Scott Soames entry on implicature in Encyclopedia of Philosophy

A potentially more restrictive understanding of entailment requires that when A entails B, the falsity of A is a necessary consequence of the falsity of B. When entailment is understood in this way, it is sometimes contrasted with logical presupposition: A proposition A logically presupposes a proposition B if and only if the truth of B is a necessary condition for A's being either true or false. The most widely discussed (putative) examples of logical presuppositions are so-called existential presuppositions, corresponding to uses of singular terms. (These are also sometimes called referential presuppositions....