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Effect algebras with a full set of states

  • Ivan Chajda EMAIL logo
Published/Copyright: November 3, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

Abstract

It is shown that every effect algebra with a full set of states can be represented as a so-called numerical algebra introduced in the paper. For numerical algebras there are introduced tense operators which indicate dynamical changes of quantum events depending on variability of states. These operators enable to recognize an effect algebra with a full set of states as a temporal logic where events are quantified by these tense operators. The problem of representation of tense operators on a given numerical algebra is solved.

MSC 2010: Primary 03B44; 03G25; 03G12; 06B23
Keywords: effect algebra; state; full set of states; numerical algebra; tense operators

(Communicated by Anatolij Dvurečenskij)

References

[1] Beltrametti, E. G.—Mączyński, M. J.: On a characterization of classical and nonclassical probabilities, J. Math. Phys. 32 (1981), 1280–1286.10.1063/1.529326Search in Google Scholar

[2] Chajda, I.—Länger, H.: Spaces of abstract events, Internat. J. Theoret. Phys. 52 (2013), 1818–1824.10.1007/s10773-012-1275-7Search in Google Scholar

[3] Chajda, I.—Länger, H.: Tense operators in spaces of numerical events, Internat. J. Theoret. Phys., 10.1007/s10773-013-1820-z.Search in Google Scholar

[4] Dorfer, G.—Dorninger, D.—Länger, H.: On algebras of multidimensional probabilities, Math. Slovaca 60 (2010), 571–582.10.2478/s12175-010-0032-8Search in Google Scholar

[5] Dorfer, G.—Dorninger, D.—Länger, H.: On the structure of numerical event spaces, Kybernetika (Prague) 46 (2010), 971–981.Search in Google Scholar

[6] Dorninger, D.—Länger, H.: On a characterization of physical systems by spaces of numerical events, ARGESIM Rep. 35 (2009), 601–607.Search in Google Scholar

[7] Dvurečenskij, A.: Representation of states on effect-tribes and effect algebras by integrals, Rep. Math. Phys. 67 (2011), 63–85.10.1016/S0034-4877(11)80011-XSearch in Google Scholar

[8] Dvurečenskij, A.—Pulmannová, S.: New Trends in Quantum Structures, Kluwer, Dordrecht, 2000.10.1007/978-94-017-2422-7Search in Google Scholar

[9] Foulis, D. J.—Bennett, M. K.: Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1325–1346.10.1007/BF02283036Search in Google Scholar

Received: 2013-2-26
Accepted: 2014-1-19
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0178
Keywords for this article
effect algebra; state; full set of states; numerical algebra; tense operators

Articles in the same Issue

  1. Research Article
  2. Effect algebras with a full set of states
  3. Research Article
  4. An approach to orthomodular lattices via lattices with an antitone involution
  5. Research Article
  6. On properties of the free BCI-algebra with one generator
  7. Research Article
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  9. Research Article
  10. The irrationality of infinite series of a special kind
  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
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  17. Research Article
  18. Uniqueness of meromorphic functions sharing a value or small function
  19. Research Article
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  21. Research Article
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