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How to Frame a Mathematician

Modelling the Cognitive Background of Proofs
Chapter
Part of the Synthese Library book series (SYLI, volume 407)

Abstract

Frames are a concept in knowledge representation that explains how the receiver, using background information, completes the information conveyed by the sender. This concept is used in different disciplines, most notably in cognitive linguistics and artificial intelligence. This paper argues that frames can serve as the basis for describing mathematical proofs. The usefulness of the concept is illustrated by giving a partial formalisation of proof frames, specifically focusing on induction proofs, and relevant parts of the mathematical theory within which the proofs are conducted; for the latter, we look at natural numbers and trees specifically.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of the HumanitiesUniversity of Duisburg-EssenEssenGermany
  2. 2.Leibniz-Institut für Deutsche SpracheDigitale SprachwissenschaftMannheimGermany
  3. 3.Institute of PhilosophyUniversity of HamburgHamburgGermany
  4. 4.Center for Information and Language ProcessingLudwig-Maximilians-Universität MünchenMunichGermany
  5. 5.Institute for German Studies, LinguisticsUniversity of Duisburg-EssenEssenGermany

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