Category Neutrality: a Type-logical Investigation Dissertation

ed, and the resulting term is given as an argument to the original α term. In this way, a quantified NP acts as a simple variable until an S is derived, at which point the meaning of the S is incorporated into the quantificational meaning of the NP. For example, a quantified NP such as every cat would have the category NP⇑S, and meaning λQ.every′(cat′)(Q). The phrase could act semantically as a referential NP, having simply a variable x for its semantics—until an S was derived, say, Every cat meows, with semantics meow′(x). At this point, the original meaning λQ.every′(cat′)(Q) would be applied to λx.meow′(x), resulting in the meaning every′(cat′)(meow′).