La Palme Reyes M., Macnamara J., Reyes G. E. and H. Zolfaghari (1999). Count nouns, mass nouns and their transformations: a category-theoretic unified semantics. Language, logic and concepts. Bradford Book, MIT Press, Cambridge, Ma, 1999, pp 427-452.

All natural languages seem to distinguish at the semantic level between count nouns (CNs) such as “dog” and mass nouns (MNs) such as “matter” (in the sense of physical stuff, not in the sense of concern or affair). Some mark the distinction at the syntactic level (e.g. one can say ” a dog”, “a portion of matter”, but not “a matter”). One syntactic difference is that usually CNs take the plural (‘dogs’) whereas MNs do not. We organize the nouns in two categories with adjoint functors between them: the plural, from CNs into MNs, and “portion of” in the opposite direction. We interpret these nominal categories into the category of kinds and the category of sup-lattices, respectively, and build adjoint functors between them which interpret the adjoint functors at the nominal level. This semantics is applied, among others, to study the 8 syllogisms, already considered in the literature, which result from “Claret is wine, wine is liquid, so claret is liquid”, by adding the particle “a” to each noun or keeping it as it is.

Count nouns, mass nouns and their transformations: a category-theoretic unified semantics