揭示条件句与概率更新之间的深层关系,统一分析框架。
Conditionals Based on Selection Functions, Modal Operators and Probabilities
- 从一般性视角出发,统合多种条件句与更新方法
- 证明了特定条件句的概率可被刻画为更新规则
- 适合逻辑学、认知科学与贝叶斯推理研究者
概率更新方法(如贝叶斯条件化)是用于描述初始信念状态(通常以先验概率函数P表示)在新信息影响下如何调整的建模工具。条件句与更新方法之间存在直观关联,尤其体现在条件化上。本文致力于深化这一研究,旨在揭示更新方法与条件连词之间的普遍联系。不同于以往聚焦单一条件句或特定更新方法的文献,本文目标是建立关于条件句与其概率之间关系的一般性结论,从而刻画某些条件连词的概率,并理解哪些更新过程可由特定条件连词表达。整体上,本文采用广义视角,涵盖大量条件句类型与广泛的更新方法,推导出它们之间相互关系的若干普遍结果。
原文摘要 · Abstract (English)
Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior probability function P, which is adjusted in light of new information. Notably, updating methods and conditional sentences seem to intuitively share a deep connection, as is evident in the case of conditionalization. The present work contributes to this line of research and aims at shedding new light on the relationship between updating methods and conditional connectives. Departing from previous literature that often focused on a specific type of conditional or a particular updating method, our goal is to prove general results concerning the connection between conditionals and their probabilities. This will allow us to characterize the probabilities of certain conditional connectives and to understand what class of updating procedures can be represented using specific conditional connectives. Broadly, we adopt a general perspective that encompasses a large class of conditionals and a wide range of updating methods, enabling us to prove some general results concerning their interrelation.
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