  Recently, it has been shown that probabilistic entailment under coherence is
weaker than model-theoretic probabilistic entailment. Moreover, probabilistic
entailment under coherence is a generalization of default entailment in System
P. In this paper, we continue this line of research by presenting probabilistic
generalizations of more sophisticated notions of classical default entailment
that lie between model-theoretic probabilistic entailment and probabilistic
entailment under coherence. That is, the new formalisms properly generalize
their counterparts in classical default reasoning, they are weaker than
model-theoretic probabilistic entailment, and they are stronger than
probabilistic entailment under coherence. The new formalisms are useful
especially for handling probabilistic inconsistencies related to conditioning
on zero events. They can also be applied for probabilistic belief revision.
More generally, in the same spirit as a similar previous paper, this paper
sheds light on exciting new formalisms for probabilistic reasoning beyond the
well-known standard ones.
