State smearing theorems and the existence of states on some atomic lattice effect algebras

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Authors	PASEKA Jan RIEČANOVÁ Zdenka
Year of publication	2011
Type	Article in Periodical
Magazine / Source	Journal of logic and computation
MU Faculty or unit	Faculty of Science
Citation
web	http://logcom.oxfordjournals.org/content/21/6/863.full.pdf+html?sid=5b6ae981-3558-4c31-9860-dab7a1e4b713
Doi	https://doi.org/10.1093/logcom/exp018
Field	General mathematics
Keywords	Non-classical logics; D-posets; effect algebras; MV-algebras; interval and order topology; states; pseudocomplementation
Description	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.
Related projects:	Mathematical structures and their physical applications