This thesis describes a description matcher for the KL-ONE knowledge representation language that is incremental and can perform partial matches. The matcher is incremental in that it can be suspended at any time, producing partial results, and later restarted. The matcher is partial in that it has a formalism for measuring the degree to which two descriptions match. Both features are supported by using four different scalar metrics for the degree of match of two descriptions: a lower bound, an upper bound, a base value, and a current estimate.