On Expressive and Model Checking Power of Propositional Program Logics

Abstract

We examine when a model checker for a propositional program logic can be used for checking another propositional program logic in spite of lack of expressive power of the first logic. We prove that (1) a branching time Computation Tree Logic CTL, (2) the propositional μ-Calculus of D. Kozen μC, and (3) the second-order propositional program logic 2M of C. Stirling enjoy the equal model checking power in spite of difference in their expressive powers CTL < μC < 2M: every listed logic has a formula such that every model checker for this particular formula for models in a class closed w.r.t. finite models, Cartesian products and power-sets can be reused for checking all formulae of these logics in all models in this class. We also suggest a new second-order propositional program logic SOEPDL and demonstrate that this logic is more expressive than 2M, is as expressive as the Second order Logic of monadic Successors of M. Rabin (S(n)S-Logic), but still enjoys equal model checking power with CTL, μC and 2M (in the same settings as above).