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The Logic of Geometric Proof

  • Ron Rood
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4045)

Abstract

Logical studies of diagrammatic reasoning—indeed, mathematical reasoning in general—are typically oriented towards proof-theory. The underlying idea is that a reasoning agent computes diagrammatic objects during the execution of a reasoning task. These diagrammatic objects, in turn, are assumed to be very much like sentences. The logician accordingly attempts to specify these diagrams in terms of a recursive syntax. Subsequently, he defines a relation ⊢ between sets of diagrams in terms of several rules of inference (or between sets of sentences and/or diagrams in case of so-called heterogeneous logics). Thus, diagrammatic reasoning is seen as being essentially a form of logical derivation. This proof-theoretic approach towards diagrammatic reasoning has been worked out in some detail, but only in a limited number of cases. For example, in case of reasoning with Venn diagrams and Euler diagrams (Shin [5] and Hammer [2]).

Keywords

External Memory Reasoning Task Base Side Relation Symbol Geometric Proof 
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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References

  1. 1.
    Barwise, J., Feferman, S. (eds.): Model-theoretic logics. Springer, New York (1985)Google Scholar
  2. 2.
    Hammer, E.: Logic and visual information. CSLI Publications, Stanford (1995)MATHGoogle Scholar
  3. 3.
    Kuratowski, K.: Introduction to set theory and topology. Pergamon, Oxford (1961)Google Scholar
  4. 4.
    Larkin, J., Simon, H.: Why a diagram is (sometimes) worth ten thousand words. Cognitive science 11, 65–99 (1987); In: Glasgow, J., Narayanan, N.H., Chandrasekaran, B.: Repr. in: Diagrammatic reasoning: cognitive and computational perspectives, pp. 69–109. MIT Press, Cambridge, AAAI Press, Menlo Park (1995)Google Scholar
  5. 5.
    Shin, S.-J.: The logical status of diagrams. Cambridge University Press, Cambridge (1994)MATHGoogle Scholar
  6. 6.
    Sierpiński, W.: Sur une nouvelle courbe continue qui remplit tout une aire plane. Bulletin international de l’Academie Polonaise des Sciences et des Lettres, Cracovie, serie A, sciences mathématiques, 462–478 (1912)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ron Rood
    • 1
  1. 1.Department of PhilosophyVrije Universiteit Amsterdam 

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