# Probabilistic propositional calculus with doubled nonstandard semantics

Kybernetika (1999)

- Volume: 35, Issue: 2, page [195]-207
- ISSN: 0023-5954

## Access Full Article

top## Abstract

top## How to cite

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)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.