Modeling Quantification with Polysemous Nouns

Babonnaud et al. (2016) introduce a framework for modeling systematic polysemy that combines Lexicalized Tree Adjoining Grammar (LTAG) with frame semantics and Hybrid Logic (HL). The components of the syntax-semantics interface are elementary LTAG trees paired with frame descriptions that are expressed by possibly underspecified HL formulas. A brief review of this framework will be given in Section 2 below. In Babonnaud et al. (2016), an inherently polysemous noun such as ‘book’, which provides referential access to both a physical and an informational object, is assumed to refer to entities of type phys(ical)-obj(ect) which have an attribute CONTENT whose value is of type information. That is, the semantic type of ‘book’ is a subtype of the complex type phys-obj ∧ 〈CONTENT〉information or info(rmation)-carrier for short (cf. Section 3 below). The physical aspect and the informational aspect are then addressed in different ways in contexts such as ‘read the book’, ‘carry the book’, ‘master the book’ or ‘a heavy book on magic’. The verb ‘read’, for instance, is analyzed as denoting a complex event that consists of two components, the perception of the physical aspect and the comprehension of the informational aspect (following Pustejovsky 1998), and thus combines with both aspects of ‘book’. By comparison, the verb ‘master’ calls for a grammatical object that denotes an entity of type information or info-carrier and semantically selects only the informational aspect in the latter case. Treating books as physical information carriers in this way gives rise to the following “quantification puzzle” as noted in Asher and Pustejovsky (2005, 2006); see also Asher (2011). While (1a) poses no problem since the domain of quantification consists of physical entities, it not obvious how to cope with (1b), which is naturally interpreted as quantifying over all contents of the books in the library.