The Infinite-Valued Łukasiewicz Logic and Probability

Janusz Czelakowski

Bulletin of the Section of Logic (2017)

  • Volume: 46, Issue: 1/2
  • ISSN: 0138-0680

Abstract

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The paper concerns the algebraic structure of the set of cumulative distribution functions as well as the relationship between the resulting algebra and the infinite-valued Łukasiewicz algebra. The paper also discusses interrelations holding between the logical systems determined by the above algebras.

How to cite

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Janusz Czelakowski. "The Infinite-Valued Łukasiewicz Logic and Probability." Bulletin of the Section of Logic 46.1/2 (2017): null. <http://eudml.org/doc/295584>.

@article{JanuszCzelakowski2017,
abstract = {The paper concerns the algebraic structure of the set of cumulative distribution functions as well as the relationship between the resulting algebra and the infinite-valued Łukasiewicz algebra. The paper also discusses interrelations holding between the logical systems determined by the above algebras.},
author = {Janusz Czelakowski},
journal = {Bulletin of the Section of Logic},
keywords = {probability; cumulative distribution function; the infinite-valued standard Łukasiewicz algebra; consequence relation},
language = {eng},
number = {1/2},
pages = {null},
title = {The Infinite-Valued Łukasiewicz Logic and Probability},
url = {http://eudml.org/doc/295584},
volume = {46},
year = {2017},
}

TY - JOUR
AU - Janusz Czelakowski
TI - The Infinite-Valued Łukasiewicz Logic and Probability
JO - Bulletin of the Section of Logic
PY - 2017
VL - 46
IS - 1/2
SP - null
AB - The paper concerns the algebraic structure of the set of cumulative distribution functions as well as the relationship between the resulting algebra and the infinite-valued Łukasiewicz algebra. The paper also discusses interrelations holding between the logical systems determined by the above algebras.
LA - eng
KW - probability; cumulative distribution function; the infinite-valued standard Łukasiewicz algebra; consequence relation
UR - http://eudml.org/doc/295584
ER -

References

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  1. [1] P. Billingsley, Probability and Measure, John Wiley & Sons, Inc., New York, NY, 1995. 
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  3. [3] P. Cintula, P. H ájek and Ch. Noguera (eds.), Handbook of Mathematical Fuzzy Logic (Studies in Logic, Volumes 37-38), College Publications, London, 2011. 
  4. [4] J. Czelakowski, O probabilistycznej interpretacji predykatw (Polish), [in:] [5]. 
  5. [5] A. Wójtowicz and J. Golińska-Pilarek (eds.), Identyczność znaku czy znak identyczności? (Identity of Sign or the Sign of Identity?),Warsaw University Press, Warsaw, 2012. 
  6. [6] J. Czelakowski, Probabilistic Interpretations of Predicates, [in:] Katalin Bimbó (ed.), J. Michael Dunn on Information Based Logics (Outstanding Contributions to Logic, Volume 8), Springer, Berlin, 2016, pp. 247–278. 
  7. [7] J. M. Dunn and G. M. Hardegree, Algebraic Methods in Philosophical Logic (Oxford Logic Guides, Oxford Science Publications, Volume 41), Oxford University Press, New York, 2001. 
  8. [8] J. M. Font, Taking degrees of truth seriously, Studia Logica 91 (2009), pp. 383–406. 
  9. [9] J.M. Font, J. Gil, A. Torrens V. and Verdú, On the infinite-valued ukasiewicz logic that preserves the degrees of truth, Archiv for Mathematical Logic 45/7 (2006), pp. 839–868. 
  10. [10] J. M. Font and R. Jansana, Leibniz filters and the strong version of a protoalgebraic logic, Archiv for Mathematical Logic 40 (2001), pp. 437–465. 
  11. [11] B. Ganter, G. Stumme, R. Wille, (eds.), Formal Concept Analysis: Foundations and Applications (Lecture Notes in Artificial Intelligence, No. 3626), Springer-Verlag, Berlin 2005. 
  12. [12] P. Hájek, Metamathematics of Fuzzy Logics, Kluwer, Dordrecht, 1998. 
  13. [13] G. Malinowski, Many-Valued Logics, Clarendon Press, Oxford, 1993. 
  14. [14] Y. Shramko and H. Wansing, Truth and Falsehood. An Inquiry into Generalized Logical Values (Trends in Logic, Volume 36), Springer, Berlin, 2011. 
  15. [15] R. Wójcicki, Theory of Logical Calculi. Basic Theory of Consequence Operations, Kluwer, Dordrecht, 1988. 
  16. [16] R. Wójcicki and G. Malinowski, (eds.), Selected Papers on Łukasiewicz Sentential Calculi, Ossolineum, Wrocław, 1977. 

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