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.