Matrix representation of finite effect algebras

Grzegorz Bińczak; Joanna Kaleta; Andrzej Zembrzuski

Kybernetika (2023)

  • Volume: 59, Issue: 5, page 737-751
  • ISSN: 0023-5954

Abstract

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In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra E we construct set of matrices M ( E ) in such a way that effect algebras E 1 and E 2 are isomorphic if and only if M ( E 1 ) = M ( E 2 ) . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most 8 .

How to cite

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Bińczak, Grzegorz, Kaleta, Joanna, and Zembrzuski, Andrzej. "Matrix representation of finite effect algebras." Kybernetika 59.5 (2023): 737-751. <http://eudml.org/doc/299156>.

@article{Bińczak2023,
abstract = {In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra $E$ we construct set of matrices $M(E)$ in such a way that effect algebras $E_1$ and $E_2$ are isomorphic if and only if $M(E_1)=M(E_2)$. The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most $8$.},
author = {Bińczak, Grzegorz, Kaleta, Joanna, Zembrzuski, Andrzej},
journal = {Kybernetika},
keywords = {effect algebra; state of effect algebra},
language = {eng},
number = {5},
pages = {737-751},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Matrix representation of finite effect algebras},
url = {http://eudml.org/doc/299156},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Bińczak, Grzegorz
AU - Kaleta, Joanna
AU - Zembrzuski, Andrzej
TI - Matrix representation of finite effect algebras
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 5
SP - 737
EP - 751
AB - In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra $E$ we construct set of matrices $M(E)$ in such a way that effect algebras $E_1$ and $E_2$ are isomorphic if and only if $M(E_1)=M(E_2)$. The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most $8$.
LA - eng
KW - effect algebra; state of effect algebra
UR - http://eudml.org/doc/299156
ER -

References

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  7. Gudder, S., , Found. Phys. 27 (1997), 287-304. MR1444965DOI
  8. Kopka, F., Chovanec, F., D -posets., Math. Slovaca 44 (1994), 21-34. MR1290269
  9. Maxima, Maxima, https://maxima.sourceforge.io. 
  10. Riečanová, Z., , Int. J. Theoret. Physics 40 (2001), 10, 1683-1691. MR1858217DOI
  11. Ji, Wei, , Fuzzy Sets Systems 236 (2014), 113-121. MR3132755DOI
  12. Wikipedia, Rouché-Capelli theorem, https://en.wikipedia.org/wiki/Rouché-Capelli_theorem. 

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