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Constraint-based reasoning via Grobner Bases

Published online by Cambridge University Press:  27 February 2009

Sivand Lakmazaheri
Sivand Lakmazaheri
Affiliation:
Department of Civil Engineering, The Catholic University of America, Washington, DC 20064, USA.
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Abstract

Constraint-based reasoning is a problem-solving approach based on deductive reasoning. In this approach, a problem is modeled in terms of hypotheses and conclusion constraints, and it is solved via constraint satisfaction. The ability to handle linear and nonlinear algebraic constraints is essential for successful application of constraint-based reasoning in engineering. Due to the scarcity of algebraic techniques for satisfying nonlinear constraints, little attention has been paid to the use of constraint-based reasoning for solving nonlinear problems. This paper examines the use of the Grobner Bases method for satisfying nonlinear constraints in the context of constraint-based reasoning. After a brief introduction to the Grobner Bases method and its role in constraint-based reasoning, two examples are presented. The first example illustrates the use of Grobner bases, in the context of constraint-based reasoning, for reasoning about the behavior of beams. The second example illustrates the geometry configuration of truss structures via constraint-based reasoning.

Keywords

Constraint-based ReasoningGrobner BasesDeductive ReasoningConstraints
Type
Articles
Information
AI EDAM , Volume 11 , Issue 1 , January 1997 , pp. 5 - 15
Copyright
Copyright © Cambridge University Press 1997

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