Fox and Spector use multiple instances of the exhaustivity operator EXH to derive the correct meaning of utterances that include pitch-focus marked disjunction in downward-entailing environments. They argue that the \ operator evaluates alternatives to be used by EXH. Though the method is sound and gets the right result, we argue that the way in which EXH would need to interact with other instances of EXH, as well as other focus-sensitive elements, is at odds with how EXH is used to (...) explain other phenomena. Specifically, the analysis in Fox and Spector predicts intervention effects for cases where EXH interacts with other focus-sensitive elements. This is problematic for many cases in which EXH is used to derive the desired inferences. We propose a different way of focus association for EXH that would work for the approach introduced in Fox and Spector as well as elsewhere. In addition, our account does not require a covert element to be focused. (shrink)

In this paper, we show that native speakers spontaneously divide the complex meaning of a new word into a presuppositional component and an assertive component. These results argue for the existence of a productive triggering algorithm for presuppositions, one that is not based on alternative lexical items nor on contextual salience. On a methodological level, the proposed learning paradigm can be used to test further theories concerned with the interaction of lexical properties and conceptual biases.