On Iterated Contraction: Syntactic Characterization, Representation Theorem and Limitations of the Levi Identity
On Iterated Contraction: Syntactic Characterization, Representation Theorem and Limitations of the Levi Identity
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论迭代收缩：句法表征、表示定理和 Levi 恒等式的局限性
DOI：
10.1007/978-3-319-67582-4_25
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
R. Pérez
中科院分区：
文献类型：
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作者：
S. Konieczny;R. Pérez
本文研究了认知状态框架下的迭代收缩，为迭代修正提供了达尔文和珀尔工作的对应版本。我们提供了迭代收缩的纯语法公设，也就是说，这些公设仅用收缩操作符表示。我们建立了这些算子的表示定理。我们的结果强调了迭代收缩和迭代修订之间的关系。特别地，我们证明了迭代修正操作符形成了一个比迭代收缩操作符更大的类。因此，在认知状态框架中，列维同一性具有局限性；也就是说，它不允许定义所有的迭代修订操作符。
In this paper we study iterated contraction in the epistemic state framework, offering a counterpart of the work of Darwiche and Pearl for iterated revision. We provide pure syntactical postulates for iterated contraction, that is, the postulates are expressed only in terms of the contraction operator. We establish a representation theorem for these operators. Our results allow to highlight the relationships between iterated contraction and iterated revision. In particular we show that iterated revision operators form a larger class than that of iterated contraction operators. As a consequence of this, in the epistemic state framework, the Levi identity has limitations; namely, it doesn’t allow to define all iterated revision operators.