  We present probabilistic approaches to check the validity of selected
connexive principles within the setting of coherence. Connexive logics emerged
from the intuition that conditionals of the form "If $\sim A$, then $A$",
should not hold, since the conditional's antecedent $\sim A$ contradicts its
consequent $A$. Our approach covers this intuition by observing that for an
event A the only coherent probability assessment on the conditional event
$A|\overline{A}$ is $p(A|\overline{A})=0$. Moreover, connexive logics aim to
capture the intuition that conditionals should express some "connection"
between the antecedent and the consequent or, in terms of inferences, validity
should require some connection between the premise set and the conclusion. This
intuition is covered by a number of principles, a selection of which we analyze
in our contribution. We present two approaches to connexivity within
coherence-based probability logic. Specifically, we analyze connections between
antecedents and consequents firstly, in terms of probabilistic constraints on
conditional events (in the sense of defaults, or negated defaults) and
secondly, in terms of constraints on compounds of conditionals and iterated
conditionals. After developing different notions of negations and notions of
validity, we analyze the following connexive principles within both approaches:
Aristotle's Theses, Aristotle's Second Thesis, Abelard's First Principle and
selected versions of Boethius' Theses. We conclude by remarking that
coherence-based probability logic offers a rich language to investigate the
validity of various connexive principles.
