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

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Yksityiskohdat

AlkuperäiskieliEnglanti
OtsikkoProceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics
ToimittajatJuhani Karhumäki, Yuri Matiyasevich, Aleksi Saarela
JulkaisupaikkaTurku
KustantajaTURKU CENTRE FOR COMPUTER SCIENCE
Sivut172-186
Sivumäärä15
ISBN (painettu)978-952-12-3547-4
TilaJulkaistu - toukokuuta 2017
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisussa
TapahtumaFourth Russian Finnish Symposium on Discrete Mathematics - Turku, Suomi
Kesto: 16 toukokuuta 201719 toukokuuta 2017
Konferenssinumero: IV
http://math.utu.fi/rufidim2017/

Julkaisusarja

NimiTUCS Lecture Notes
KustantajaTurku Centre for Computer Science
Numero26
ISSN (painettu)1797-8823

Conference

ConferenceFourth Russian Finnish Symposium on Discrete Mathematics
LyhennettäRuFiDiM
MaaSuomi
KaupunkiTurku
Ajanjakso16/05/1719/05/17
www-osoite

Tiivistelmä

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.

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