Definability in dynamic logic

摘要

We study the expressive power of various versions of Dynamic Logic and compare them with each other as well as with standard languages in the logical literature. One version of Dynamic Logic is equivalent to the infinitary logic Lω1,ωCK but regular Dynamic Logic is strictly less expressive. In particular, the ordinals ωω and ωω·2 are indistinguishable by formulas of regular Dynamic Logic. We also study the effects of including array assignments and/or random assignments on the expressive power of Dynamic Logic.