Representing Focus Scoping over New

1. Syntax of focus Example (1) illustrates the locus/scope/antecedent syntax for focus. Focused phrases are marked with a feature F (Jackendoff 1972). The operator ∼k marks the scope of F (Rooth 1992), and index k marks an antecedent in the syntax or discourse representation with respect to which the scope of the focus is partially redundant. Redundancy is characterized semantically either in terms of alternatives (Rooth 1991) or a generalized notion of entailment (Schwarzschild 1999). In the first option, the indexing 3 ∼ 2 is licensed because the alternative set contributed by the question is consistent with the focus-determined alternative set associated with the answer. Specifically, every proposition of the form ‘y ate the last piece of cake’, where y is a person, is a proposition of the form ‘y ate the last piece of cake’, where y is an entity. In the entailment option, it is licensed because the proposition ‘somebody ate the last piece of cake’ entails the proposition ‘some entity ate the last piece of cake’. Technically, the constraints introduced by the redundancy operator are presuppositions about the interpretation of the antecedent.