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Probabilistic propositional calculus with doubled nonstandard semantics
Kybernetika, Tome 35 (1999) no. 2, pp. 195-207 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The classical propositional language is evaluated in such a way that truthvalues are subsets of the set of all positive integers. Such an evaluation is projected in two different ways into the unit interval of real numbers so that two real-valued evaluations are obtained. The set of tautologies is proved to be identical, in all the three cases, with the set of classical propositional tautologies, but the induced evaluations meet some natural properties of probability measures with respect to nonstandard supremum and infimum operations induced in the unit interval of real numbers.
The classical propositional language is evaluated in such a way that truthvalues are subsets of the set of all positive integers. Such an evaluation is projected in two different ways into the unit interval of real numbers so that two real-valued evaluations are obtained. The set of tautologies is proved to be identical, in all the three cases, with the set of classical propositional tautologies, but the induced evaluations meet some natural properties of probability measures with respect to nonstandard supremum and infimum operations induced in the unit interval of real numbers.
Classification : 03B48, 03B50, 28E10, 68Q55, 68T37
Keywords: propositional language; nonstandard semantics 
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Kramosil, Ivan. Probabilistic propositional calculus with doubled nonstandard semantics. Kybernetika, Tome 35 (1999) no. 2, pp. 195-207. http://geodesic.mathdoc.fr/item/KYB_1999_35_2_a3/

[1] Church A.: Introduction to Mathematical Logic. Part I. Second edition. Princeton Univ. Press, Princeton, NJ 1956 | MR | Zbl

[2] Halmos P. R.: Measure Theory. D. van Nostrand, New York – Toronto – London 1950 | MR | Zbl

[3] Kramosil I.: Extensional processing of probability measures. Internat. J. Gen. Systems 22 (1994), 2, 159–170 | DOI | Zbl

[4] Kramosil I.: Nonstandard approach to possibility measures. Internat. J. Uncertainty, Fuzziness and Knowledge–Based Systems 4 (1996), 3, 275–301 | DOI | MR | Zbl

[5] Kramosil I.: Probabilistic first–order predicate calculus with doubled nonstandard semantics. In: IPMU 98 (Information Processing and Management of Uncertainty) – Proceedings of the Conference, vol. 2, Paris, July 6 – 10, 1998. Paris, La Sorbonne, pp. 1390–1397