Propositional dynamic logic with local assignment

Abstract

We propose an extension of Propositional Dynamic Logic which allows a new kind of program terms—local assignments to propositional variables. They are very close to the known array assignments in Dynamic Logic beacuse they allow us to change the truth values of predicate variables. In this logic, many notions, like equivalence of programs, looping and finitely branching, are expressible on a propositional level. In fact, we show that the resulting logic is equivalent in expressive power to first-order logic augmented by a device to express transitive closures. In other words, it is (modulo extra predicate symbols) equivalent to first-order dynamic logic. Not suprisingly, therefore, the validity problem for this extension is Π 1 1-complete.