A Semantics for Nominal Comparatives

This work adopts the perspective of plural logic and measurement theory in order rst to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantiier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the rst to examine comparatives within plural logic, a step which appears necessary, but which also harbors speciic analytical problems examined here. Since nominal comparatives involve plural and mass reference, we begin with a domain of discourse upon which a lattice structure (Link's) is imposed , and which maps (via abstract dimensions such as weight in kilograms) to concrete measures (in N,R+). The mapping must be homomorphic and Archimedean. Comparisons begin as simple predicates on dimensions or measures ; from these we derive classes of predicates on the domain, i.e., generalized determiners (quantiiers), and show, e.g., how monotonicity properties follow in the derivation. This results in a proposal for a logical language which includes derived determiners, and which is an attractive target for semantics interpretation; it also turns out that some interesting comparative determin-ers are rst order, at least when restricted to nonparametric and noncollective predications.