Kolmogorov-type conditional probabilities among distinct contexts

Sven Aerts

Karl Svozil

Kolmogorov's axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another context. As the respective probabilities need not (but, depending on the physical/model realization, can) be of the Born rule type, this generalizes approaches to quantum probabilities by Aufféves and Grangier, which in turn are inspired by Gleason's theorem.

Ehtibar N. Dzhafarov, Janne V. Kujala

Adam Stokes

We present an alternative approach to modeling Einstein-Podolsky-Rosen-Bohm (EPRB)-type experiments. The basis for our approach will be to replace the conventional Kolmogorov theory of probability, with the more general Dempster-Schafer theory of evidence. This leads to the identification of a distinct type of epistemic uncertainty, which is not present in Kolmogorov theory, but which is relevant in modeling experiments with operationally incompatible observables. Our treatment naturally yields conditional relative frequencies, which are perfectly compatible with classical determinism and locality, but which do not satisfy Bell-type inequalities.

Ehtibar N. Dzhafarov, Janne V. Kujala

Yoshiharu Tanaka, Masanori Ohya, Andrei Yu. Khrennikov +1 more

Recently, it has been reported that conventional probability law can be violated in the context dependent phenomena which are “adaptive” to the environment or experimental settings. Also, it has been discussed that non-Kolmogorov probability, e.g. quantum probability, is available for modeling such a context dependent phenomenon. In this study, we investigate context-dependency of human perception process for optical illusion of Schröder stair, and we propose the non-Kolmogorov probabilistic model for the illusion.