Skip to main content
SpringerLink
Log in

On the Convergence with Fixed Regulator in Residuated Structures

  • Conference paper
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5590))

  • 1238 Accesses

Abstract

The convergence with a fixed regulator has been studied for lattice ordered groups and MV-algebras. In this paper we present some particular results for the case of perfect MV-algebras using Di Nola-Lettieri functors and we extend the notion of convergence with a fixed regulator for residuated lattices. The main results consist of proving that any locally Archimedean MV-algebra has a unique v-Cauchy completion and that in an Archimedean residuated lattice the v-limit is unique.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belluce, L.P., Di Nola, A.: Yosida type representation for perfect MV-algebras. Math. Log. Quart. 42, 551–563 (1996)

    Article  MATH  Google Scholar 

  2. Černák, Š., Liihová, J.: Convergence with a regulator in lattice ordered groups. Tatra Mountains Mathematical Publications 30, 35–45 (2005)

    MATH  Google Scholar 

  3. Černák, Š.: Convergence with a fixed regulator in Archimedean lattice ordered groups. Mathematica Slovaca 2, 167–180 (2006)

    MATH  Google Scholar 

  4. Černák, Š.: Convergence with a fixed regulator in lattice ordered groups and applications to MV-algebras. Soft Computing 12(5), 453–462 (2008)

    Article  MATH  Google Scholar 

  5. Cignoli, R., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundation of Many-valued Reasoning. Kluver academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  6. Ciungu, L.C.: Classes of residuated lattices. An. Univ. Craiova Ser. Mat. Inform. 33, 189–207 (2006)

    MATH  Google Scholar 

  7. Georgescu, G., Liguori, F., Martini, G.: Convergence in MV-algebras. Soft Computing 4, 41–52 (1997)

    MATH  Google Scholar 

  8. Georgescu, G., Leuştean, I.: Convergence in perfect MV-algebras. Journal of Mathematical Analysis and Applications 228(1), 96–111 (1998)

    Article  MATH  Google Scholar 

  9. Georgescu, G., Popescu, A.: Similarity Convergence in Residuated Structures. Logic Journal of IGPL 13(4), 389–413 (2005)

    Article  MATH  Google Scholar 

  10. Di Nola, A., Letieri, A.: Perfect MV-algebras are categoricaly equivalent to abelian ℓ-groups. Studia Logica 53, 417–432 (1994)

    Article  Google Scholar 

  11. Di Nola, A.: Algebraic analysis of Łukasiewicz logic, ESSLLI, Summer school, Utrecht (August 1999)

    Google Scholar 

  12. Kowalski, T., Ono, H.: Residuated lattices: An algebraic glimpse at logics without contraction, Monograph (2001)

    Google Scholar 

  13. Mundici, D.: Interpretation of AF C *-algebras in Lukasiewicz calculus. J. Funct. Analysis 65, 15–63 (1986)

    Article  MATH  Google Scholar 

  14. Ono, H.: Substructural logics and residuated lattices-an introduction. In: 50 Years of Studia Logica, Trends in Logic, vol. 21, pp. 193–228. Kluwer Academic Publisher, Dordrecht (2003)

    Google Scholar 

  15. Turunen, E.: Mathematics behind fuzzy logic. In: Advances in Soft Computing. Physica-Verlag, Heildelberg (1999)

    Google Scholar 

  16. Ward, M., Dilworth, R.P.: Residuated lattices. Transactions of the American Mathematical Society 45, 335–354 (1939)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Polytechnical University of Bucharest, Splaiul Independenţei 313, Bucharest, Romania

    Lavinia Corina Ciungu

Authors
  1. Lavinia Corina Ciungu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. ISIB-CNR, Corso Stati Uniti 4, 35127, Padova, Italy

    Claudio Sossai

  2. ISIB-CNR, Corso Stati Uniti, 4, 35127, Padova, Italy

    Gaetano Chemello

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ciungu, L.C. (2009). On the Convergence with Fixed Regulator in Residuated Structures. In: Sossai, C., Chemello, G. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2009. Lecture Notes in Computer Science(), vol 5590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02906-6_77

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02906-6_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02905-9

  • Online ISBN: 978-3-642-02906-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation