I think where the contrast is drawn in this entry between entailment and implication, this should really be a constrast between entailment and Grice's more specific term "implicature".
The things said about implication are possibly true of some uses of that word, but not of its use in mathematical logic.
I suppose in fact the same kind of point can be made about the entry as a whole. The principal uses of the term "entailment" in mathematical logic are not associated with pragmatics but with truth conditional semantics. In that context A entails B if the truth conditions for B are a subset of those for A.
I am not myself well versed in pragmatics, and am not familiar with its use in pragmatics.
Roger Jones (rbj at rbjones.com)