This paper deals with terminological representation languages for KL-ONE-type knowledge representation systems. Such languages are based on the two primitive syntactic types called concepts and roles, which are usually represented model-theoretically as sets and binary relations respectively. Rather than following the model-theoretic route, we show that the semantics can be naturally accommodated in the context of an equational algebra of relations interacting with sets. Equational logic is then a natural vehicle for computing subsumptions, both of concepts and of roles. We thus propose the algebraic rather than model-theoretic computation of subsumption.
Also in Lehmann, F. (ed.) (1992), Semantic Networks in Artificial Intelligence, Modern Applied Mathematics and Computer Science Series 24, Pergamon Press, Oxford, UK.