A Game-Theoretic Account of Implicature

I use game theory, decision theory, and situation theory to model a class of implicatures. Two types of relevance are distinguished and used to construct a model of Gricean communication between speaker and addressee. 1 I n t r o d u c t i o n Grice's[5] account of nonnatural communication includes as a corollary an account of how more can be communicated than what is saidJ ,Conversely 2, the Gricean principle of cooperation is essential to the full range of nonnatural communication, not just to implicature. Much information can be extracted from an utterance relative to constraints an addressee knows or is a t tuned to, but not all this incremental information 3 can be said to be communicated. Implicature is, roughly, communicated information beyond what is said. In this paper, I develop a game-theoretic account of a subclass of implicatures within the framework of situation theory 4. A formal account of the model developed here together with a derivation of important properties of implicature and the Gricean maxims can be found in Parikh [13]. 2 O n R e l e v a n c e There appear to be two distinct notions of relevance. The first notion, which I will call relevancez (or logical relevance), is that of a relational property of a proposition with respect to a set of propositions that , *I would like to thank David Israel and Rohit Parikh for helpful conversations. 1 See Grice [7]. ~A thorough discussion of this can be found in Parikh [14]. 3See Israel and Perry [9]. 4See Barwise and Perry[4] and Barwise[2].