The syntax, semantics and an axiom system for an extension of Propositional Dynamic Logic (PDL) for order of magnitude qualitative reasoning which formalizes the concepts of closeness and distance is introduced in this paper. In doing this, we use some of the advantages of PDL: firstly, we exploit the possibility of constructing complex relations from simpler ones for defining the concept of closeness and other programming commands such as
while ... do
repeat ... until
; secondly, we employ its theoretical support in order to show that the satisfiability problem is decidable and the completeness of our system. Moreover, the specific axioms of our logic have been obtained from the
set of formulas needed in our definition of qualitative sum of small, medium and large numbers. We also present some of the advantages of our approach on the basis of an example.