The occurrence of split utterances (SUs) in dialogue raises many puzzles for grammar formalisms, from formal to pragmatic and even philosophical issues. This paper presents an account of some of the formal details that grammars need to incorporate in order to accommodate them. Using Dynamic Syntax (DS), we illustrate how by incorporating essential interaction with the context into the grammar itself, we can deal with speaker change in SUs: not only its effects on indexicals I and you, but also the multiple illocutionary forces that can arise. We also introduce a Split Turn Taking Puzzle (STTP) showing that the current speaker and the agent of the resulting speech act are not necessarily the same.
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