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

ZDENKA RIECANOVA; JAN PASEKA

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

机译：状态涂片定理和某些原子晶格效应代数上的状态的存在

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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.

机译：当事件可能是不相容的，不清晰的，模糊的或不精确的时，状态代数和概率代数作为逻辑结构的存在仍然是一个悬而未决的问题。只有少数具有状态的效应代数族是已知的。我们将展示一些效果代数族，其中存在伪补码，其表示状态的存在。即，那些是阿基米德原子晶格效应代数，它们显着地占主导地位或s-紧凑产生或可扩展以完成晶格效应代数。

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《Journal of logic and computation》 |2011年第6期|p.863-882|共20页
作者
ZDENKA RIECANOVA; JAN PASEKA;
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作者单位

Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology,Ilkovicova 3, SK-812 19 Bratislava, Slovak Republic;

Department of Mathematics and Statistics, Faculty of Science,Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic;

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正文语种 eng
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关键词
non-classical logics; D-posets; effect algebras; MV-algebras; interval and order topology; states; pseudocomplementation;

机译：非经典逻辑;D姿势;效果代数MV-代数间隔和顺序拓扑;状态;伪补码;

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

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