Decidability of ALC(D) for concrete domains with the EHD-property

Reasoning for Description logics with concrete domains and w.r.t. general TBoxes easily becomes undecidable. For particular, restricted concrete domains decidablity can be regained. We introduce a novel way to integrate a concrete domain D into the well-known description logic ALC, we call the resulting logic ALC(D). We then identify sufficient conditions on D that guarantee decidability of the satisfiability problem, even in the presence of general TBoxes. In particular, we show decidability of ALC(D) for several domains over the integers, for which decidability was open. More generally, this result holds for all negation-closed concrete domains with the EHD-property, which stands for the existence of a homomorphism is definable. Such technique has recently been used to show decidability of CTL∗ with local constraints over the integers.