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Algebra Logika, 2011, Volume 50, Number 4, Pages 533–546 (Mi al500)  

This article is cited in 3 scientific papers (total in 3 papers)

Quantification over propositional formulas in probability logic: decidability issues

S. O. Speranskii

Novosibirsk State University, Novosibirsk, Russia

Abstract: 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, quantification over propositions, decidability.

Full text: PDF file (195 kB)
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English version:
Algebra and Logic, 2011, 50:4, 365–374

Bibliographic databases:

UDC: 510.647+510.5
Received: 26.01.2011
Revised: 29.03.2011

Citation: S. O. Speranskii, “Quantification over propositional formulas in probability logic: decidability issues”, Algebra Logika, 50:4 (2011), 533–546; Algebra and Logic, 50:4 (2011), 365–374

Citation in format AMSBIB
\Bibitem{Spe11}
\by S.~O.~Speranskii
\paper Quantification over propositional formulas in probability logic: decidability issues
\jour Algebra Logika
\yr 2011
\vol 50
\issue 4
\pages 533--546
\mathnet{http://mi.mathnet.ru/al500}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2893587}
\zmath{https://zbmath.org/?q=an:06116201}
\transl
\jour Algebra and Logic
\yr 2011
\vol 50
\issue 4
\pages 365--374
\crossref{https://doi.org/10.1007/s10469-011-9148-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000295735600006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053926466}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. O. Speranskii, “Collapsing probabilistic hierarchies. I”, Algebra and Logic, 52:2 (2013), 159–171  mathnet  crossref  mathscinet  isi
    2. S. O. Speranski, “A note on hereditarily $\Pi_1^0$- and $\Sigma_1^0$-complete sets of sentences”, J. Logic Comput., 26:5 (2016), 1729–1741  crossref  mathscinet  zmath  isi  scopus
    3. S. O. Speranski, “Quantifying over events in probability logic: an introduction”, Math. Struct. Comput. Sci., 27:8 (2017), 1581–1600  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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