Terminological reasoning and partial inductive definitions

There are two motivations for this paper. (i) In terminological systems in the tradition of KL-ONE the taxonomic and conceptual knowledge of a particular problem domain can be represented by so called concepts. The intensional definitions of these concepts can be analyzed and checked for plausibility using certain reasoning services (e.g. subsumption) that make the user conscious of some of the consequences of his definitions. A hybrid knowledge base can then rely on these checked definitions. In this paper a terminological formalism is embedded into the formalism of partial inductive definitions (PID) such that a flexible environment for experimenting with this kind of hybrid systems and the terminological formalism itself is obtained. (ii) Terminological formalisms provide (terminating) decision procedures for their reasoning services dealing with a restricted kind of quantification. Mapping these algorithms to PID improves the understanding of control and explicit quantification in PID