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We devote this article to the axiomatization/completeness ofP  R  S  P  D   L  0—a variant of iteration-freeP  D  Lwith parallel composition. Our results are based on the following: although the program operation of parallel composition is not modally definable in the ordinary language ofP  D  L, 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 ofP  D  Lenlarged 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.

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