Managing Automatically Formed Mathematical Theories

  • Simon Colton
  • Pedro Torres
  • Paul Cairns
  • Volker Sorge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4108)


The HR system forms scientific theories, and has found particularly successful application in domains of pure mathematics. Starting with only the axioms of an algebraic system, HR can generate dozens of example algebras, hundreds of concepts and thousands of conjectures, many of which have first order proofs. Given the overwhelming amount of knowledge produced, we have provided HR with sophisticated tools for handling this data. We present here the first full description of these management tools. Moreover, we describe how careful analysis of the theories produced by HR – which is enabled by the management tools – has led us to make interesting discoveries in algebraic domains. We demonstrate this with some illustrative results from HR’s theories about an algebra of one axiom. The results fueled further developments, and led us to discover and prove a fundamental theorem about this domain.


Theory Formation Left Identity Horn Clause Java Code Construction History 
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 2006

Authors and Affiliations

  • Simon Colton
    • 1
  • Pedro Torres
    • 1
    • 4
  • Paul Cairns
    • 2
  • Volker Sorge
    • 3
  1. 1.Department of ComputingImperial CollegeLondonUK
  2. 2.UCL Interaction CentreUniversity CollegeLondonUK
  3. 3.School of ComputingUniversity of BirminghamUK
  4. 4.Supported by Fundação para a Ciência e a Tecnologia,(SFRH/BD/12437/2003) 

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