The hierarchical approach to modeling knowledge and common knowledge
The hierarchical approach to modeling knowledge and common knowledge
复制标题
知识和公共知识建模的分层方法
DOI：
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发表时间：
1999
影响因子：
0.6
通讯作者：
Moshe Y. Vardi
中科院分区：
文献类型：
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作者：
Ronald Fagin;J. Geanakoplos;Joseph Y. Halpern;Moshe Y. Vardi
摘要。经济学家和计算机科学家使用的一种表示代理人的知识或信念的方法，涉及信念的无限层次。这样的层次结构包括一个主体对世界状态的信念，他对其他主体对世界信念的信念，他对其他主体对世界信念的信念等等。(经济学家通常用不确定性空间的概率分布来为信念建模。相比之下，计算机科学家已经根据一组世界（直观地说，智能体认为可能的世界）对信念进行了建模。我们考虑一个可数无限层次何时能完全描述agent的不确定性的问题。我们为这个物业提供了各种必要和充分的条件。事实证明，基于概率的方法可以被视为满足这些条件之一，这就解释了为什么在这种情况下，一个可数的层次结构就足够了。这些条件还表明，可数层次结构是否足够可能取决于底层状态空间中状态的“丰富度”。我们还考虑了可数层次结构是否足以满足“有趣”事件集的问题，并表明答案取决于“有趣”的定义。
Abstract. One approach to representing knowledge or belief of agents, used by economists and computer scientists, involves an infinite hierarchy of beliefs. Such a hierarchy consists of an agent's beliefs about the state of the world, his beliefs about other agents' beliefs about the world, his beliefs about other agents' beliefs about other agents' beliefs about the world, and so on. (Economists have typically modeled belief in terms of a probability distribution on the uncertainty space. In contrast, computer scientists have modeled belief in terms of a set of worlds, intuitively, the ones the agent considers possible.) We consider the question of when a countably infinite hierarchy completely describes the uncertainty of the agents. We provide various necessary and sufficient conditions for this property. It turns out that the probability-based approach can be viewed as satisfying one of these conditions, which explains why a countable hierarchy suffices in this case. These conditions also show that whether a countable hierarchy suffices may depend on the “richness” of the states in the underlying state space. We also consider the question of whether a countable hierarchy suffices for “interesting” sets of events, and show that the answer depends on the definition of “interesting”.