Soft Computing

, Volume 12, Issue 4, pp 341–352 | Cite as

On some properties of quasi-MV algebras and \(\sqrt{^{\prime}}\) quasi-MV algebras. Part II

  • Félix Bou
  • Francesco Paoli
  • Antonio Ledda
  • Hector Freytes


The present paper is a sequel to Paoli F, Ledda A, Giuntini R, Freytes H (On some properties of QMV algebras and \(\sqrt{^{\prime}}\)QMV algebras, submitted). We provide two representation results for quasi-MV algebras in terms of MV algebras enriched with additional structure; we investigate the lattices of subvarieties and subquasivarieties of quasi-MV algebras; we show that quasi-MV algebras, as well as cartesian and flat \(\sqrt{^{\prime}}\) quasi-MV algebras, have the amalgamation property.


Residuated Lattice Cardinal Number Congruence Lattice Labelling Function Amalgamation Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aglianò P, Ursini A (1997) On subtractive varieties III. Algebra Universalis 37:296–333zbMATHCrossRefMathSciNetGoogle Scholar
  2. Blok WJ, Ferreirim IMA (2000) On the structure of hoops. Algebra Universalis 43:233–257zbMATHCrossRefMathSciNetGoogle Scholar
  3. Chajda I (1995) Normally presented varieties. Algebra Universalis 34:327–335zbMATHCrossRefMathSciNetGoogle Scholar
  4. Cignoli R, D’Ottaviano IML, Mundici D (1999) Algebraic foundations of many-valued reasoning. Kluwer, DordrechtGoogle Scholar
  5. Di Nola A, Lettieri A (1999) Equational characterization of all varieties of MV algebras. J Algebra 221(2):463–474zbMATHCrossRefMathSciNetGoogle Scholar
  6. Galatos N (2005) Minimal varieties of residuated lattices. Algebra Universalis 52(2):215–239CrossRefMathSciNetGoogle Scholar
  7. Giuntini R, Ledda A, Paoli F (2007) Expanding quasi-MV algebras by a quantum operator. Studia Logica (in press)Google Scholar
  8. Grätzer G, Lakser H (1973) A note on the implicational class generated by a class of structures. Can Math Bull 16:603–605zbMATHGoogle Scholar
  9. Gumm HP, Ursini A (1984) Ideals in universal algebra. Algebra Universalis 19:45–54zbMATHCrossRefMathSciNetGoogle Scholar
  10. Komori Y (1981) Super Łukasiewicz propositional logics. Nagoya Math J 84:119–133zbMATHMathSciNetGoogle Scholar
  11. Kowalski T, Ono H (2000) Splittings in the variety of residuated lattices. Algebra Universalis 44:283–298zbMATHCrossRefMathSciNetGoogle Scholar
  12. Ledda A, Konig M, Paoli F, Giuntini R (2006) MV algebras and quantum computation. Studia Logica 82(2):245–270zbMATHCrossRefMathSciNetGoogle Scholar
  13. Lewin R, Sagastume M, Massey P (2004) MV* algebras. Logic J IGPL 12(6):461–483zbMATHCrossRefMathSciNetGoogle Scholar
  14. Lipparini P (1995) n-Permutable varieties satisfy nontrivial congruence identities. Algebra Universalis 33(2):159–168zbMATHCrossRefMathSciNetGoogle Scholar
  15. McKenzie R, McNulty GF, Taylor WF (1987) Algebras, lattices, varieties. Wadsworth & Brooks-Cole, MontereyzbMATHGoogle Scholar
  16. Mundici D (1987) Bounded commutative BCK algebras have the amalgamation property. Math Jpn 32:279–282zbMATHMathSciNetGoogle Scholar
  17. Paoli F, Ledda A, Giuntini R, Freytes H (submitted)On some properties of QMV algebras and \(\sqrt{^{\prime}}\)QMV algebras (submitted) downloadable from &id_corso=38Google Scholar
  18. Salibra A (2003) Topological incompleteness and order incompleteness in lambda calculus. ACM Trans Comput Logic 4(3):379–401CrossRefMathSciNetGoogle Scholar
  19. Spinks M (2003) Contributions to the theory of Pre-BCK Algebras. PhD Thesis, Monash UniversityGoogle Scholar
  20. Ursini A (1994) On subtractive varieties I. Algebra Universalis 31: 204–222zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Félix Bou
    • 1
  • Francesco Paoli
    • 2
  • Antonio Ledda
    • 2
  • Hector Freytes
    • 2
  1. 1.IIIA-CSICBellaterraSpain
  2. 2.Department of EducationUniversity of CagliariCagliariItaly

Personalised recommendations