Skip to main content
SpringerLink
Log in

Conditionals and Independence in Many-Valued Logics

  • 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))

Abstract

Formulas and valuations in boolean logic are a traditional source of examples of “events” and “possible worlds”. However, many events of interest in everyday life are more general than yes-no events, as described in boolean logic. Their possible outcomes typically range over a continuous spectrum, which after a suitable normalization can be restricted within the unit real interval [0,1].

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. Aguzzoli, S., Gerla, B., Marra, V.: De Finetti’s no-Dutch-Book criterion for Gödel logic. Studia Logica 90, 25–41 (2008); Special issue on Many-valued Logic and Cognition. Ju, S., et al. (eds.)

    Article  MATH  Google Scholar 

  2. Cignoli, R., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning. In: Trends in Logic, vol. 7. Kluwer/Springer, Dordrecht, New York (2000)

    Google Scholar 

  3. De Finetti, B.: Sul significato soggettivo della probabilitá. Fundamenta Mathematicae 17, 298–329 (1931); Translated into English as On the Subjective Meaning of Probability. In: Monari, P., Cocchi, D. (eds.) Probabilitá e Induzione, Clueb, Bologna, pp. 291–321 (1993)

    MATH  Google Scholar 

  4. De Finetti, B.: La prévision: ses lois logiques, ses sources subjectives. Annales de l’Institut H. Poincaré 7, 1–68 (1937); Translated into English by Kyburg Jr., H.E.: Foresight: Its Logical Laws, its Subjective Sources. In: Kyburg Jr., H.E., Smokler, H.E. (eds.) Studies in Subjective Probability, 7, 53–118. Wiley, New York (1980); Second edition published by Krieger, New York, pp. 53–118, 1980.

    MATH  Google Scholar 

  5. De Finetti, B.: Theory of Probability, vol. 1. John Wiley and Sons, Chichester (1974)

    MATH  Google Scholar 

  6. Emch, G.G.: Mathematical and Conceptual Foundations of 20th Century Physics. North-Holland, Amsterdam (1984)

    MATH  Google Scholar 

  7. Hájek, P.: Metamathematics of fuzzy logic. Trends in Logic, vol. 4. Kluwer/ Springer, Dordrecht, New York (1998)

    MATH  Google Scholar 

  8. Kroupa, T.: Every state on semisimple MV-algebra is integral. Fuzzy Sets and Systems 157, 2771–2782 (2006)

    Article  MATH  Google Scholar 

  9. Kühr, J., Mundici, D.: De Finetti theorem and Borel states in [0,1]-valued algebraic logic. International Journal of Approximate Reasoning 46, 605–616 (2007)

    Article  MATH  Google Scholar 

  10. Łukasiewicz, J., Tarski, A.: Investigations into the Sentential Calculus. In: [16], pp. 38–59

    Google Scholar 

  11. Mundici, D.: Bookmaking over infinite-valued events. International J. Approximate Reasoning 43, 223–240 (2006)

    Article  MATH  Google Scholar 

  12. Mundici, D.: Faithful and invariant conditional probability in Łukasiewicz logic. In: Makinson, D., Malinowski, J., Wansing, H. (eds.) Proceedings of the conference Trends in Logic IV, Torun, Poland. Trends in Logic, vol. 28, pp. 213–232. Springer, New York (2008)

    Google Scholar 

  13. Panti, G.: Invariant measures in free MV-algebras. Communications in Algebra 36, 2849–2861 (2008)

    Article  MATH  Google Scholar 

  14. Pap, E. (ed.): Handbook of Measure Theory, I,II. North-Holland, Amsterdam (2002)

    MATH  Google Scholar 

  15. Paris, J.: A note on the Dutch Book method. In: De Cooman, G., Fine, T., Seidenfeld, T. (eds.) Proceedings of the Second International Symposium on Imprecise Probabilities and their Applications, ISIPTA 2001, Ithaca, NY, USA, pp. 301–306. Shaker Publishing Company (2001), http://www.maths.man.ac.uk/DeptWeb/Homepages/jbp/

  16. Tarski, A.: Logic, Semantics, Metamathematics. Clarendon Press, Oxford (1956); reprinted, Hackett, Indianapolis (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florence, Viale Morgagni 67/a, 50134, Florence, Italy

    Daniele Mundici

Authors
  1. Daniele Mundici
    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

Mundici, D. (2009). Conditionals and Independence in Many-Valued Logics. 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_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02906-6_3

  • 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