Abstract
We extend de Finetti’s No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.
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Aguzzoli, Stefano, Brunella Gerla, and Corrado Manara, ‘Poset representation for Gödel and nilpotent minimum logics’, in Lluís Godo (ed.), Symbolic and quantitative approaches to reasoning with uncertainty. 8th European conference, ECSQARU 2005, Barcelona, Spain, July 6-8, 2005. Proceedings. Berlin: Springer. Lecture Notes in Computer Science 3571. Lecture Notes in Artificial Intelligence, 2005, pp. 662–674.
Aguzzoli, Stefano, Brunella Gerla, and Vincenzo Marra, ‘Defuzzifying formulas in Gödel logic through finitely additive measures’, in Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2008), 2008, pp. 1886–1893.
D’Antona Ottavio M., Vincenzo Marra.: ‘Computing coproducts of finitely presented Gödel algebras’,. Ann. Pure Appl. Logic 142(1-3), 202–211 (2006)
de Finetti, Bruno, Teoria delle probabilità: sintesi introduttiva con appendice critica. Volumi primo e secondo, Giulio Einaudi Editore, Turin, 1970. Nuova Biblioteca Scientifica Einaudi, 25* et 25**. English translation in B. de Finetti, Theory of probability: a critical introductory treatment. Vol. 1 & 2. Translated by Antonio Machì and Adrian Smith. Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, London-New York-Sydney, 1974 & 1975.
Gerla Brunella.: ‘MV-algebras, multiple bets and subjective states’,. Internat. J. Approx. Reason., 25(1), 1–13 (2000)
Hájek Petr.: Metamathematics of fuzzy logic, vol. 4 of Trends in Logic—Studia Logica Library. Kluwer Academic Publishers, Dordrecht (1998)
Horn Alfred.: ‘Free L-algebras’,. J. Symbolic Logic 34, 475–480 (1969)
Horn Alfred.: ‘Logic with truth values in a linearly ordered Heyting algebra’,. J. Symbolic Logic 34, 395–408 (1969)
Kühr Jan., Daniele Mundici.: ‘De Finetti theorem and Borel states in [0, 1]- valued algebraic logic’,. Internat. J. Approx. Reason. 46, 3 605–616 (2007)
Mundici Daniele.: ‘Bookmaking over infinite-valued events’,. Internat. J. Approx. Reason. 43(3), 223–240 (2006)
Paris, Jeff, ‘A note on the Dutch Book method’, in Proceedings of the Second International Symposium on Imprecise Probabilities and their Applications (ISIPTA 2001), 2001, pp. 301–309. Available at http://www.maths.man.ac.uk/DeptWeb/Homepages/jbp/.
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Aguzzoli, S., Gerla, B. & Marra, V. De Finetti’s No-Dutch-Book Criterion for Gödel logic. Stud Logica 90, 25–41 (2008). https://doi.org/10.1007/s11225-008-9142-5
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DOI: https://doi.org/10.1007/s11225-008-9142-5