A Completeness Result for a Propositional Dynamic Logic

Abstract

Propositional modal logic of programs has been introduced by Fischer and Ladner [1], following ideas of Pratt [4]. We shall call it propositional dynamic logic (PDL) following the terminology of Heral, Meyer and Pratt. In the following we prove the completeness of a rather natural set of axioms for this logic and for an extension of it obtained by allowing the inverse operation which converts a program into its inverse.