Diagrammatic Representation and Inference

Volume 2317 of the series Lecture Notes in Computer Science pp 46-60


Using Animation in Diagrammatic Theorem Proving

  • Daniel WintersteinAffiliated withDivision of Informatics, University of Edinburgh
  • , Alan BundyAffiliated withDivision of Informatics, University of Edinburgh
  • , Corin GurrAffiliated withDivision of Informatics, University of Edinburgh
  • , Mateja JamnikAffiliated withSchool of Computer Science, University of Birmingham

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Diagrams have many uses in mathematics, one of the most ambitious of which is as a form of proof. The domain we consider is real analysis, where quantification issues are subtle but crucial. Computers offer new possibilities in diagrammatic reasoning, one of which is animation. Here we develop animated rules as a solution to problems of quantification. We show a simple application of this to constraint diagrams, and also how it can deal with the more complex questions of quantification and generalisation in diagrams that use more specific representations. This allows us to tackle difficult theorems that previously could only be proved algebraically.