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Many-valued logics

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Triangular Norms

Part of the book series: Trends in Logic ((TREN,volume 8))

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Abstract

The study of many-valued logic was initiated by Jan Lukasiewicz around 1920. He started with a three-valued logic, introducing in particular an implication for it (see [Lukasiewicz 1920, 1930] and [Lukasiewicz & Tarski 1930], a selection of Lukasiewicz’s papers can be found in [Borkowski 1970]). Another important step was the study of intuitionistic logic in [Heyting 1930, Gödel 1932], significant contributions were also made in, e.g., [Post 1921], [Moisil 1940, 1941] and [McNaughton 1951, Chang 1958, Rose & Rosser 1958] (for surveys on many-valued logics we refer to the monographs [Rosser & Turquette 1952, Rescher 1969] and [Gottwald 1989, 200x]).

The same thing cannot at the same time both belong and not belong to the same object and in the same respect. [...] Of any object, one thing must be either asserted or denied.

Aristotle

Logic changes from its very foundations if we assume that in addition to truth and falsehood there is also some third logical value or several such values.

Jan Lukasiewicz

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© 2000 Springer Science+Business Media Dordrecht

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Klement, E.P., Mesiar, R., Pap, E. (2000). Many-valued logics. In: Triangular Norms. Trends in Logic, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9540-7_11

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  • DOI: https://doi.org/10.1007/978-94-015-9540-7_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5507-1

  • Online ISBN: 978-94-015-9540-7

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