Measures and conditioning

摘要

This special issue collects papers as extended versions of presentations given during FSTA in Liptovsky Jan (Slovakia), in January 2004. We grouped the papers in three groups. The first group of three papers is devoted to probability. Andrei Khrennikov shows that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state-space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. He starts with the conventional formula of total probability for contextual (conditional) probabilities and then he rewrite it by eliminating combinations of incompatible contexts from consideration. This approach gives the possibility to apply quantum-like models in domains of science different from quantum theories, e.g., in economics, finance, social sciences, cognitive sciences, psychology. Stan Gudder considers three criteria for describing non-disturbance between quantum measurements. While previous discussions of these criteria considered sharp measurements, he treats more general measurements that may be unsharp (or fuzzy). It has been shown that in the sharp case, the three criteria are equivalent to compatibility of the measurements. He shows that only the third criterion is equivalent to compatibility for the general fuzzy case.