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Axiomathes

, Volume 16, Issue 1–2, pp 123–136 | Cite as

N-Valued Logics and Łukasiewicz–Moisil Algebras

  • George Georgescu
Article

Abstract

Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras, , (which are well-understood) to the more general category \({\cal L}\)M n of Łukasiewicz–Moisil Algebras. Furthermore, the relationships of LM n -algebras to other many-valued logical structures, such as the n-valued Post, MV and Heyting logic algebras, are investigated and several pertinent theorems are derived. Applications of Łukasiewicz–Moisil Algebras to biological problems, such as nonlinear dynamics of genetic networks – that were previously reported – are also briefly noted here, and finally, probabilities are precisely defined over LM n -algebras with an eye to immediate, possible applications in biostatistics.

Keywords

categories N-valued logics and Łukasiewicz–Moisil logic algebras categories of Łukasiewicz–Moisil algebras the fundamental logic adjunction theorem equivalences between pairs of different categories of n-valued logic algebras colimits limits and adjointness relations in biology category of boolean algebras Post MV and Heyting logic algebras universal or global properties of categories of logic algebras full and faithful adjoint functors between certain categories of logic algebras and the boolean logic category the logic(s) of life itself biological applications of Łukasiewicz–Moisil Algebras defining probabilities over LMn-algebras and their potential applications in biostatistics 

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© Springer 2006

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  • George Georgescu

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