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Playing with Diagrams

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Book cover Theory and Application of Diagrams (Diagrams 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1889))

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Abstract

This paper extends work that developed a programmed model of reasoning about geometric propositions. The system reasons by manipulating representations of diagrams and noticing newly emerged facts that are construed as inferences. The system has been explored as a means of verifying diagrammatic demonstrations of classical geometric propositions and for constructing diagrammatic demonstrations of conclusions supplied for the system. The process of discovering propositions to be demonstrated is a more difficult task. This paper argues that central to the discovery process is systematic manipulation of diagrams - playing - and observing consistent relations among features of the diagram as manipulations are made and observed. The play results in the creation of an “episode” of diagram behaviors which is examined for regularities from which a general proposition might be proposed. The paper illustrates this process and discusses the advantages and limitations of this system and of other computational models of diagrammatic reasoning.

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Author information

Authors and Affiliations

  1. University of Michigan, 205 Zina Pitcher Place, Ann Arbor, Michigan, USA

    Robert K. Lindsay

Authors
  1. Robert K. Lindsay
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Hartford, Dana Hall 230, 200 Bloomfield Avenue, West Hartford, Connecticut, 06117, USA

    Michael Anderson

  2. School of Psychology ESRC Centre for Research in Development, Instruction and Training, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Peter Cheng

  3. Computer Science Department, University of Hamburg, Vogt-Koelln-Str. 30, 22527, Hamburg, Germany

    Volker Haarslev

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© 2000 Springer-Verlag Berlin Heidelberg

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Lindsay, R.K. (2000). Playing with Diagrams. In: Anderson, M., Cheng, P., Haarslev, V. (eds) Theory and Application of Diagrams. Diagrams 2000. Lecture Notes in Computer Science(), vol 1889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44590-0_27

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  • DOI: https://doi.org/10.1007/3-540-44590-0_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67915-8

  • Online ISBN: 978-3-540-44590-6

  • eBook Packages: Springer Book Archive

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