Chapter

Verification: Theory and Practice

Volume 2772 of the series Lecture Notes in Computer Science pp 395-406

Qualitative Theorem Proving in Linear Constraints

  • Vijay ChandruAffiliated withIndian Institute of Science, Computer Science & Automation
  • , Jean-Louis LassezAffiliated withComputer Science, Coastal Carolina University

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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.