Extending a resolution prover for inequalities on elementary functions

Authors:
Behzad Akbarpour;Lawrence C. Paulson
Affiliations:
Computer Laboratory, University of Cambridge, England;Computer Laboratory, University of Cambridge, England
Venue:
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Year:
2007

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Abstract

Experiments show that many inequalities involving exponentials and logarithms can be proved automatically by combining a resolution theorem prover with a decision procedure for the theory of real closed fields (RCF). The method should be applicable to any functions for which polynomial upper and lower bounds are known. Most bounds only hold for specific argument ranges, but resolution can automatically perform the necessary case analyses. The system consists of a superposition prover (Metis) combined with John Harrison's RCF solver and a small amount of code to simplify literals with respect to the RCF theory.