Grice, Hoare and Nash: some comments on conversational implicature

ABSTRACT. We consider the special case of a particularized conversational implicature which arises when one agent, A, has a a goal G and makes a statement relevant to her situation. The other agent B then says something, and an implicature arises from B's utterance which can only be understood in terms of the goal. It turns out that Hoare semantics, developed originally for proving program correctness,is relevant here.

A second point is Grice's principle of cooperation. As we are all aware, not all conversations are "fully" cooperative. For instance, an American tourist and a street hawker in India may negotiate the price of a carved elephant which the latter is offering to the former. The cooperation arises from the fact that both want the sale to take place, but there is also an opposition as the tourist wants to pay less and the hawker wants to charge more. What will each say?

The Well known come on uttered by a young man to his date, "Would like to come to my apartment and see my etchings?" provides another such case.

We suggest that a principle formulated by John Nash in his "The Bargaining Problem" provides the proper generalization for the mix of cooperation and competition which prevails in such dialogues.