Skip Navigation



Journal of Logic and Computation Advance Access published online on March 10, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp016
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Leustean, I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Metric Completions of MV-algebras with States: An Approach to Stochastic Independence

Ioana Leustean

Faculty of Mathematics and Computer Science, University of Bucharest, Romania and Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany.
E-mail: ileustean{at}mathematik.tu-darmstadt.de

Received 10 October 2008.

The state theory on MV-algebras is a generalization of Boolean probability theory and is a counterpart of the theory of states defined on lattice-ordered groups. We first investigate the metric space naturally associated to an MV-algebra with a state. The metric completion of anMV-algebra is defined and characterized in relation with the geometric properties of the corresponding state. We propose a concept of independent probability MV-algebras, attempting to solve an open problem from Riecan and Mundici.

Keywords: MV-algebras; states; metric completion; probability MV-algebras; stochastic independence



References

  1. Bigard A, Keimel K, Wolfenstein S. Groupes et anneaux réticulés (1977) Springer. Vol. 608 of Lectures Notes in Mathematics.
  2. Chang CC. Algebraic analysis of many valued logics. Transactions of the American Mathematical Society (1958) 88:467–490.[CrossRef]
  3. Cignoli R, D’Ottaviano IML, Mundici D. Algebraic Foundations of Many-Valued Reasoning (2000) Kluwer.
  4. Cuculescu I, Onicescu O. Probability Theory on Boolean Algebras of Events (1976) Editura Academiei Republicii Socialiste Romania.
  5. Dvurecenskij A. States on Pseudo MV-Algebras. Studia Logica (2001) 68:301–327.[CrossRef]
  6. Flondor P, Leustean I. Tensor products of MV-algebras. Soft Computing (2003) 7:446–457.[Web of Science]
  7. Fremlin DH. Measure Theory (1995) Available at http://www.essex.ac.uk/maths/staff/fremlin/mt.htm.
  8. Georgescu G, Liguori F, Martini G. Convergence in MV-algebras. Mathware & Soft Computing (1997) 4:41–52.
  9. Goodearl KR, Handelman DE. Metric completions of partially ordered abelian groups. Indiana University Mathematics Journal (1980) 29:861–895.[CrossRef][Web of Science]
  10. Goodearl KR. Partially Ordered Abelian Groups with Interpolation (1986) American Mathematical Society.
  11. Kelley JL. General Topology. The University Series in Higher Mathematics (1955) D. Van Nostrand Company.
  12. Kroupa T. Every state on semisimple MV-algebra is integral. Fuzzy Sets and Systems (2006) 157:2771–2782.[CrossRef][Web of Science]
  13. Kroupa T. Representation and extension of states on MV-algebras. Archive for Mathematical Logic (2006) 45:381–392.[CrossRef][Web of Science]
  14. Leustean I. Tensor products of probability MV-algebras. Journal of Multiple-Valued Logic and Soft Computing. (in press).
  15. Martinez J. Tensor products of partially ordered groups. Pacific Journal of Mathematics (1972) 41:771–789.[Web of Science]
  16. Mundici D. Interpretation of AFC*-algebras in Lukasiewicz sentential calculus. J. Functional Analysis (1986) 65:15–63.[CrossRef]
  17. Mundici D. Averaging the truth-value in Lukasiewicz logic. Studia Logica (1995) 55:113–127.[CrossRef]
  18. Mundici D. Tensor products and the Loomis-Sikorski theorem for MV-algebras. Advances in Applied Mathematics (1999) 22:227–248.[CrossRef][Web of Science]
  19. Panti G. Invariant measures in free MV-algebras. Communications in Algebra Volume (2008) 36:2849–2861.[CrossRef]
  20. Riecan B, Mundici D. Probability inMV-algebras. In: Handbook of Measure Theory—Pap E, ed. (2002) North-Holland. 869–909.

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Leustean, I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?