Conversational implicatures, whether they are quantity-based or relation-based, depend critically on features of the context. They have been largely considered as defying any formalistic treatment in logical semantics. The interaction between speaker and hearer has seemed to be beyond any mathematical theorizing and the task has been thrown away into a pragmatic "waste-basket." Even in pragmatics, those who follow the functional approach, e.g. Dinsmore (1979) and Leech (1983), cast doubt on any formalistic account of conversational implicatures. In fact, with some exceptions such as Gazdar (1979), Atlas and Levinson (1981) and Horn (1989), conversational implicatures and the explicating processes have been informally stated, due to the recalcitrant nature of the notion of the speaker's intention. However, as Parikh (1991) shows in the case of ambiguity, game theory provides a means of dealing with such a task. Following Parikh's assumption that communication is an interactive, strategic process that involves interplay of inferences about the participants' intentions, I attempt to show that the structure of non-logical inferences is subject to a mathematical game-theoretic analysis
