Function is an ambiguous concept, whereas having explicit and precise concepts is critical for building a systematic science of engineering design. Based on Bunge's scientific ontology, this paper is devoted to developing an explicit and precise concept of function for design science. First, we attempt to clarify the concept of behavior, which is closely related to function and is also shown as an ambiguous concept in engineering. Second, the concept of action is imported from scientific ontology into design science. Third, a scientific ontology based concept of function is proposed, together with an ontology-based functional taxonomy. A case of a function definition of a civil aircraft type demonstrates that the proposed concept of function is more explicit and precise than previous ones, and it can lead to better functional design results.