The AP is normally placed before the noun which it modifies. This yields an attributive construction. In the attributive construction, the noun displays agreement with the adjective:

The AP can also be placed after the Noun Phrase (NP). This yields an appositive construction. In the appositive construction, there is no agreement between the noun and the adjective:

In the attributive construction, the adjective restricts the denotation of the Noun Phrase (NP). In formal semantic terms: the denotation of the NP is not equal to the intersection of the denotation of the NP and the AP. Attributive adjectives are perfectly compatible with negative and universal quantifiers, for the adjective restricts the denotation of the NP to which the quantifier is applied:

The phrase no naughty boy refers in all possible worlds to a subset of the set of individuals to which the phrase no boy refers. The two phrases may accidentally have the same reference in a situation in which all boys are naughty, but that is a matter for pragmatics. In the appositive construction, the adjective cannot restrict the denotation of the NP. In formal semantic terms: the denotation of the NP must be equal to the intersection of the denotation of the NP and the AP. Therefore appositives are said to be non-restrictive. Bare appositive adjectives are therefore grammatical to the extent that they can corefer with NPs. Since bare adjectives are not negative (downwards entailing), they are incompatible with negated NPs:

Appositive adjectives are grammatical in case they are accompanied by a quantifying conjunction yielding a denotation for the AP as a whole that allows of coreference with a negated NP, and coreference is by definition non-restrictive. In the examples below, the appositive phrase does not restrict the denotation of the negated NP:

Such examples involve a quantification over all the values of the AP, and this apparently makes possible the type of coreference characteristic of an appositive interpretation.