Can Logical Probability Be Viewed as a Measure of Degrees of Partial Entailment?

A new account of partial entailment is developed. Two
meanings of the term ‘partial entailment’ are distinguished, which
generalise two distinct aspects of deductive entailment. By one
meaning, a set of propositions A entails a proposition q if, supposed
that all the elements of A are true, q must necessarily be true
as well. By the other meaning, A entails q inasmuch the informative
content of q is encapsulated in the informative content of A: q
repeats a part of what the elements of A, taken together, convey. It
is shown that while the two ideas are coextensive with respect to
deductive inferences, they have not a common proper explicatum
with respect to the notion of partial entailment. It is argued that
epistemic inductive probability is adequate as an explicatum of
partial entailment with respect to the first meaning while it is at
odds with the second one. A new explicatum of the latter is proposed
and developed in detail. It is shown that it does not satisfy
the axioms of probability.