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Journal of Logic and Computation Advance Access published online on March 13, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp018
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

State Smearing Theorems and the Existence of States on Some Atomic Lattice Effect Algebras

Zdenka Riecanová

Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovicova 3, SK-812 19 Bratislava, Slovak Republic.
E-mail: zdenka.riecanova{at}stuba.sk

Jan Paseka

Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlárská 2, 611 37 Brno, Czech Republic.
E-mail: paseka{at}math.muni.cz

Received 28 September 2008.


  Abstract

The existence of states and probabilities on effect algebras as logical structures when events may be non-compatible, unsharp, fuzzy or imprecise is still an open question. Only a few families of effect algebras possessing states are known. We are going to show some families of effect algebras, the existence of a pseudocomplementation on which implies the existence of states. Namely, those are Archimedean atomic lattice effect algebras, which are sharply dominating or s-compactly generated or extendable to complete lattice effect algebras.

Keywords: Non-classical logics; D-posets; effect algebras; MV-algebras; interval and order topology; states; pseudocomplementation


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