PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 39(53), pp. 97--106 (1986)
CHARACTERIZATION OF A FULL SET OF PROBABILITIES ON SOME POSETS
J. B. GillMichigan State University, East Lansing, Michigan 48824, USA
Abstract: 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 (MSC2000): 28C99; 06A99
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