Pulmannová, Sylvia Functional properties of transition probability spaces. (English) Zbl 0638.03060 Rep. Math. Phys. 24, No. 1, 81-86 (1986). It is shown that every (not necessarily symmetric) transition probability space in the sense of B. Mielnik [Commun. Math. Phys. 9, 55-80 (1968; Zbl 0164.295)] can be considered as a functional logic [M. J. Maczyński, Int. J. Theor. Phys. 11, 149-156 (1974)]. A characterization of those functional logics which correspond to transition probability spaces is presented. Meanwhile I found that P. C. Deliyannis [ibid. 23, 217-226 (1984; Zbl 0547.03043)] proved similar results by different methods not using the functional representation of logics. Reviewer: S.Pulmannová Cited in 3 Documents MSC: 03G12 Quantum logic 81P05 General and philosophical questions in quantum theory 81P20 Stochastic mechanics (including stochastic electrodynamics) Keywords:quantum logic; transition probability space; functional logics; functional representation of logics Citations:Zbl 0164.295; Zbl 0547.03043 PDFBibTeX XMLCite \textit{S. Pulmannová}, Rep. Math. Phys. 24, No. 1, 81--86 (1986; Zbl 0638.03060) Full Text: DOI References: [1] Mielnik, B., Commun. Math. Phys., 9, 55 (1968) [2] Ma̧czyński, M., Int. J. Theoret. Phys., 8, 353 (1973) [3] Ma̧czyński, M., Int. J. Theoret. Phys., 11, 149 (1974) [4] Belinfante, J., J. Math. Phys., 17, 285 (1976) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.