In this paper we present the Kuaba Ontology, a vocabulary for Design Rationale described in an ontology definition language that allows attributing semantics to recorded Design Rationale content, and defining rules that enable performing computable operations and inferences on this content. This vocabulary extends the argumentation structure of the Issue Based Information System (IBIS) enriching this argumentation structure by explicating the representation of the decisions made during design and their justifications, and the relations between the argumentation elements and generated artifacts. It consists also of integrating this argumentation structure with descriptions of the produced artifact, and with information about the design history. In addition, we propose to support the design process through the use of the semantic descriptions defined by formal models of the artifacts. Representing Design Rationale using an ontology definition language and the artifacts formal model, enables a type of software reuse at the highest abstraction level, where rationales are reemployed in designing a new artifact. This kind of reuse is possible in knowledge domains where there are formal models describing the artifacts, in particular, in the Software Design domain.