Résumé
We demonstrate how the specifics of the semantics for mass nouns can be integrated in a recent type-theoretical framework with rich lexical semantics, similarly to collective plural readings. We also explore the significance of an higher-order type system for gradable predicates and other complex predications, as well as the relevance of a multi-sorted approach to such phenomena. All the while, we will detail the process of analysis from syntax to semantics and ensure that compositionality and computability are kept. The distinction between massive and countable entities is similar to a clas-sical type/token distinction — as an example of the type/token distinction, "the bike" can refer both to a single physical bicycle (as in the sentence "the bike is in the garage") but also the the class of all bicycles (as in the sentence "the bike is a common mode of transport in Amsterdam"). However, linguists such as Brendan Gillon warn against such a generalisation (long made in the literature) and remark that, as far as the language is concerned, mass nouns are more alike to the collective readings of pluralised count nouns. Among the many similarities is, for instance, the identical behaviour of plurals and mass nouns with cumulat-ive readings: "Both the pens on the desk and the pens in storage use black ink, so I only have black pens" and "There is red wine on display and red wine in the back, so we only have red" are logically similar (see [5] for discussion). Several different approaches have been proposed to account for the specific semantic issues of mass nouns, from Godehard Link's augmented mereological approach in [12] to David Nicolas' revision of plural logic in [25], all remarking upon this similarity. Many different formalisms, using advanced type theories for the purpose of modelling semantics, have been recently proposed, see e. g. [1,3]. Among those, we proposed a semantic framework based on a multi-sorted logic with higher-order types in order to account for notoriously difficult phenomena pertaining (among many others) for many helpful discussions.