Intersective modifier
In linguistics, an intersective modifier is an expression which modifies another by delivering the intersection of their denotations. 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. 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 to valid reasoning patterns such as the following.