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@article{1082298,
author = {Chajda, Ivan and Paseka, Jan},
article_location = {NEW YORK},
article_number = {10},
doi = {http://dx.doi.org/10.1007/s00500-012-0857-x},
keywords = {Effect algebra; Lattice effect algebra; Tense operators; Dynamic effect algebra},
language = {eng},
issn = {1432-7643},
journal = {Soft computing},
title = {Dynamic effect algebras and their representations},
volume = {16},
year = {2012}
}
TY - JOUR
ID - 1082298
AU - Chajda, Ivan - Paseka, Jan
PY - 2012
TI - Dynamic effect algebras and their representations
JF - Soft computing
VL - 16
IS - 10
SP - 1733-1741
EP - 1733-1741
PB - Springer-Verlag GmbH
SN - 14327643
KW - Effect algebra
KW - Lattice effect algebra
KW - Tense operators
KW - Dynamic effect algebra
N2 - For lattice effect algebras, the so-called tense operators were already introduced by Chajda and KolaA (TM) ik. Tense operators express the quantifiers "it is always going to be the case that" and "it has always been the case that" and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra.
ER -
CHAJDA, Ivan and Jan PASEKA. Dynamic effect algebras and their representations. \textit{Soft computing}. NEW YORK: Springer-Verlag GmbH, 2012, vol.~16, No~10, p.~1733-1741. ISSN~1432-7643. Available from: https://dx.doi.org/10.1007/s00500-012-0857-x.
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