An Ontology for Engineering Mathematics

Thomas R. Gruber and Greg R. Olsen. (1994). An ontology for engineering mathematics. In J. Doyle, P. Torasso, and E. Sandewall (Eds.), Fourth International Conference on Principles of Knowledge Representation and Reasoning, Gustav Stresemann Institut, Bonn, Germany, Morgan Kaufmann, 1994.

Possibly the first refereed publication of an AI ontology, explicitly called out as an ontology.  Defines a formal axiomatization of the mathematics sufficient to represent modern engineering models. The HTML version of this paper is deeply cross indexed and contains the entire ontology in machine and human readable form.

Original abstract: 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.