This work presents a knowledge representation model and the conceptual architecture of an integrated design environment to support recording design rationale, as well as use of design rationale, during design of software artifacts. In our representation approach, we propose the use of the formal semantics of artifacts provided by design methods to represent design rationale using the vocabulary defined in the Kuaba ontology. This vocabulary described in a formal ontologies specification language allows defining a set of rules and computable operations that support the reuse of designs in the production of new software artifacts. This representation approach enables a type of software design reuse at the highest abstraction level, where rationales can be integrated and re-employed in designing a new artifact.