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.

On a textbook semantics for modification, an intersective modifier denotes 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.

1. $[\![{\text{blue}}]\!]=\{x\,|\,x{\text{ is blue }}\}$
2. $[\![{\text{blue pig}}]\!]=\{x\,|\,x{\text{ is blue }}\}\cap \{x\,|\,x{\text{ is a pig }}\}$

Such meanings can be composed either by introducing an interpretation rule Predicate Modification which hard-codes intersectivity. However, this mode of composition can also be delivered by standard Function Application if the modifier is given a higher semantic type, either lexically or by applying a type shifter.

1. Predicate Modification Rule: If $\alpha$ is a branching node with daughters $\beta$ and $\gamma$ where $[\![\beta ]\!],[\![\gamma ]\!]\in {\mathcal {D}}_{\langle e,t\rangle }$, then $[\![\alpha ]\!]=\lambda x_{e}\,.\,x\in [\![\beta ]\!]\cap [\![\gamma ]\!]$.

See also

• Adjective
• Grammatical modifier
• Prepositional phrase
• Relative clause
• https://en.wiktionary.org/wiki/intersective#Adjective