Propositional Dynamic Logic with Storing, Recovering and Parallel Composition

This work extends Propositional Dynamic Logic (PDL) with parallel composition operator and four atomic programs which formalize the storing and recovering of elements in data structures. A generalization of Kripke semantics is proposed that instead of using set of possible states it uses structured sets of possible states. This new semantics allows for representing data structures and using the five new operator one is capable of reasoning about the manipulation of these data structures. The use of the new language (PRSPDL) is illustrated with some examples. We present sound and complete set of axiom schemata and inference rules to prove all the valid formulas for a restricted fragment called RSPDLo.