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].
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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.)
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)
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)
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.
De Finetti, B.: Theory of Probability, vol. 1. John Wiley and Sons, Chichester (1974)
Emch, G.G.: Mathematical and Conceptual Foundations of 20th Century Physics. North-Holland, Amsterdam (1984)
Hájek, P.: Metamathematics of fuzzy logic. Trends in Logic, vol. 4. Kluwer/ Springer, Dordrecht, New York (1998)
Kroupa, T.: Every state on semisimple MV-algebra is integral. Fuzzy Sets and Systems 157, 2771–2782 (2006)
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)
Łukasiewicz, J., Tarski, A.: Investigations into the Sentential Calculus. In: [16], pp. 38–59
Mundici, D.: Bookmaking over infinite-valued events. International J. Approximate Reasoning 43, 223–240 (2006)
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)
Panti, G.: Invariant measures in free MV-algebras. Communications in Algebra 36, 2849–2861 (2008)
Pap, E. (ed.): Handbook of Measure Theory, I,II. North-Holland, Amsterdam (2002)
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/
Tarski, A.: Logic, Semantics, Metamathematics. Clarendon Press, Oxford (1956); reprinted, Hackett, Indianapolis (1983)
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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
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DOI: https://doi.org/10.1007/978-3-642-02906-6_3
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