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This paper descibes the PROTÉGÉ-II architecture for the construction of knowledge-based systems from reusable components: problem-solving methods and knowledge bases. We argue that these components are easier to reuse when their terminologies are described as formal ontologies. We define declarative mapping relations that we use to connect pre-existing methods to new domains and knowledge bases. With PROTÉGÉ-II and a set of mapping relations, we are able to reuse the same problem-solving method with two disparate tasks: (1) configuring the parts of an elevator system and (2) identifying plausible configurations of helices in a ribosome molecular strand.