Probabilistic propositional calculus with doubled nonstandard semantics
Kybernetika (1999)
- Volume: 35, Issue: 2, page [195]-207
- ISSN: 0023-5954
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topKramosil, Ivan. "Probabilistic propositional calculus with doubled nonstandard semantics." Kybernetika 35.2 (1999): [195]-207. <http://eudml.org/doc/33421>.
@article{Kramosil1999,
abstract = {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.},
author = {Kramosil, Ivan},
journal = {Kybernetika},
keywords = {propositional language; nonstandard semantics; propositional language; nonstandard semantics},
language = {eng},
number = {2},
pages = {[195]-207},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Probabilistic propositional calculus with doubled nonstandard semantics},
url = {http://eudml.org/doc/33421},
volume = {35},
year = {1999},
}
TY - JOUR
AU - Kramosil, Ivan
TI - Probabilistic propositional calculus with doubled nonstandard semantics
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 2
SP - [195]
EP - 207
AB - 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.
LA - eng
KW - propositional language; nonstandard semantics; propositional language; nonstandard semantics
UR - http://eudml.org/doc/33421
ER -
References
top- Church A., Introduction to Mathematical Logic, Part I. Second edition. Princeton Univ. Press, Princeton, NJ 1956 Zbl1016.03500MR1435972
- Halmos P. R., Measure Theory, D. van Nostrand, New York – Toronto – London 1950 Zbl0283.28001MR0033869
- Kramosil I., 10.1080/03081079308935203, Internat. J. Gen. Systems 22 (1994), 2, 159–170 (1994) Zbl0797.60002DOI10.1080/03081079308935203
- Kramosil I., 10.1142/S0218488596000172, Internat. J. Uncertainty, Fuzziness and Knowledge–Based Systems 4 (1996), 3, 275–301 (1996) Zbl1232.28022MR1400996DOI10.1142/S0218488596000172
- 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 (1998)
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