Gentzen-type axiomatization for PAL

AbstractThe aim of propositional algorithmic logic (PAL) is to investigate the properties of simple nondeterministic while-program schemes on propositional level. We present finite, cut-free, Gentzen-type axiomatization of PAL. As a corollary from completeness theorem, we obtain the small-model theorem and algorithm for checking the validity of PAL formulas

An elementary proof of the completeness of PDL

AbstractWe give an elementary proof of the completeness of the Segerberg axions for Propositional Dynamic Logic