“common knowledge”的概念、定义、翻译、参考文献-科学参考

common knowledge

Logic

In epistemic logic, with knowledge operators $K_{i}$ corresponding to a set of agents, any formula that is known by all agents, that all agents know to be known by all agents, such that all agents know that all agents know to be known by all agents, etc. Formally, let the operators $K_{i}$ represent the knowledge of $n$ agents; then a common knowledge operator corresponds to the infinitary conjunction:
- • $C φ = φ \land ⋀_{i_{0}, \dots, i_{m < n}} (K_{i_{0}} . . . K_{i_{m}} φ)$
That is, $C$ is the weakest modal operator such that $C φ$ entails that for any sequence of knowledge operators $K_{i_{0}}, . . ., K_{i_{m}}$ , the formula $K_{i_{0}} . . . K_{i_{m}} φ$ is true. Alternatively, if one defines an intermediate operator corresponding to ‘everyone knows’:
- • $E φ = K_{0} φ \land . . . \land K_{n - 1} φ$
Then common knowledge captures the infinitary conjunction:
- • $C φ = φ \land E φ \land . . . \land \underset{n times}{\underset{︸}{E . . . E}} φ \land . . .$
Common knowledge of $φ$ is stronger than the related notion of mutual knowledge of $φ$ , that is, that $φ$ is known by all agents.

Economics

When everyone knows a piece of information, and everyone knows that everyone knows that information, and so on without limit. The content of this definition can be appreciated by comparing it to mutual knowledge: everyone knows a piece of information but does not necessarily know if anyone else knows it. The assumption of common knowledge is frequently used in game theory.

单词	common knowledge
释义	common knowledge Logic In epistemic logic, with knowledge operators $K_{i}$ corresponding to a set of agents, any formula that is known by all agents, that all agents know to be known by all agents, such that all agents know that all agents know to be known by all agents, etc. Formally, let the operators $K_{i}$ represent the knowledge of $n$ agents; then a common knowledge operator corresponds to the infinitary conjunction: • $C φ = φ \land ⋀_{i_{0}, \dots, i_{m < n}} (K_{i_{0}} . . . K_{i_{m}} φ)$ That is, $C$ is the weakest modal operator such that $C φ$ entails that for any sequence of knowledge operators $K_{i_{0}}, . . ., K_{i_{m}}$ , the formula $K_{i_{0}} . . . K_{i_{m}} φ$ is true. Alternatively, if one defines an intermediate operator corresponding to ‘everyone knows’: • $E φ = K_{0} φ \land . . . \land K_{n - 1} φ$ Then common knowledge captures the infinitary conjunction: • $C φ = φ \land E φ \land . . . \land \underset{n times}{\underset{︸}{E . . . E}} φ \land . . .$ Common knowledge of $φ$ is stronger than the related notion of mutual knowledge of $φ$ , that is, that $φ$ is known by all agents. Economics When everyone knows a piece of information, and everyone knows that everyone knows that information, and so on without limit. The content of this definition can be appreciated by comparing it to mutual knowledge: everyone knows a piece of information but does not necessarily know if anyone else knows it. The assumption of common knowledge is frequently used in game theory.
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