RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra Logika, 2013, Volume 52, Number 2, Pages 236–254 (Mi al584)  

This article is cited in 1 scientific paper (total in 1 paper)

Collapsing probabilistic hierarchies. I

S. O. Speranskii

Novosibirsk State University, Novosibirsk, Russia

Abstract: We study hierarchies of validity problems for prefix fragments in probability logic with quantifiers over propositional formulas, denoted $\mathcal{QPL}$, and its versions. It is proved that if a subfield $\mathfrak F$ of reals is definable in the standard model of arithmetic by a second-order formula without set quantifiers, then the validity problem over $\mathfrak F$-valued probability structures for $\Sigma_4$-$\mathcal{QPL}$-sentences is $\Pi^1_1$-complete; as a consequence, the corresponding hierarchy of validity problems collapses. Moreover, in proving this fact, we state that an $\Pi^1_1$-полнота $\forall\exists$-theory of Presburger arithmetic with a single free unary predicate is $\Pi^1_1$-complete, which generalizes a well-known result of Halpern relating to the entire theory mentioned.

Keywords: probability logic, quantifiers over propositions, computational complexity, expressiveness.

Full text: PDF file (232 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2013, 52:2, 159–171

Bibliographic databases:

UDC: 510.647+510.5
Received: 01.08.2012
Revised: 05.03.2013

Citation: S. O. Speranskii, “Collapsing probabilistic hierarchies. I”, Algebra Logika, 52:2 (2013), 236–254; Algebra and Logic, 52:2 (2013), 159–171

Citation in format AMSBIB
\Bibitem{Spe13}
\by S.~O.~Speranskii
\paper Collapsing probabilistic hierarchies.~I
\jour Algebra Logika
\yr 2013
\vol 52
\issue 2
\pages 236--254
\mathnet{http://mi.mathnet.ru/al584}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3134785}
\transl
\jour Algebra and Logic
\yr 2013
\vol 52
\issue 2
\pages 159--171
\crossref{https://doi.org/10.1007/s10469-013-9230-0}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000321627100007}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884951364}


Linking options:
  • http://mi.mathnet.ru/eng/al584
  • http://mi.mathnet.ru/eng/al/v52/i2/p236

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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
    Number of views:
    This page:226
    Full text:39
    References:55
    First page:37

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019