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英文文献：The Cycles Approach-周期的方法
英文文献作者：Jose Alvaro Rodrigues-Neto
英文文献摘要：
The cycles approach uses graph theory and linear algebra to study models of knowledge, characterized by a state space, a set of players and their partitions. In finite state spaces, there is a simple formula for the cyclomatic number; i.e., the dimension of cycle spaces of a model. We prove that the cyclomatic number is the minimum number of cycle equations that must be checked to guarantee the existence of a common prior, and explain why some cycle equations are automatically satisfied. If the cyclomatic number is zero, a common prior always exists, regardless of the probabilistic information given by players.posteriors. There is an isomorphism taking cycles into cycle equations; adding cycles is the counterpart of multiplying the corresponding cycle equations. With these tools, we study the processes of learning and forgetting, as well as properties of sub models (i.e., restricting attention to a proper subset of players), and decompositions of the set of players in subsets. We analyze how individual learning translates into more common knowledge or cycle destruction.
循环方法使用图论和线性代数来研究知识模型，其特征是一个状态空间、一组参与者及其划分。在有限状态空间中，圈数有一个简单的公式;即，模型的循环空间的维数。证明了圈数是保证共同先验存在所必须检验的最小循环方程数，并解释了某些循环方程自动满足的原因。如果圈数为零，一个公共先验总是存在，而不管玩家。后验者所给出的概率信息。有一个同构把循环变成循环方程;循环的加法是对应循环方程的乘法的对应物。通过这些工具，我们研究了学习和遗忘的过程，以及子模型的属性(即，将注意力限制在适当的玩家子集)，以及玩家集合在子集中的分解。我们分析个人学习如何转化为更普遍的知识或循环破坏。
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