PDL with Data Constants

Abstract Extending the Propositional Dynamic Logic with new (propositional) constants and axioms for them, we obtain a conservative extension and call it Combinatory PDL (CPDL). Due to capturing the ‘identity of states’ in CPDL, its expressive power, as compared to PDL, strongly increases. In CPDL we include α∩β (the intersection of the programs α and β), ga (the complement of the program α)—both of them being inexpressible in PDL—and formulas α⊂β and α=β as well as all traditional PDL operators (α−1, α∩β, α∗, αβ, A?). The axioms proposed are shown to be Kripke complete. CPDL is shown highly undecidable.