| Title:
|
Probabilistic propositional calculus with doubled nonstandard semantics (English) |
| Author:
|
Kramosil, Ivan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
[195]-207 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
propositional language |
| Keyword:
|
nonstandard semantics |
| MSC:
|
03B48 |
| MSC:
|
03B50 |
| MSC:
|
28E10 |
| MSC:
|
68Q55 |
| MSC:
|
68T37 |
| idZBL:
|
Zbl 1274.68535 |
| idMR:
|
MR1690945 |
| . |
| Date available:
|
2009-09-24T19:24:48Z |
| Last updated:
|
2015-04-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135280 |
| . |
| Reference:
|
[1] Church A.: Introduction to Mathematical Logic.Part I. Second edition. Princeton Univ. Press, Princeton, NJ 1956 Zbl 1016.03500, MR 1435972 |
| Reference:
|
[2] Halmos P. R.: Measure Theory.D. van Nostrand, New York – Toronto – London 1950 Zbl 0283.28001, MR 0033869 |
| Reference:
|
[3] Kramosil I.: Extensional processing of probability measures.Internat. J. Gen. Systems 22 (1994), 2, 159–170 Zbl 0797.60002, 10.1080/03081079308935203 |
| Reference:
|
[4] Kramosil I.: Nonstandard approach to possibility measures.Internat. J. Uncertainty, Fuzziness and Knowledge–Based Systems 4 (1996), 3, 275–301 Zbl 1232.28022, MR 1400996, 10.1142/S0218488596000172 |
| Reference:
|
[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 |
| . |
