Propositional Dynamic Logic of Looping and Converse

Abstract

Dynamic logic [5,6,15,16] applies concepts from modal logic to a relational semantics of programs to yield various systems for reasoning about the before-after behavior of programs. Analogues to the modal logic assertions ?p (possibly p) and ?p(necessarily p) are the dynamic logic constructs <a>p and [a]p. If a is a program and p is an assertion about the state of a computation, then ,<a>p asserts that after executing a, p can be the case, and [a]p asserts that after executing a, p must be the case.