Geodesic
Characterization of a Full set of Probabilities on some Posets
Publications de l'Institut Mathématique, _N_S_39 (1986) no. 53, p. 97

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We define algebraic structures which contain all Boolean algebras pseudo-Boolean algebras, and orthocomplenented posets, as special cases; then we introduce the notion of orthonogality and, after defining probability in the usual way, we characterize those among our new structures that admit a full set of probabilities. Some special cases of the main result about characterization are considered and, especially, a result concerning orthocomplemented posets is derived from it. Also, sufficient conditions for the existence of a full set of probabilities on a pseudo-Boolean poset is obtained.
Classification : 28C99 06A99 
@article{PIM_1986_N_S_39_53_a14,
     author = {J. Gill},
     title = {Characterization of a {Full} set of {Probabilities} on some {Posets}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {97 },
     publisher = {mathdoc},
     volume = {_N_S_39},
     number = {53},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1986_N_S_39_53_a14/}
}
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J. Gill. Characterization of a Full set of Probabilities on some Posets. Publications de l'Institut Mathématique, _N_S_39 (1986) no. 53, p. 97 . http://geodesic.mathdoc.fr/item/PIM_1986_N_S_39_53_a14/