Qualitative Theorem Proving in Linear Constraints

  • Vijay Chandru
  • Jean-Louis Lassez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2772)

Abstract

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Vijay Chandru
    • 1
  • Jean-Louis Lassez
    • 2
  1. 1.Indian Institute of ScienceComputer Science & AutomationBangaloreIndia
  2. 2.Computer ScienceCoastal Carolina UniversityUSA

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