Connotation is considered to be part of pragmatics.
What other parts does pragmatics have, besides connotation? (I can't think of none, but I don't really know anything.)
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Pragmatics is concerned with the meaning of utterances in context, that is, wrt common knowledge and previous discourse. One example would be the resolution of anaphors and, more interestingly, figurative speech such as idioms (e.g. “kick the bucket”). It’s also concerned with the coherence of discourse, mainly topic-focus articulation.