@inproceedings{873ee97b3f8f4e80806d7dcaebe369ae,
title = "Strong completeness for Markovian logics",
abstract = "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.",
keywords = "markov process, logics, probability distributions, sub-probability distributions, arbitrary distributions",
author = "Dexter Kozen and Radu Mardare and Prakash Panangaden",
year = "2013",
month = oct,
day = "15",
doi = "10.1007/978-3-642-40313-2\_58",
language = "English",
isbn = "9783642403125",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer-Verlag",
pages = "655--666",
editor = "Chatterjee, \{K. \} and J. Sgall",
booktitle = "Mathematical Foundations of Computer Science 2013",
note = "38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 ; Conference date: 26-08-2013 Through 30-08-2013",
}