Compositional (post-coordinated) terminologies are one potential solution to the problem of content completeness. However, they have the potential to render data incomparable. For computers to determine that compositional expressions are comparable, the relations between the composed components that are understood implicitly by human readers must be represented explicitly for computer manipulation. We discuss a technique for discovering and formalizing the implicit semantic relationships in two vocabularies: the International Classification of Disease Version 9 Clinical Modification (ICD9-CM), and SNOMED-Reference Terminology (SNOMED-RT). The results of this technique are used to augment the existing SNOMED-RT relation ontology, which is a necessary step in automated concept mapping between systems. The reference terminology must contain all the semantics implicit in the classification in order to map concepts between the two representations. We also provide an explicit representation of the implied semantics of ICD9-CM. This tabulation will be useful for other knowledge engineering efforts involving ICD9-CM.