  System Z+ [Goldszmidt and Pearl, 1991, Goldszmidt, 1992] is a formalism for
reasoning with normality defaults of the form "typically if phi then + (with
strength cf)" where 6 is a positive integer. The system has a critical
shortcoming in that it does not sanction inheritance across exceptional
subclasses. In this paper we propose an extension to System Z+ that rectifies
this shortcoming by extracting additional conditions between worlds from the
defaults database. We show that the additional constraints do not change the
notion of the consistency of a database. We also make comparisons with
competing default reasoning systems.
