A Semantics and Complete Algorithm for Subsumption in the CLASSIC Description Logic

This paper analyzes the correctness of the subsumption algorithm used in classic, a description logic-based knowledge representation system that is being used in practical applications. In order to deal e ciently with individuals in classic descriptions, the developers have had to use an algorithm that is incomplete with respect to the standard, model-theoretic semantics for description logics. We provide a variant semantics for descriptions with respect to which the current implementation is complete, and which can be independently motivated. The soundness and completeness of the polynomial-time subsumption algorithm is established using description graphs, which are an abstracted version of the implementation structures used in classic, and are of independent interest.