Not few but all quantifiers can be negated: towards a referentially transparent semantics of quantified noun phrases

The main concern of this paper is to introduce not as a noun phrase negation operator. It is used in order to compositionally derive structures such as not(many)(bicycles). However, noun phrase negation is part of a much larger account of plural semantics and quantification, guided by the notion of referential transparency. Therefore the paper splits into two parts: the first part gives a minimal background on a referential transparent NP semantics. A foundation of the semantics of plural count nouns in terms of ordered set bipartitions is given. This includes as a side effect a significant reduction in the number of possible quantifier denotations and a derivation of the conservativity universal. The second part deals with not and how it interacts with an negation and anaphoric accessibility.