Deterministic Propositional Dynamic Logic: Finite Models, Complexity, and Completeness

Abstract

Let p be a formular in deterministic propositional dynamic logic. A decision procedure for the satisfiability of p is given along with a construction of a finite model for every satisifiable p. The decision procedure runs in deterministic time 2^cn and the size of the model is bounded by n^2 * 4^n, where n is the lenth of p. Finally, a complete axiomatization for deterministic propositional dynamic logic is given, based on the Segerberg axioms for propositional dynamic logic.