On the Dynamics of Conversation

On one familiar and traditional picture, linguistic communication is a matter of the expression and transmission of a proposition across a common ground, with the proposition determined as a function of its semantic value. What general properties of a system of linguistic communication indicate whether or not it can, even in principle, be modeled along these traditional lines? This is a fundamental question in natural language semantics and pragmatics, and one relevant to a full understanding and assessment of non-traditional models of communication—notably, those found in the dynamic semantics tradition. The question is, in part, about what properties make a semantics and prag- matics for a language fragment “robustly dynamic” as opposed to “static”. We formalize one natural version of this question and answer it, in the pro- cess extending earlier results of van Benthem and Veltman. According to our result, the characterizing feature of the traditional picture—of ‘staticness’, on one precisification—is this: the updates to the common ground induced by every sentence of the relevant language fragment exhibit idempotence and commutativity. The result naturally raises the question whether natural languages exhibit failures of idempotence or commutativity. We examine the issue, bringing out some ways in which putative failures of idempotence and commutativity can, and cannot, be explained by appeal to context-sensitivity.
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