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01.02.2010 | Original Paper

Classes of examples of pseudo-MV algebras, pseudo-BL algebras and divisible bounded non-commutative residuated lattices

verfasst von: Afrodita Iorgulescu

Erschienen in: Soft Computing | Ausgabe 4/2010

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Abstract

We illustrate by classes of examples the close connections existing between pseudo-MV algebras, on the one hand, and pseudo-BL algebras and divisible bounded non-commutative residuated lattices, on the other hand. We use equivalent definitions of these algebras, as particular cases of pseudo-BCK algebras. We analyse the strongness, the pseudo-involutive center and the filters for each example.

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Buşneag D, Iorgulescu A, Rudeanu S (2008) On filters and deductive systems in algebra of logic (submitted)

Ceterchi R (1999) On algebras with implications, categorically equivalent to pseudo-MV algebras. In: The proceedings of the fourth international symposium on economic informatics. INFOREC Printing House, Bucharest, Romania, pp 912–916

Ceterchi R (2001) Pseudo-Wajsberg Algebras (A special issue dedicated to the memory of Gr. C. Moisil). Mult Val Logic 6(1–2):67–88MATHMathSciNet

Chang CC (1958) Algebraic analysis of many valued logics. Trans Am Math Soc 88:467–490MATHCrossRef

Di Nola A, Georgescu G, Iorgulescu A (2002a) Pseudo-BL algebras: part I. Multi Val Logic 8(5–6):673–714MATHMathSciNet

Di Nola A, Georgescu G, Iorgulescu A (2002b) Pseudo-BL algebras: part II. Multi Val Logic 8(5–6):717–750MATHMathSciNet

Dvurecenskij A (2001) States on pseudo MV-algebras. Stud Log 68:301–327MATHCrossRefMathSciNet

Dvurečenskij A (2002) Pseudo MV-algebras are intervals in l-groups. J Aust Math Soc 72:427–445MATHCrossRefMathSciNet

Dvurecenskij A, Giuntini R, Kowalski T (2009) On the structure of pseudo BL-algebras and pseudo hoops in quantum logics (submitted)

Dymek G (2006) Bipartite pseudo MV-algebras. Discuss Math Gen Algebra Appl 26:183–197MATHMathSciNet

Dymek G, Walendziak A (2007) On maximal ideals of pseudo MV-algebras. Comment Math 47:117–126MATHMathSciNet

Flondor P, Georgescu G, Iorgulescu A (2001) Pseudo-t-norms and pseudo-BL algebras. Soft Comput 5(5):355–371MATHCrossRef

Font JM, Rodriguez AJ, Torrens A (1984) Wajsberg algebras. Stochastica VIII(1):5–31MathSciNet

Georgescu G, Iorgulescu A (1999) Pseudo-MV Algebras: a noncommutative extension of MV algebras. In: The proceedings of the fourth international symposium on economic informatics. Bucharest, Romania, pp 961–968

Georgescu G, Iorgulescu A (2000) Pseudo-BL algebras: a noncommutative extension of BL algebras. In: Abstracts of the fifth international conference FSTA 2000. Slovakia, pp 90–92

Georgescu G, Iorgulescu A (2001a) Pseudo-BCK algebras: an extension of BCK algebras. In: Proceedings of DMTCS’01: combinatorics, computability and logic. Springer, London, pp 97–114

Georgescu G, Iorgulescu A (2001b) Pseudo-MV algebras. Mult Val Log 6(1–2):95–135MATHMathSciNet

Hájek P (1996) Metamathematics of fuzzy logic. Institute of Computer Science, Academy of Science of Czech Report, Technical report 682

Hájek P (1998) Metamathematics of fuzzy logic. Kluwer Academic Publishers, DordrechtMATH

Iorgulescu A (2004a) On pseudo-BCK algebras and porims. Sci Math Japonicae 10(16):293–305MathSciNet

Iorgulescu A (2004b) Classes of BCK algebras: Part III, Preprint Series of the Institute of Mathematics of the Romanian Academy, preprint nr. 3/2004, pp 1–37

Iorgulescu A (2005) Pseudo-Iséki algebras. Connection with pseudo-BL algebras. J Multiple Valued Log Soft Comput 11(3–4):263–308MATHMathSciNet

Iorgulescu A (2006a) Classes of pseudo-BCK algebras: part I. J Multiple Valued Log Soft Comput 12(1–2):71–130MATHMathSciNet

Iorgulescu A (2006b) Classes of pseudo-BCK algebras: part II. J Multiple Valued Log Soft Comput 12(5–6):575–629MATHMathSciNet

Iorgulescu A (2008a) On BCK algebras—part II: new algebras. The ordinal sum (product) of two bounded BCK algebras. Soft Comput 12(9):835–856. doi:10.1007/s00500-007-0239-y (Online first)MATHCrossRef

Iorgulescu A (2008b) On BCK algebras—part III: classes of examples of proper MV algebras, BL algebras and divisible bounded residuated lattices, with or without condition (WNM) (submitted)

Iséki K (1966) An algebra related with a propositional calculus. Proc Jpn Acad 42:26–29MATHCrossRef

Mundici D (1986a) MV-algebras are categorically equivalent to bounded commutative BCK-algebras. Math Jpn 31(6):889–894MATHMathSciNet

Mundici D (1986b) Interpretation of AF C-algebras in Lukasiewicz sentential calculus. J Funct Anal 65:15–63MATHCrossRefMathSciNet

Rachunek J (2002) A non-commutative generalization of MV-algebras. Czechoslovak Math J 52:255–273MATHCrossRefMathSciNet

Swamy KLN (1965) Dually residuated lattice ordered semigroups. Math Ann 159:105–114MATHCrossRefMathSciNet

Titel: Classes of examples of pseudo-MV algebras, pseudo-BL algebras and divisible bounded non-commutative residuated lattices
verfasst von: Afrodita Iorgulescu
Publikationsdatum: 01.02.2010
Verlag: Springer-Verlag
Erschienen in: Soft Computing / Ausgabe 4/2010
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-009-0405-5

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