The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks

Zdena Riečanová

Kybernetika (2008)

  • Volume: 44, Issue: 3, page 430-440
  • ISSN: 0023-5954

Abstract

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Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which can be obtained by “State Smearing Theorem” from a state on its sharp elements.

How to cite

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Riečanová, Zdena. "The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks." Kybernetika 44.3 (2008): 430-440. <http://eudml.org/doc/33938>.

@article{Riečanová2008,
abstract = {Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which can be obtained by “State Smearing Theorem” from a state on its sharp elements.},
author = {Riečanová, Zdena},
journal = {Kybernetika},
keywords = {non-classical logics; effect algebras; MV-algebras; blocks; states; non-classical logics; effect algebras; MV-algebras; blocks; states},
language = {eng},
number = {3},
pages = {430-440},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks},
url = {http://eudml.org/doc/33938},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Riečanová, Zdena
TI - The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 3
SP - 430
EP - 440
AB - Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which can be obtained by “State Smearing Theorem” from a state on its sharp elements.
LA - eng
KW - non-classical logics; effect algebras; MV-algebras; blocks; states; non-classical logics; effect algebras; MV-algebras; blocks; states
UR - http://eudml.org/doc/33938
ER -

References

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