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The logics taught and used at high schools are not the same

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Details

Original languageEnglish
Title of host publicationProceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics
EditorsJuhani Karhumäki, Yuri Matiyasevich, Aleksi Saarela
Place of PublicationTurku
PublisherTURKU CENTRE FOR COMPUTER SCIENCE
Pages172-186
Number of pages15
ISBN (Print)978-952-12-3547-4
Publication statusPublished - May 2017
Publication typeA4 Article in a conference publication
EventFourth Russian Finnish Symposium on Discrete Mathematics - Turku, Finland
Duration: 16 May 201719 May 2017
Conference number: IV
http://math.utu.fi/rufidim2017/

Publication series

NameTUCS Lecture Notes
PublisherTurku Centre for Computer Science
Number26
ISSN (Print)1797-8823

Conference

ConferenceFourth Russian Finnish Symposium on Discrete Mathematics
Abbreviated titleRuFiDiM
CountryFinland
CityTurku
Period16/05/1719/05/17
Internet address

Abstract

Typical treatises on propositional and predicate logic do not tell how to deal with undefined expressions, such as division by zero. However, there seems to be a sound (albeit inexplicit) reasoning system that addresses undefined expressions, because equations and inequations involving them are routinely solved in schools and universities without running into fundamental inconsistencies. In this study we discover this school logic and formalize its semantics. The need to do so arose when developing software that gives students feedback on every reasoning step of their solution, instead of just telling whether the roots that they finally report are the correct roots. The problem of undefined expressions has been addressed in computer science. However, school logic proves different from those approaches. School logic is based on a Kleene-style third “undefined” truth value and the treatment of “⇒” and “⇔” not as propositional operators but as reasoning operators.

ASJC Scopus subject areas

Keywords

  • logic

Publication forum classification

Field of science, Statistics Finland