信仰融合的不可能性
Impossibility in Belief Merging
摘要：
为了研究信念合并的社会属性，更好地理解不可能性，我们从三个方面扩展了Konieczny和Pino Pérez提出的基于逻辑的信念合并框架。首先，在信息表征的层面上，我们从信念基础过渡到复杂的认知状态。第二，配置文件表示为功能的有限社会的一套认识状态（一种矢量），而不是作为多集的认识状态。第三，我们扩展了一套理性假设，以考虑社会选择理论的经典假设的认识论版本：标准域，帕累托财产，无关的替代品的独立性和独裁者的缺席。这些社会公设的认识论版本本质上是根据有限命题逻辑给出的。我们陈述了这些算子的一些表示定理。这些扩展和表示定理使我们能够建立阿罗不可能性定理的认识论和非常一般的版本。我们的结果的一个有趣的特征是，它适用于认知状态的不同表示;例如条件，有序条件函数，当然还有总前序。
英文摘要：
With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino Pérez. First, at the level of representation of the information, we pass from belief bases to complex epistemic states. Second, the profiles are represented as functions of finite societies to the set of epistemic states (a sort of vectors) and not as multisets of epistemic states. Third, we extend the set of rational postulates in order to consider the epistemic versions of the classical postulates of Social Choice Theory: Standard Domain, Pareto Property, Independence of Irrelevant Alternatives and Absence of Dictator. These epistemic versions of social postulates are given, essentially, in terms of the finite propositional logic. We state some representation theorems for these operators. These extensions and representation theorems allow us to establish an epistemic and very general version of Arrow's Impossibility Theorem. One of the interesting features of our result, is that it holds for different representations of epistemic states; for instance conditionals, Ordinal Conditional functions and, of course, total preorders.
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