Variable elimination and chaining in a resolution-based prover for inequalities

  • W. W. Bledsoe
  • Larry M. Hines
Wednesday Morning

DOI: 10.1007/3-540-10009-1_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 87)
Cite this paper as:
Bledsoe W.W., Hines L.M. (1980) Variable elimination and chaining in a resolution-based prover for inequalities. In: Bibel W., Kowalski R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg

Abstract

A modified resolution procedure is described which has been designed to prove theorems about general linear inequalities. This prover uses "variable elimination", and a modified form of inequality chaining (in which chaining is allowed only on so called "shielding terms"), and a decision procedure for proving ground inequality theorems. These techniques and others help to avoid the explicit use of certain axioms, such as the transitivity and interpolation axioms for inequalities, in order to reduce the size of the search space and to speed up proofs. Several examples are given along with results from a computer implementation. In particular this program has proved some difficult theorems such as: The sum of two continuous functions is continuous.

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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • W. W. Bledsoe
    • 1
  • Larry M. Hines
    • 1
  1. 1.The University of TexasAustin

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