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An optimization approach to order of magnitude reasoning

Published online by Cambridge University Press:  27 February 2009

Jayant R. Kalagnanam  and
Urmila M. Diwekar
Jayant R. Kalagnanam
Affiliation:
Center for Energy & Environmental Studies, Department of Engineering & Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Urmila M. Diwekar
Affiliation:
Center for Energy & Environmental Studies, Department of Engineering & Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
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Abstract

An approach for transforming the order of magnitude relation between two variables into an algebraic equality or inequality constraint is provided. In order to derive the order of magnitude relation between any two variables, a nonlinear optimization problem is solved for the minimum and maximum values of the ratio between the two variables, subject to two classes of constraints. The first class of constraints corresponds to the quantitative model and the second class of constraints corresponds to the qualitative model. The optimization approach is shown to provide more precise inferences as compared to the conventional constraint satisfaction approaches. Moreover, this approach provides a crucial step in developing unified frameworks that allow the incorporation of qualitative information at various levels of abstraction into numerical frameworks used for reasoning with quantitative models.

Keywords

O(M) ReasoningAl and Optimization
Type
Research Article
Information
AI EDAM , Volume 8 , Issue 3 , Summer 1994 , pp. 207 - 217
Copyright
Copyright © Cambridge University Press 1994

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