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 efficiently 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.