Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general.

中文翻译：

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关于加强迭代信念修正的逻辑：适当的序数区间算子

Darwiche 和 Pearl 在 1997 年发表的开创性文章概述了迭代信念修正逻辑的一些基本原则。这些原则，即 DP 假设，已以多种替代方式得到补充。大多数建议都导致了一种“还原论”的形式，它将信念状态与世界的排序相结合。然而，这一立场最近被批评为强得无法接受。其他建议，例如流行原则 (P)，又名“独立性”，具有“可接受”运营商的特征，值得称赞的是更加温和。在本文中，我们用许多新条件补充了 DP 假设和 (P)。虽然 DP 假设约束了先验和后验条件信念集之间的关系，我们的新原则特别控制了通过不同修订从共同先验获得的两个后验条件信念集之间的关系。我们展示了来自包含字典和约束修订的结果族中的运算符，可以表示为与“适当序数间隔”（POI）分配相关的相关信念状态，这是一种比简单的世界排序更细粒度的结构。我们通过注意到这些算子满足许多 AGM 时代假设的迭代版本（包括超级膨胀）来结束论文，这对于一般的可允许算子来说是不合理的。可以表示为与“适当序数间隔”（POI）分配相关的信念状态，这是一种比世界的简单排序更细粒度的结构。我们通过注意到这些算子满足许多 AGM 时代假设的迭代版本（包括超级膨胀）来结束论文，这对于一般的可允许算子来说是不合理的。可以表示为与“适当序数间隔”（POI）分配相关的信念状态，这是一种比世界的简单排序更细粒度的结构。我们通过注意到这些算子满足许多 AGM 时代假设的迭代版本（包括超级膨胀）来结束论文，这对于一般的可允许算子来说是不合理的。