How to Frame a Mathematician: Modelling the Cognitive Background of Proofs

Bernhard Fisseni; Deniz Sarikaya; Martin Schmitt; Bernhard Schröder

doi:10.1007/978-3-030-15655-8_19

How to Frame a Mathematician: Modelling the Cognitive Background of Proofs

Bernhard Fisseni, Deniz Sarikaya, Martin Schmitt, Bernhard Schröder

History, Archeology, Arts, Philosophy and Ethics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

8 Citations (Scopus)

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.

Original language	English
Title of host publication	Synthese Library
Publisher	Springer Science and Business Media B.V.
Pages	417-436
Number of pages	20
ISBN (Electronic)	978-3-030-15655-8
ISBN (Print)	978-3-030-15654-1
DOIs	https://doi.org/10.1007/978-3-030-15655-8_19
Publication status	Published - 2019

Publication series

Name	Synthese Library
Volume	407
ISSN (Print)	0166-6991
ISSN (Electronic)	2542-8292

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

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10.1007/978-3-030-15655-8_19

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How to Frame a Mathematician: Modelling the Cognitive Background of Proofs

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