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Probabilities of conditionals and previsions of iterated conditionals

机译：迭代条件的条件和预防的概率

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We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability to be the conditional probability. In our approach, however, we avoid triviality because the import-export principle is invalid. We then analyze an example of reasoning under partial knowledge where, given a conditional if A then Cas information, the probability of A should intuitively increase. We explain this intuition by making some implicit background information explicit. We consider several (generalized) iterated conditionals, which allow us to formalize different kinds of latent information. We verify that for these iterated conditionals the prevision is greater than or equal to the probability of A. We also investigate the lower and upper bounds of the Affirmation of the Consequent inference. We conclude our study with some remarks on the supposed "independence" of two conditionals, and we interpret this property as uncorrelation between two random quantities. (C) 2020 Elsevier Inc. All rights reserved.
机译：我们分析了条件随机量框架中所选迭代条件。我们指出，检查刘易斯的琐碎结果是有意义的，这表明条件必须满足其概率是条件概率的概率。但是，在我们的方法中，我们避免了琐碎性，因为进出口原则无效。然后，我们在局部知识下分析一个推理的示例，其中，给定条件如果当那么CAS信息，则A应该直观地增加的概率。我们通过明确的隐式背景信息解释这种直觉。我们考虑几个（普遍的）迭代条件，这让我们正规化不同类型的潜在信息。我们验证，对于这些迭代条件，预防大于或等于A的概率。我们还研究了所造推断的肯定的较低和上限。我们在两种条件的假定“独立性”的一些评论中得出结论，我们将该财产解释为两种随机数量之间的不相关性。 （c）2020 Elsevier Inc.保留所有权利。

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