| Abstract
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We describe an ontology for mathematical m … We describe an ontology for mathematical modeling in engineering. The ontology includes conceptual foundations for scalar, vector, and tensor quantities, physical dimensions, units of measure, functions of quantities, and dimensionless quantities. The conceptualization builds on abstract algebra and measurement theory, but is designed explicitly for knowledge sharing purposes. The ontology is being used as a communication language among cooperating engineering agents, and as a foundation for other engineering ontologies. In this paper we describe the conceptualization of the ontology, and show selected axioms from definitions. We describe the design of the ontology and justify the important representation choices. We offer evaluation criteria for such ontologies and demonstrate design techniques for achieving them. rate design techniques for achieving them.
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