A Concept Language with Role-Forming Predicate Restrictions

The development of language constructs for defining concept and role terms is an important goal of research on description logic formalisms. However, most decidable descriptions logics only support the definition of roles with very limited properties. For more complex roles, e.g. roles needed to represent Allen's temporal relations, a higher expressivity is required. This paper formally introduces a new description logic formalism called ALCRP(D). It is a descendant of ALC(D) and thus allows one to represent abstract and concrete information. Furthermore, it contains a new operator for defining roles based on predicates over (concrete) properties of objects. In previous work by the authors, reasoning in ALCRP(D) was proven to be undecidable in general. In this report we show that reasoning in ALCRP(D) is decidable if certain restrictions are posed on the structure of terminologies. In fact, the free combinability of some operators has to be restricted. The representational expr..