The paper settles a research branch in the realm of logic-oriented, hybrid knowledge representation. Terminological knowledge representation and reasoning can now be utilized for more realistic applications as an integral component of a computationally complete, declarative hybrid knowledge representation formalism with integrated special-purpose reasoners of concrete domains such as real-closed fields or finite-domain constraints. The paper presents technical results exploring the impact of "role interaction" on the decidability of the subsumption problem of terminological logics. In particular, decision procedures are presented for common reasoning problems in an expressive terminological logic that is parametrized by a concrete domain. A refined minimal belief logic which avoids certain problems concerning the non-propositional case (which ocurred surprisingly) is the basis of the model-theoretic semantics of a very general generic rule formalism integrating goal-directed (i.e., top-down) and data-driven (i.e., bottom-up) reasoning in a declarative manner. A mechanical engineering application (production planning of lathes) is used to demonstrate how the theoretical results can be employed in realistic applications
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