A sentence like ‘the boy stopped working’ gives the inference that he was working before. Is this inference an implicature or a presupposition? Is it possible that it is both?
There are a lot of conflicting definitions of "implicature" out there (and a few of "presupposition"), but the Linguistics 101 version is usually that implicatures can be cancelled out without making the sentence nonsensical, while presuppositions cannot. If I say "the boy stopped working, but he was never working", that's nonsensical, so it's not an implicature.
But is it a presupposition, or just part of the meaning of the sentence? The 101 definition here is that presuppositions persist when you negate the whole sentence. If you say "the boy didn't stop working", then you're still saying that the boy was working previously. In other words, if I ask you "did the boy stop working", an answer of either "yes" or "no" will mean the boy was working previously. Therefore, this is a presupposition.