Geodesic
Quantification over propositional formulas in probability logic: decidability issues
Algebra i logika, Tome 50 (2011) no. 4, pp. 533-546

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A language for reasoning about probability is generalized by adding quantifiers over propositional formulas to the language. Then relevant decidability issues are considered. In particular, the results presented demonstrate that a rather weak fragment of the new language has an undecidable validity problem. On the other hand, it is stated that a restricted version of the validity problem is decidable for $\forall\exists$-sentences.
Keywords: probability logic, decidability.
Mots-clés : quantification over propositions 
@article{AL_2011_50_4_a5,
     author = {S. O. Speranskii},
     title = {Quantification over propositional formulas in probability logic: decidability issues},
     journal = {Algebra i logika},
     pages = {533--546},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2011_50_4_a5/}
}
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S. O. Speranskii. Quantification over propositional formulas in probability logic: decidability issues. Algebra i logika, Tome 50 (2011) no. 4, pp. 533-546. http://geodesic.mathdoc.fr/item/AL_2011_50_4_a5/