A new theory of quantifiers and term connectives (Q735412)

In the semantic theory for natural language (particularly, for English), developed by Montague et al., type-shifting and lambda-conversion play an essential role in analysing noun and determiner phrases. In this paper, the author simplifies these complicated processes by providing individual-like objects, called shadows, which are built up on individuals by term connectives (conjunction, disjunction, and negation) but considered as entities of the same semantic type as individuals. This approach is applied to quantification as well, so that quantification is reduced to be a denotation of shadows. Showing how the notion of shadow works for analysing noun and determiner phrases with several concrete examples (in English), a semantical theory and a deductive system are proposed with a formal language covering the notion, of which expansion and enrichment are also discussed.