a ke-based procedure for the main TBox and ABox reasoning tasks for the description logic $dlssx$, in short $shdlssx$. The logic $shdlssx$, representable in the decidable multi-sorted quantified set-theoretic fragment $flqsr$, combines the high scalability and efficiency of rule languages such as the Semantic Web Rule Language (SWRL) with the expressivity of description logics. %In fact it supports, among other features, Boolean operations on concepts and roles, role constructs such as the product of concepts and role chains on the left hand side of inclusion axioms, and role properties such as transitivity, symmetry, reflexivity, and irreflexivity. Our algorithm is based on a variant of the kespace system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the $gamma$-rule. The novel system, called keg, turns out to be an improvement of the system introduced in cite{RR2017} and of standard first-order ke x cite{dagostino94}. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that the performances of the keg-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.
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