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Jan \L{}ukasiewicz (Definition)

Jan \Lukasiewicz (1878 - 1956) Polish mathematician and logician mainly concerned with logic in mathematics probably best known for the three-valued logics, the Polish notation, the law of excluded middle and the axiomatizations of much classical propositional logic. He studied at the University of Lwów, earning doctorates in mathematics and philosophy in 1902. In 1919 he was Minister of Education in Poland. After WWII, he was exiled to Belgium. Arguably, the 3-valued logics named after him was the first published report of a non-Boolean, or non-Chrysippean logic (with only two logic values, `true' or `false', in the Chrysippean case). Subsequently, \Lukasiewicz logic algebras were constructed by Grigore Moisil in 1940-1945 to define `nuances' in logics, or many-valued logics, as well as 3-state control logic (electronic) circuits. \Lukasiewicz-Moisil ($LM_n$ ) logic algebras were defined axiomatically after 1969 as n-valued logic algebra representations and extensions of the \Lukasiewcz (3-valued) logics; then, the universal properties of categories of $LM_n$ -logic algebras were also investigated and reported in a series of recent publications. Recently, several modifications of $LM_n$ -logic algebras are under consideration as valid candidates for representations of quantum logics, as well as for modeling non-linear biodynamics in genetic `nets' or networks, as well as in single-cell organisms, or in tumor growth.




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See Also: genetic nets, algebraic category of LMn logic algebras, analytics and formal logics in meta-mathematics

Other names:  Jan \L{ }ukasiewicz, Jan \L ukasiewicz, Jan Lukasiewicz
Keywords:  many-valued logics, logic algebra, Chrysippean logic, Boolean logic, \L{}ukasiewicz and Post logic algebras
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Cross-references: growth, genetic nets, biodynamics, quantum logics, valid, modifications, series, universal properties, extensions, representations, algebra, circuits, many-valued logics, logic algebras, propositional logic, Polish notation, logic
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This is version 14 of Jan \L{}ukasiewicz, born on 2006-08-16, modified 2008-08-21.
Object id is 8255, canonical name is JanLukasiewicz.
Accessed 2845 times total.

Classification:
AMS MSC01A60 (History and biography :: History of mathematics and mathematicians :: 20th century)
 03G20 (Mathematical logic and foundations :: Algebraic logic :: Lukasiewicz and Post algebras)
 03G10 (Mathematical logic and foundations :: Algebraic logic :: Lattices and related structures)
 03G30 (Mathematical logic and foundations :: Algebraic logic :: Categorical logic, topoi)
 03G12 (Mathematical logic and foundations :: Algebraic logic :: Quantum logic)
 92B05 (Biology and other natural sciences :: Mathematical biology in general :: General biology and biomathematics)

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