States on symmetric logics: extensions-Reference-Cited by-同舟云学术

States on symmetric logics: extensions

Published:2016-04-01 Issue:2 Volume:66 Page:359-366
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Bikchentaev Airat¹,Navara Mirko²

Affiliation:

1. N. I. Lobachevskii Institute of Mathematics and Mechanics Kazan Federal University Kremlevskaya 18, 420008 Kazan RUSSIAN FEDERATION

2. Center for Machine Perception Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague Technická 2 166 27 Prague 6 CZECH REPUBLIC

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2015-0141/pdf

Reference16 articles.

1. Bikchentaev, A. M.: States on symmetric logics: conditional probability and independence, Lobachevskii J. Math. 30 (2009), 101–106.

2. Bikchentaev, A. M.—Yakushev, R. S.: States on symmetric logics: conditional probability and independence II, Internat. J. Theoret. Phys. 53 (2014), 397–408, DOI: 10.1007/s10773-013-1824-8.

3. De Simone, A.—Navara, M.—PTáK, P.: Extending states on finite concrete logics, Internat. J. Theoret. Phys. 46 (2007), 2046–2052.

4. De Simone, A.—Navara, M.—PTáK, P.: States on systems of sets that are closed under symmetric difference, Math. Nachr. 288 (2015), 1995–2000. DOI 10.1002/mana.201500029.

5. DiedonnÉ, J. A.: Foundations of Modern Analysis, Academic Press, New York, 1969.

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