| Because of the close relationship between dynamic logic and computer programming language,dynamic logic can not only directly provide the algorithm which is convenient for computer processing,but also provide theoretical basis for computer to understand natural language.Therefore,dynamic logic is the most important part of artificial intelligence logic.Propositional dynamic logic(PDL)is the basic system of dynamic logic,so propositional dynamic logic is a good entry point to study dynamic logic.On the basis of Harel et al.(2000),Benevides(2014),among many others,this paper mainly focuses on propositional dynamic logic(and its extension).It is hoped that this research can not only promote the further development of dynamic logic,but also provide formal support for knowledge representation,knowledge reasoning and model construction in artificial intelligence.This paper starts with the most basic regular propositional dynamic logic.Firstly,the paper elaborates the related concepts of propositional dynamic logic system,and gives the deductive system and related properties of regular propositional dynamic logic.Then,the paper focuses on the extended system of propositional dynamic logic—propositional dynamic logic with bisimilar and logically equivalent programs,analyzes the elements of PDL and methods of how to extend propositional dynamic logic system,and finally discusses the other extended systems of propositional dynamic logic,and further summarizes the main ways of extensions and uses of propositional dynamic logic.The organization of the paper is as follows:The first chapter is an introduction,which briefly introduces the background,significance,status at home and abroad,basic ideas and main contents of the research.The second chapter mainly introduces the basic knowledge of regular propositional dynamic logic,including syntax,semantics,deductive system,basic properties and completeness of regular propositional dynamic logic.On the basis of explaining the regular propositional dynamic logic system,it briefly discusses the irregular propositional dynamic logic system,and elaborates the related properties and conclusions of the system.The third chapter elaborates the extension system of propositional dynamic logic—propositional dynamic logic with bisimilar and logically equivalent programs.By introducing the elements and construction modes of PDL+,the main ways of extensions and uses of propositional dynamic logic are further discussed.The fourth chapter briefly discusses the relationship between propositional dynamic logic and mathematical structuralism from the perspective of structuralism.The fifth chapter briefly describes the shortcomings of this study and the future research.The sixth chapter is the conclusion. |
