Skip to main content
SpringerLink
Log in

On Certain Quasivarieties of Quasi-MV Algebras

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present paper. We especially focus on quasivarieties whose generators either are subalgebras of the standard square quasi-MV algebra S, or can be obtained therefrom through the addition of some fixpoints for the inverse.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bou F., Paoli F., Ledda A., Freytes H.: ‘On some properties of quasi-MV algebras and \({\sqrt{'}}\) quasi-MV algebras. Part II’. Soft Computing 12(4), 341–352 (2008)

    Article  Google Scholar 

  2. Bou F., Paoli F., Ledda A., Spinks M., Giuntini R.: ‘The logic of quasi-MV algebras’. Journal of Logic and Computation 20(2), 619–643 (2010)

    Article  Google Scholar 

  3. Chang, C. C., and H. J. Keisler, Model Theory, North Holland, Amsterdam, 19922

  4. Cignoli R., D’OttavianoI. M. L., Mundici D.: Algebraic Foundations of Many-Valued Reasoning. Kluwer, Dordrecht (1999)

    Google Scholar 

  5. Kowalski T., Paoli F.: ‘On some properties of quasi-MV algebras and \({\sqrt{'}}\) quasi-MV algebras. Part III’. Reports on Mathematical Logic 45, 161–199 (2010)

    Google Scholar 

  6. Kowalski T., Paoli F., Giuntini R., Ledda A.: ‘The lattice of subvarieties of \({\sqrt{'}}\) quasi-MV algebras’. Studia Logica 95, 37–61 (2010)

    Article  Google Scholar 

  7. Kowalski, T., F. Paoli, and M. Spinks, ‘Quasi-subtractive varieties’, Journal of Symbolic Logic, forthcoming.

  8. Ledda A., Konig M., Paoli F., Giuntini R.: ‘MV algebras and quantum computation’. Studia Logica 82(2), 245–270 (2006)

    Article  Google Scholar 

  9. Paoli F., Ledda A., Giuntini R., Freytes H.: ‘On some properties of quasi-MV algebras and \({\sqrt{'}}\) quasi-MV algebras. Part I’. Reports on Mathematical Logic 44, 31–63 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Cagliari & R.A.S., Via Is Mirrionis 1, Cagliari, Italy

    A. Ledda

  2. University of Cagliari, Via Is Mirrionis 1, Cagliari, Italy

    F. Paoli

  3. Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3010, Australia

    T. Kowalski

Authors
  1. A. Ledda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Kowalski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Paoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Kowalski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ledda, A., Kowalski, T. & Paoli, F. On Certain Quasivarieties of Quasi-MV Algebras. Stud Logica 98, 149–174 (2011). https://doi.org/10.1007/s11225-011-9331-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-011-9331-5

Keywords

Search

Navigation