Strong Completeness for Markovian Logics [chapter]

Dexter Kozen, Radu Mardare, Prakash Panangaden
2013 Lecture Notes in Computer Science  
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
more » ... lled 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.
doi:10.1007/978-3-642-40313-2_58 fatcat:s4tjn3zftzghdpdvyft5pofgke