Geodesic
Bounded lattices with antitone involutions and properties of MV-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 31-42.

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We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by L or A(L) to obtain all axioms of MV-algebra.
Keywords: antitone involution, distributive lattice, implication algebra, MV-algebra 
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Chajda, Ivan; Emanovský, Peter. Bounded lattices with antitone involutions and properties of MV-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 31-42. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a1/

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[2] R.L.O. Cignoli, I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer Acad. Publ. doi: Dordrecht/Boston/London 2000

[3] I. Chajda and R. Halas, Abbott's groupoids, Multiple Valued Logic, to appear.

[4] I. Chajda, R. Halas and J. Kühr, Distributive lattices with sectionally antitone involutions, preprint 2003.