Abstract
Developing a good formalism and an efficient decision procedure for the instance checking problem is desirable for practical application of description logics. The data complexity of the instance checking problem is coNP-complete even for Horn knowledge bases in the basic description logic ALC. In this paper, we present and study weakenings with PTIME data complexity of the instance checking problem for Horn knowledge bases in regular description logics. We also study cases when the weakenings are an exact approximation. In contrast to previous related work of other authors, our approach deals with the case when the constructor ∀ is allowed in premises of program clauses that are used as terminological axioms.
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