A Preliminary Study On Probabilistic Dynamic Cognitive Logic Based On A General Framework

Epistemic logic is used to deal with reasoning about knowledge.In order to deal with uncertain knowledge,Fagin and Halpern introduce probabilistic language and develop into a probabilistic epistemic logic.Based on Kripke model,probability space is introduced and the semantic interpretation of probabilistic language is given.Probabilistic epistemic logic has great advantages in dealing with uncertain knowledge reasoning,but it is a static language.In order to describe the change of uncertain knowledge,Kooi.introduces dynamic updating language based on probabilistic epistemic logic and developes into a probabilistic dynamic epistemic logic which is based on the Kripke model in the case of discrete probability spaces.The semantic explanation of probability operator and update operator is given.The main work of this paper is to extend their Kripke model to the general frame.Based on the algebraic properties of general frame,probability function is introduced to generate probability space,and the semantic interpretation of probabilistic language is given naturally.In this paper,some other effective expressions are introduced and an extension of the original axiomatic system is given by using the condition of the restriction of the general frame on the assignment.By means of the algebraic semantics of modal logic and the inner relation of the general frame,it is proved that the extended axiomatic system is complete with respect to the general frame.