Abstract
It has recently been shown that first-order- and datalog-rewritability of ontology-mediated queries (OMQs) with expressive ontologies can be checked in NExpTime using a reduction to CSPs. In this paper, we present a case study for OMQs with Boolean conjunctive queries and a fixed ontology consisting of a single covering axiom \(A \sqsubseteq F \sqcup T\), possibly supplemented with a disjointness axiom for T and F. The ultimate aim is to classify such OMQs according to their data complexity: \(\textsc {AC}^0\), L, NL, P or coNP. We report on our experience with trying to distinguish between OMQs in P and coNP using the reduction to CSPs and the Polyanna software for finding polymorphisms.
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