Iterated belief revision requires information about the current beliefs. This information is represented by mathematical structures called doxastic states. Most literature concentrates on how to revise a doxastic state and neglects that it may exponentially grow. This problem is studied for the most common ways of storing a doxastic state. All four of them are able to store every doxastic state, but some do it in less space than others. In particular, the explicit representation (an enumeration of the current beliefs) is the more wasteful on space. The level representation (a sequence of propositional formulae) and the natural representation (a history of natural revisions) are more succinct than it. The lexicographic representation (a history of lexicographic revision) is even more succinct than them.

中文翻译：

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在迭代信念修正中代表状态


迭代信念修正需要有关当前信念的信息。该信息由称为信念状态的数学结构表示。大多数文献都集中于如何纠正迷信状态，而忽略了它可能呈指数级增长。研究这个问题的最常见的存储信念状态的方法。它们四个都能够存储每一种信念状态，但有些存储空间比其他存储空间小。特别是，显式表示（当前信念的枚举）在空间上更加浪费。层次表示（命题公式的序列）和自然表示（自然修正的历史）比它更简洁。词典编纂的表述（词典编纂的历史）比它们还要简洁。