Skip to main content

Part of the book series: Applied Logic Series ((APLS,volume 15))

Abstract

One of the basic principles of probability theory is that the set of the events of a trial is a Boolean algebra. It is the case when we consider that the trial follows the laws of classical logic. On the other hand, there exist many trials which are based on a many-valued logic. In this case one can accept the hypothesis that the set of the events has a structure of MV-algebra [Di Nola et al., to appear] .

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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. C. C. Chang. Algebraic analysis of many valued logics. Trans. AMS, 88, 467–490, 1958.

    Article  Google Scholar 

  2. A. Csàszàr. Sur la structure des espaces de probabilité conditionelle. Acta Math. Acad. Sci. Hung., 6, 337–361, 1955.

    Article  Google Scholar 

  3. A. Di Nola, G. Georgescu and A. Lettieri. Extending Probabilities to states of MV-Algebras, Collegium Logicum. Annals of the Kurt-GödelSociety, to appear.

    Google Scholar 

  4. I. R. Goodman, H. T. Nguyen and E. A. Walker. Conditional Inference and Logic for Intelligent Systems,North- Holland, 1991.

    Google Scholar 

  5. R. Grigolia. Algebraic analysis of Lukasiewicz-Tarski’s n-valued systems. In Selected paper in Lukasiewicz Sentential Calculi, Ossalineum, Wroclaw, 1977.

    Google Scholar 

  6. U. Höhle and S. Weber. Uncertainty measures, realizations and entropies, preprint.

    Google Scholar 

  7. A. Horn and A. Tarski. Measures in Boolean algebras. Trans. AMS, 64, 467–497, 1948.

    Article  Google Scholar 

  8. P. H. Krauss. Representation of conditional probability measures on Boolean algebras. Acta Math. Acad. Sci. Hung., 19, 228–241, 1968.

    Article  Google Scholar 

  9. D. Mundici. Interpretation of AFC*-algebras in Lukasiewicz sentential calculus. J. of Functional Analysis, 65, 15–63, 1986.

    Article  Google Scholar 

  10. D. Mundici. Averaging the truth-value in Lukasiewicz logic. Studia Logica, 55, 113–127, 1995.

    Article  Google Scholar 

  11. A. Renyi. On a new axiomatic theory of probability. Acta Math. Acad. Sci. Hung., 6, 285–335, 1955.

    Article  Google Scholar 

  12. R. Sikorski. Boolean Algebras, Springer-Berlin, 1964.

    Google Scholar 

  13. S. Weber. Conditioning on MV-Algebras and Additive Measures, Part II, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Di Nola, A., Georgescu, G., Lettieri, A. (1999). Conditional States in Finite-Valued Logics. In: Dubois, D., Prade, H., Klement, E.P. (eds) Fuzzy Sets, Logics and Reasoning about Knowledge. Applied Logic Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1652-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-1652-9_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5324-4

  • Online ISBN: 978-94-017-1652-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics