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dc.contributor.authorKozen, Dexter
dc.contributor.authorMardare, Radu
dc.contributor.authorPanangaden, Prakash
dc.description.abstractIn 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.en_US
dc.subjectAumann algebraen_US
dc.subjectMarkovian logicen_US
dc.titleStrong Completeness for Markovian Logicsen_US
dc.typetechnical reporten_US

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