It is an idea which lies on the rhetorical side of the dichotomy between logic and rhetoric. First, a distinction is drawn between Propositional Content and Illocutionary Force. Clearly in some sense it was both. From H's end it feels like S intended to make H think something which he happens to know is false. Both Searle and Grice imply that conversational implicatures do a great deal of work in conversation.
Every utterance is surrounded by a cloud of conversational implicatures.
They arise because both speaker and hearer have certain assumption, principally that both are cooperating in having a conversation. This is to circumvent certain criticisms of Grice raised by Sacks and by Levinson. I have to study for an exam. He calls them Quantity , Quality , Relation and Manner . Make your contribution easy to understand given the state of knowledge of the hearer.