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A Rational Reconstruction of a System for Experimental Mathematics

  • Jacques Carette
  • William M. Farmer
  • Volker Sorge
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4573)

Abstract

In previous papers we described the implementation of a system which combines mathematical object generation, transformation and filtering, conjecture generation, proving and disproving for mathematical discovery in non-associative algebra. While the system has generated novel, fully verified theorems, their construction involved a lot of ad hoc communication between disparate systems. In this paper we carefully reconstruct a specification of a sub-process of the original system in a framework for trustable communication between mathematics systems put forth by us. It employs the concept of biform theories that enables the combined formalisation of the axiomatic and algorithmic theories behind the generation process. This allows us to gain a much better understanding of the original system, and exposes clear generalisation opportunities.

Keywords

Logical Consequence Binary Operation Theorem Prover General Language Axiomatic Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jacques Carette
    • 1
  • William M. Farmer
    • 1
  • Volker Sorge
    • 2
  1. 1.Department of Computing and Software, McMaster University, Hamilton, OntarioCanada
  2. 2.School of Computer Science, University of BirminghamUK

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