Iteration-free PDL with storing, recovering and parallel composition: a complete axiomatization

Abstract

We devote this paper to the axiomatization/completeness of PRSPDL0 - a variant of iteration-free PDL with parallel composition. Our results are based on the following: although the program operation of parallel composition is not modally definable in the ordinary language of PDL, it becomes definable in a modal language strengthened by the introduction of propositional quantifiers. Instead of using axioms to define the program operation of parallel composition in the language of PDL enlarged with propositional quantifiers, we add an unorthodox rule of proof that makes the canonical model standard for the program operation of parallel composition and we use large programs for the proof of the Truth Lemma.