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States on symmetric logics: extensions

  • Airat Bikchentaev EMAIL logo and Mirko Navara EMAIL logo
Published/Copyright: June 5, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 2

Abstract

We continue the study of symmetric logics, i.e., collections of subsets generalizing Boolean algebras and closed under the symmetric difference. We contribute to several open questions. One of them is whether there is á non-Boolean symmetric logic such that all states on it are Δ-subadditive.

Keywords: orthomodular poset; quantum logic; state; symmetric difference; Boolean algebra; set representation
MSC 2010: Secondary 60A05; 60A10; 60B15; 81P10

  1. Dedicated to Professor Anatolij Dvurecenskij

    (Communicated by Sylvia Pulmannová)

Acknowledgement

The authors thank the anonymous referees and non-anonymous colleagues for remarks that helped to improve the paper.

References

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Received: 2014-2-12
Accepted: 2014-9-3
Published Online: 2016-6-5
Published in Print: 2016-4-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0141
Keywords for this article
orthomodular poset; quantum logic; state; symmetric difference; Boolean algebra; set representation

Articles in the same Issue

  1. Research Article
  2. Holistic logical arguments in quantum computation
  3. Research Article
  4. States with values in the Łukasiewicz groupoid
  5. Research Article
  6. On realization of effect algebras
  7. Research Article
  8. States on symmetric logics: extensions
  9. Research Article
  10. Extensions and measurability in quantum measure spaces
  11. Research Article
  12. Convex subalgebras of upper bounded GMV-algebras
  13. Research Article
  14. Combining boolean algebras and ℓ-groups in the variety generated by chang’s mv-algebra
  15. Research Article
  16. Large rigid sets of algebras with respect to embeddability
  17. Research Article
  18. Conformal algebras, vertex algebras, and the logic of locality
  19. Research Article
  20. Extension of measures on pseudo-D-lattices
  21. Research Article
  22. Note on a parameter switching method for nonlinear ODEs
  23. Research Article
  24. Compatibility for probabilistic theories
  25. Research Article
  26. Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras
  27. Research Article
  28. Commutativity in a synaptic algebra
  29. Research Article
  30. Discrete averaged mixing applied to the logarithmic distributions
  31. Research Article
  32. Automorphisms of decompositions
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