Strong Completeness for Markovian Logics

  • Dexter Kozen
  • Radu Mardare
  • Prakash Panangaden
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)


In this paper we present Hilbert-style axiomatizations for three logics for reasoning about continuous-space Markov processes (MPs): (i) a logic for MPs defined for probability distributions on measurable state spaces, (ii) a logic for MPs defined for sub-probability distributions and (iii) a logic defined for arbitrary distributions. These logics are not compact so one needs infinitary rules in order to obtain strong completeness results.

We propose a new infinitary rule that replaces the so-called Countable Additivity Rule (CAR) currently used in the literature to address the problem of proving strong completeness for these and similar logics. Unlike the CAR, our rule has a countable set of instances; consequently it allows us to apply the Rasiowa-Sikorski lemma for establishing strong completeness. Our proof method is novel and it can be used for other logics as well.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dexter Kozen
    • 1
  • Radu Mardare
    • 2
  • Prakash Panangaden
    • 3
  1. 1.Computer Science DepartmentCornell UniversityIthacaUSA
  2. 2.Department of Computer ScienceAalborg UniversityDenmark
  3. 3.School of Computer ScienceMcGill UniversityMontrealCanada

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