On the standard view, logic is concerned with reasoning, more in particular with fixing criteria for the soundness and validity of arguments. If we apply standard logic in natural language semantics, we inherit this basic trait, and can only expect our logical semantics to have descriptive and explanatory value for the kind of linguistic phenomena that are related closely enough to what the logic is about. Reasoning is just one particular language game. And if we think of our daily

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... , it does not have the same central position it has in logic. Co operative information exchange seems a more prevailing linguistic activity. It is reasonable to assume that such a predominant function has a distinctive influence on the structure of natural language, which forms the subject matter of linguistics. For example, it is a widespread (and age-old) idea, that the organization of dis course is largely determined by a mostly implicit process of raising and resolving issues, and that even sentential structure, including the intonational contour of ut terances, can only be properly understood, if we take that to heart. If there is some truth in this, then linguistic semanticists should be worried by the fact that by and large they base themselves on a logical paradigm that is biased to such an extent towards reasoning rather than exchange of information. As a response to this fear, one might point out that Gricean pragmatics is as much part of an overall theory of meaning, as logical semantics is. And the Cooperation Principle, which is at the heart of it, precisely is a principle of ration ality which governs information exchange. Grice proposed to use it in the expla nation of linguistic phenomena that lie beyond the reach of logical semantics as such. Among other things, he employed the principle in a defense of standard logic -in particular the truth functional analysis of the logical connectives against the allegation that it leaves important aspects of meaning unaccounted for. He argued that standard logic together with the general assumption that we follow the Cooperation Principle does provide us with the means to account for such ad ditional features of meaning. Hence, we are in no need to replace the standard logical analysis by some other type of interpretation, we only have to combine logical semantics with general pragmatic strategies to cover the relevant facts. One way to look at the logical investigations carried out in the present pa per, is to view them as an attempt to tum the Cooperation Principle as such into the key notion of logical semantics. Instead of centering the logic around the ex-© 1999 by Jeroen Groenendijk Tanya Matthews and Devon Strolovitch (eds), SALT IX 109-126, Ithaca, NY: Cornell University.