Inlinguistics, anintersective modifier is an expression whichmodifies another by delivering theintersection of theirdenotations. One example is the English adjective "blue", whose intersectivity can be seen in the fact that being a "blue pig"entails being both blue and a pig. By contrast, the English adjective "former" is non-intersective since a "former president" is neither former nor a president.[1][2]
When a modifier is intersective, its contribution to the sentence's truth conditions do not depend on the particular expression it modifies. This means that one can test whether a modifier is intersective by seeing whether it gives rise tovalid reasoning patterns such as the following.[3]
With a non-intersective modifiers such as "skillful", the equivalentdeduction would not be valid.[4]
Modifiers can beambiguous, having both intersective and nonintersective interpretations. For instance, the example below has an intersective reading on which Oleg is both beautiful and a dancer, but it also has a merelysubsective reading on which Oleg dances beautifully but need not himself be beautiful.[5]
On a textbook semantics for modification, an intersective modifierdenotes the set of individuals which have the property in question. When the modifier modifies a modifiee which also denotes a set of individuals, the resulting phrase denotes the intersection of their denotations.[6]
Such meanings can becomposed either by introducing an interpretation rulePredicate Modification which hard-codes intersectivity. However, this mode of composition can also be delivered by standardFunction Application if the modifier is given a highersemantic type, either lexically or by applying atype shifter.[6]
