Complexity for probability logic with quantifiers over propositions

摘要

In the present article, the quantifiers over propositions are first introduced into the language for reasoning about probability, then the complexity issues for validity problems dealing with the corresponding hierarchy of probabilistic sentences are investigated. We prove, among other things, the ∏_1~1 completeness for the general validity and also indicate the least level in the hierarchy for which the validity problem is undecidable.