PlanetPhysics/Jan Lukasiewicz

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 Lw\'ow, earning doctorates in mathematics and philosophy in 1902. In 1919 he was Minister of Education in Poland. After WWII, he lived in 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). The discovery of the 3-valued logics by \L{}ukasiewicz is at least as important as the discovery by Brouwer of Intuitionistic logics, and is an intensely studied field in the extended form of many-valued logics and logic algebras. Thus, subsequently, generalized \L{}ukasiewicz logic algebras were constructed by Grigore Moisil in 1940-1945 to define `nuances' in logics, or [[../LM_nLogicAlgebra/|many-valued logics]], as well as 3-state control logic (electronic) circuits (and other important industrial logic devices including fuzzy [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] developed half a century later in Japan and USA by followers of Zadeh's fuzzy logic theory). \L ukasiewicz-Moisil ($L{M}_n$) logic algebras were defined axiomatically after 1969 by George Georgescu as n-valued logic algebra [[../CategoricalGroupRepresentation/|representations]] and extensions of the \L ukasiewcz (3-valued) logics; then, the universal properties of [[../AlgebraicCategoryOfLMnLogicAlgebras/|categories of $L{M}_n$ -logic algebras]] were also investigated and reported in a series of recent publications. Recently, several modifications of $L{M}_n$-logic algebras are under consideration as valid candidates for representations of [[../LQG2/|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.