Towards a Suppositional Inquisitive Semantics

One of the primary usages of language is to exchange information. This can be done directly, as in Will Susan sing? No, she won't, but it is also often done in a less direct way, as in If Pete plays the piano, will Susan sing? No, if Pete plays the piano, Susan won't sing. In the latter type of exchange, both participants make a certain supposition, and exchange information under the assumption that this supposition holds. This paper develops a semantic framework for the analysis of this kind of information exchange. Building on earlier work in inquisitive semantics, it introduces a notion of meaning that captures informative, inquisitive, and suppositional content, and discusses how such meanings may be assigned in a natural way to sentences in a propositional language. The focus is on conditionals, which are the only kind of sentences in a propositional language that introduce non-trivial suppositional content.