Common knowledge is one of the fundamental concepts of group knowledge.Due to development in such areas as artificial intelligence，game theory，computer science，and decision science，etc.，analyzing as precisely as possible logic characteristics of common knowledge has become an urgent need for related disciplines.Based on logic characteristics of common knowledge，We analyze the dilemma and causation to obtain common knowledge in practice，and present the weak form of common knowledge.

We also analyze the attempts at and the results from using the formal and axiomatic methods，compare relations among different formal interpretations of common knowledge.By analyzing，we point out that the central character of common knowledge is its hierarchical infinity for which the common knowledge cannot be obtained in reality and it is the reason for the requirement to weaken common knowledge in practice.We take the Coordinated Attack Problem as an example，and point out that the fundamental causation of Coordinated Attack Problem is the strong presupposition of common knowledge which is needless because approximate coordination is in real coordinated action.Therefore，to weaken common knowledge is the general way for resolving the game problem.

Guided by this，We define the concept of almost common belief and puts forward the Chinese naming method of weak common belief for the first time，distinguish between almost common belief and weak common belief.We point out that the almost common belief is the result of weakening at one time both the characters“common”and“knowledge”of common knowledge while the weak common belief is the weakness of the belief degree of common belief，and the result of weakening only the character of“knowledge”of common knowledge.

As epistemological base of game theory，common knowledge has been questioned just because of its accessibility is no picnic.The assumption of common knowledge is doubtlessly overestimated in practice.Therefore，it is of value to probe into philosophical foundation or epistemological foundation of game theory concerned with common knowledge.The best method to descript epistemological foundation of game theory is to analyze common knowledge，weaken its form，and apply it to different areas，with the help of most important advance in modern epistemological logic.Here，we focus on the cases of common p-belief and almost common belief.Common pbelief is a portable one to resolve the probabilistic coordinated attack problem.It is very difficult to solve coordinated attack problem if common knowledge is prerequisite in the attack.However，this demand is not so strong in practical decision making，so approximate common knowledge is the fundamental method to weaken common knowledge.From the angle of game theory，it is possible to acquire coordination attack of high probability through common pbelief by transforming the coordinated attack into a strategic form game.We think that common p-belief lays an epistemic foundation for the solution of coordination attack from the point view of probability.As a substitute for common knowledge，almost common belief can perform the similar function in the coordination game theory.In an experiment we made，it is clear that almost common belief also provides equilibrium for coordination games.People are always affected by cultural background when they encounter with coordination games.It is just the cultural background provides the almost common belief in the experiment we made.In the coordination games，players always put the convention in the first place；otherwise，they will act concretely by using almost common belief which is provided by common cultural background.

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