A Preliminary Study On Logic Of Probabilistic Dynamic Epistemic

Epistemic logic is a modal logic used to reason about information,including higher order information.Probabilistic epistemic logic can be used to reason about information and information change,but higher order information is overlooked.In this paper I combine probabilistic logic with dynamic epistemic logic yielding a new logic,probabilisti dynamic epistemic logic(PDEL),that deals with changing probabilities and takes higher order information into account.At last,I provide a sound and complete proof system for PDEL.Part one:first,epistemic logic can be introuduced.Epistemic logic is suited to deal with stituations involving more than one agent.In this way epistemic logic also deals with higher order information,i.e,information about information.Dynamic epistemic logics are extensions of epistemic logic which can be used to reason about information and information change.At the same time,it's false to express the effect of one's degree of belief when he acquired the matter of incorporating new information.And then introduce PEL.PEL can be described a process of change belief,but higher order infornation is overlooked,so combined DEL and PEL,then we get PDEL,a logic for reasoning about probability,information,and information change that takes higher order infornation into account.Part two:Probabilistic epistemic models are introuced.The language of PDEL can be interpreted on these models and by making a dynamic version of PEL,we can get PDEL.Part three:I introuce a method for making models for specific stituations and provide syntax,semantics and complete proof system for PDEL.And at last,I give a example for use PDEL.And at last,I give an example for using PDEL.Part four:I comment on the PDEL,and give some problems for further research in the future.