  We make a probabilistic analysis related to some inference rules which play
an important role in nonmonotonic reasoning. In a coherence-based setting, we
study the extensions of a probability assessment defined on $n$ conditional
events to their quasi conjunction, and by exploiting duality, to their quasi
disjunction. The lower and upper bounds coincide with some well known t-norms
and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their
dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are
rules for which any finite family of conditional events p-entails the
associated quasi conjunction and quasi disjunction. We examine some cases of
logical dependencies, and we study the relations among coherence, inclusion for
conditional events, and p-entailment. We also consider the Or rule, where quasi
conjunction and quasi disjunction of premises coincide with the conclusion. We
analyze further aspects of quasi conjunction and quasi disjunction, by
computing probabilistic bounds on premises from bounds on conclusions. Finally,
we consider biconditional events, and we introduce the notion of an
$n$-conditional event. Then we give a probabilistic interpretation for a
generalized Loop rule. In an appendix we provide explicit expressions for the
Hamacher t-norm and t-conorm in the unitary hypercube.
