Iceberg Semantics for Classifier and Measure Phrases

As nominal elements, classifiers and measures are interpreted as i-sets. The notion of i-set has to be extended for this, because neither is of the same type as the interpretations of normal NPs. Classifier i-sets and measure i-sets are introduced. Section 10.2 gives the Iceberg semantics for measure phrases. Measure functions are taken to be continuous and additive functions from objects into measure values, and the body of the interpretation of a measure is taken to be a measure function. It is proved that, given a reasonable assumption that Iceberg semantics does not accept ‘points of matter’, the continuity of the measure function entails that any base for it overlaps. It follows from this that measure i-sets are mess mass. Since the measure is the head of the measure phrase, Rothstein’s generalization that measure phrases are mass follows from the compositional theory of Iceberg bases. Section 10.3 gives the Iceberg semantics for classifiers. Different types of classifiers are analyzed, with special attention to different kinds of portion classifiers: classifiers that portion mass stuff into a disjoint, and hence count, sets of portions. It is shown, for each type of classifier, that the resulting classifier phrase is count, deriving the other side of Rothstein’s generalization. Section 10.4 discusses operations shifting between classifier and measure interpretations with special attention to portion shift. The final section Sect. 10.5 charts the total system of possible shifts between measures and classifiers.