Functional properties of transition probability spaces (Q1099174)

It is shown that every (not necessarily symmetric) transition probability space in the sense of \textit{B. Mielnik} [Commun. Math. Phys. 9, 55-80 (1968; Zbl 0164.295)] can be considered as a functional logic [\textit{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 \textit{P. C. Deliyannis} [ibid. 23, 217-226 (1984; Zbl 0547.03043)] proved similar results by different methods not using the functional representation of logics.