Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilities of conditionals and previsions of iterated conditionals   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 $C$ as 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.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: supr-con