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The sentence "The boss fired the employee who is always late" invites the defeasible inference that the speaker is attempting to convey that the lateness caused the firing (cf. The boss fired the employee who is from Philadelphia, which does not invite an analogous inference). We argue that such inferences cannot be understood in terms of familiar approaches to extrasemantic enrichment such as implicature, impliciture, explicature, or species of local enrichment already in the literature. Rather, we propose that they arise from more basic cognitive strategies, grounded in processes of coherence establishment, that thinkers use to make sense of the world. Attention to such cases provides a richer and more varied landscape of extrasemantic enrichment than has been appreciated to date.