Skip to main content
SpringerLink
Log in

States on Hilbert Algebras

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

In this paper we develop a theory of Bosbach and Riečan states on non-trivial Hilbert algebras.

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. Balbes, R., and Ph. Dwinger, Distributive Lattices, Univ. of Missouri Press, 1974.

  2. Bosbach B. (1982) ‘Residuation groupoids’. Resultate der Mathematik 5: 107–122

    Google Scholar 

  3. Buşneag C. (2007) ‘Valuations on residuated lattices’. Anals of the University of Craiova, Math. Comp. Sci. Ser., vol. 34(1): 5–10

    Google Scholar 

  4. Buşneag, D., Contributions to the study of Hilbert algebras (in romanian), Ph. D. Thesis, Univ. of Bucharest, 1985.

  5. Buşneag D. (1988) ‘Hilbert algebras of fractions and maximal Hilbert algebras of quotients’. Kobe J. Math. 5: 161–172

    Google Scholar 

  6. Buşneag D. (2003) ‘On extensions of pseudo-valuation on Hilbert algebra’. Discrete Mathematics 263: 11–24

    Article  Google Scholar 

  7. Buşneag D. (2006) Categories of algebraic logic. Editura Academiei Române, Bucharest

    Google Scholar 

  8. Ciungu L. ‘States on pseudo-BCK algebras’, Math. Reports 10 (60) 1(2008), 17–36.

    Google Scholar 

  9. Diego, A., ‘Sur les algèbres de Hilbert’, Coll. Logique Math., Serie A, No. 21, Gauthier-Villars, Paris, (1966), 1–54.

  10. Dvurečenskij A. (2001) ‘States on pseudo-MV algebras’. Studia Logica 68: 301–327

    Article  Google Scholar 

  11. Dvurečenskij A., Pulmannova S. (2000) New trends in quantum structures. Kluver & Ister Science, Bratislava

    Google Scholar 

  12. Dvurečenskij A., Rachůnek J. (2006) ‘On Riečan and Bosbach states for bounded non-commutative RL-monoids’. Math. Slovaca 5: 487–500

    Google Scholar 

  13. Georgescu G. (2004) ‘Bosbach states of fuzzy structures’. Soft Computing 8: 217–230

    Google Scholar 

  14. Kôpka F., Chovanec F. (1994) ‘D-posets’. Math. Slovaca, 44: 21–34

    Google Scholar 

  15. Mundici D. (1995) ‘Averaging the truth value in Lukasiewicz sentential logic’. Studia Logica. Special issue in honor of Helena Rasiowa 55: 113–127

    Google Scholar 

  16. Porta, H., ‘Sur quelques algèbres de la logique’, Portugaliae Math., vol. 40, Fasc. 1 (1981), 41–47.

  17. Riečan B. (2000) ‘On the probability on BL-algebras’. Acta Math. Nitra 4: 3–13

    Google Scholar 

  18. Taşcău, D., ‘Some properties of the operationx \({{\sqcup{y} = ({x} \to {y}) \to (({y} \to {x}) \to {x})}}\) in a Hilbert algebra’, Anals of the University of Craiova, Math. Comp. Sci. Ser., vol. 34 (1) (2007), 79–82.

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Craiova, Craiova, Romania

    Cătălin Buşneag

Authors
  1. Cătălin Buşneag
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cătălin Buşneag.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buşneag, C. States on Hilbert Algebras. Stud Logica 94, 177–188 (2010). https://doi.org/10.1007/s11225-010-9229-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-010-9229-7

Keywords

2000 AMS Subject Classification

Search

Navigation