Representation and extension of states on MV-algebras

Archive for Mathematical Logic 45 (4):381-392 (2005)

MV-algebras stand for the many-valued Łukasiewicz logic the same as Boolean algebras for the classical logic. States on MV-algebras were first mentioned [20] in probability theory and later also introduced in effort to capture a notion of `an average truth-value of proposition' [15] in Łukasiewicz many-valued logic. In the presented paper, an integral representation theorem for finitely-additive states on semisimple MV-algebra will be proven. Further, we shall prove extension theorems concerning states defined on sub-MV-algebras and normal partitions of unity generalizing in this way the well-known Horn-Tarski theorem for Boolean algebras
Keywords MV-algebra  state  integral representation  partition of unity
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Reprint years 2006
DOI 10.1007/s00153-005-0286-y
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References found in this work BETA

A Theorem About Infinite-Valued Sentential Logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.

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Citations of this work BETA

State-Morphism MV-Algebras.Antonio Di Nola & Anatolij Dvurečenskij - 2009 - Annals of Pure and Applied Logic 161 (2):161-173.
States on Polyadic MV-Algebras.George Georgescu - 2010 - Studia Logica 94 (2):231-243.

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