Public Update Logic

The change of the world's information has mostly been left out of consideration in public announcement logic. Yet the information of the world can change at any possible moment, and about the world's information the agents have can correspondingly change . So it becomes a cult issue to provide formal means of analysis of information change recently in the field of dynamic epistemic logic (DEL).Barteld Kooi [2006] constructs a public announcement logic which can model the world's information change on the basis of H van Ditmarsch [2004b]. Group knowledge is quite important in DEL, for the effects and the information of the agents mostly depend on their group knowledge . Dr. Guo Mei-yun has established a PAL system PAL(RC,D,E) incorporated with common knowledge and group knowledge in his doctoral dissertation . Based on their study , in this paper we introduce a public substitution operator to the system of PAL(RC,D,E),then we can gain an extended system public update logic PUL .In the proof of the system's completeness we follow Barteld Kooi [20006]'s route . using reduction axioms ,we reduce PUL's completeness to that of PAL(RC,D,E) This method not only makes it easy to gain a completeness proof system ,but also makes it clear for us to see that the introduction of public substitution operator does no enhance the language's expression.Finally ,we conclude the paper and give some problems for further research.