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2017 | 46 | 1/2 |

Tytuł artykułu

The Infinite-Valued Łukasiewicz Logic and Probability

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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.

Rocznik

Tom

46

Numer

1/2

Daty

wydano
2017-06-30

Twórcy

  • Opole University, Institute of Mathematics ans Informarics

Bibliografia

  • [1] P. Billingsley, Probability and Measure, John Wiley & Sons, Inc., New York, NY, 1995.
  • [2] R. L. O. Cignoli, I. M. L. D’Ottaviano, D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer, Dordrecht, 2000.
  • [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] J. Czelakowski, O probabilistycznej interpretacji predykatw (Polish), [in:] [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] 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] 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] J. M. Font, Taking degrees of truth seriously, Studia Logica 91 (2009), pp. 383–406.
  • [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] 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] 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] P. Hájek, Metamathematics of Fuzzy Logics, Kluwer, Dordrecht, 1998.
  • [13] G. Malinowski, Many-Valued Logics, Clarendon Press, Oxford, 1993.
  • [14] Y. Shramko and H. Wansing, Truth and Falsehood. An Inquiry into Generalized Logical Values (Trends in Logic, Volume 36), Springer, Berlin, 2011.
  • [15] R. Wójcicki, Theory of Logical Calculi. Basic Theory of Consequence Operations, Kluwer, Dordrecht, 1988.
  • [16] R. Wójcicki and G. Malinowski, (eds.), Selected Papers on Łukasiewicz Sentential Calculi, Ossolineum, Wrocław, 1977.

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bwmeta1.element.ojs-doi-10_18778_0138-0680_46_1_2_05