Probabilistic Dynamic Logic of Phenomena and Cognition

The purpose of this paper is to develop further the main concepts of Phenomena Dynamic Logic (P-DL) and Cognitive Dynamic Logic (C-DL), presented in the previous paper. The specific character of these logics is in matching vagueness or fuzziness of similarity measures to the uncertainty of models. These logics are based on the following fundamental notions: generality relation, uncertainty relation, simplicity relation, similarity maximization problem with empirical content and enhancement (learning) operator. We develop these notions in terms of logic and probability and developed a Probabilistic Dynamic Logic of Phenomena and Cognition (P-DL-PC) that relates to the scope of probabilistic models of brain. In our research the effectiveness of suggested formalization is demonstrated by approximation of the expert model of breast cancer diagnostic decisions. The P-DL-PC logic was previously successfully applied to solving many practical tasks and also for modelling of some cognitive processes.