PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Discussiones Mathematicae - General Algebra and Applications

2004 | 24 | 1 | 31-42
Tytuł artykułu

### Bounded lattices with antitone involutions and properties of MV-algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
31-42
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-06-20
poprawiono
2004-04-30
Twórcy
autor
• Department of Algebra and Geometry, Palacký University, Faculty of Sciences, Tomkova 40, 779-00 Olomouc, Czech Republik
autor
• Department of Mathematics, Palacký University, Pedagogical Faculty, Zizkovo nám. 5, 771-40 Olomouc, Czech Republik
Bibliografia
• [1] J.C. Abbott, Semi-boolean algebra, Mat. Vestnik 4 (1967), 177-198.
• [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.
Typ dokumentu
Bibliografia
Identyfikatory