help from readers of the book "NonMonotonic Reasoning"by G. Antoniou

I ask any readers of the book "NonMonotonic Reasoning" by Grigoris
Antoniou for help in figuring out the example on
page 32 of the text:

He gives a default theory T= (W,D) with W = {a} and D containing the
following defaults:

delta1 = a: ~b / ~b, delta2 = b : c / c.

For process II = (delta1) .....

For II = (delta2,delta1) we have In(II) = Th(a,c,~b) and Out(II) =
{~c,b}

My quesion is how can II(delta2,delta1) be a Process of T when the
Prerequisite of delta 2 ie "b" NEVER occurs
in W even after the application of delta 1? I think the only way the
text is consistent is if delta2's prerequisite is "~b"
and not "b" as printed in the text. That way, application of delta1
puts the "~b" consequent into the database. However, the author goes
on to say II` = (delta1,delta2) is NOT a process of T thereby
contradicting my conjecture.

Thanks in advance.

.