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Kite Pseudo Effect Algebras

Anatolij Dvurečenskij

Foundations of Physics 43 (11):1314-1338 (2013)

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(1 other version)Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.details The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among effect algebras and such structures as orthoalgebras and orthomodular posets are investigated, as are morphisms and group- valued measures (or charges) on effect algebras. It is proved that there is a universal group for every effect algebra, as well as a universal vector space over an arbitrary field. Download Export citation Bookmark 58 citations
States on Pseudo Effect Algebras and Integrals.Anatolij Dvurečenskij - 2011 - Foundations of Physics 41 (7):1143-1162.details We show that every state on an interval pseudo effect algebra E satisfying an appropriate version of the Riesz Decomposition Property (RDP for short) is an integral through a regular Borel probability measure defined on the Borel σ-algebra of a Choquet simplex K. In particular, if E satisfies the strongest type of RDP, the representing Borel probability measure can be uniquely chosen to have its support in the set of the extreme points of K. Download Export citation Bookmark 2 citations
Atomic Effect Algebras with the Riesz Decomposition Property.Anatolij Dvurečenskij & Yongjian Xie - 2012 - Foundations of Physics 42 (8):1078-1093.details We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any σ-orthocomplete atomic effect algebra with the Riesz Decomposition Property is an MV-effect algebras, and we apply this result for pseudo-effect algebras and for states. Download Export citation Bookmark 1 citation
On the Structure of Pseudo BL-algebras and Pseudo Hoops in Quantum Logics.A. Dvurečenskij, R. Giuntini & T. Kowalski - 2010 - Foundations of Physics 40 (9-10):1519-1542.details The main aim of the paper is to solve a problem posed in Di Nola et al. (Multiple Val. Logic 8:715–750, 2002) whether every pseudo BL-algebra with two negations is good, i.e. whether the two negations commute. This property is intimately connected with possessing a state, which in turn is essential in quantum logical applications. We approach the solution by describing the structure of pseudo BL-algebras and pseudo hoops as important families of quantum structures. We show when a pseudo hoop (...) Download Export citation Bookmark 2 citations

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