Subsective adjectives

How should we analyze attributive adjectives, in general? Well, first, we should assign nouns like linguist a syntactic category—call it $n$. Further, if we take nouns to denote properties (i.e., sets of entities—those to which the noun applies), then we can say that the semantic type associated with the syntactic category $n$ is the type $(e → t)$ of characteristic functions of entities.

Thus for example ant can be given the lexical entry in (1).

$⟨\textit{ant}, (λx.\ct{ant}(x))⟩ ⊢ n$

Because attributive adjectives modify nouns—and can apparently do so recursively (silly fake purple… ant)—we should give them a category that allows them to take a noun on their right and give back something of the same category. Thus they should have the syntactic category $(n/n)$. As a result, they must have the semantic type $((e → t) → (e → t))$.

Intersective adjectives

Since we would like intersective adjectives to contribute both the entailment that the noun they modify is true of the predicated-of entity, and the entailment that they themselves are true of the predicated-of entity when they occur predicatively, we can assign them lexical entries like in (2) (for round).

$⟨\textit{round}_{attr}, (λf.(λx.\ct{round}(x) ∧ f(x)))⟩ ⊢ (n/n)$

Note that, here, I’m using the abbreviation

\[p ∧ q\]

for

\[p = q = \true\]

In addition to this lexical entry, we should ensure that we also have a lexical entry for round when it occurs in predicative position, as in (3).

The chair is round.

Crucially, (3) is entailed by the sentence the chair is a round stool. To account for the predicative use, we can assign round the additional lexical entry in (4), according to which its syntactic category is $ap$ and its semantic type is thus $(e → t)$ (instead of $((e → t) → (e → t))$).

$⟨\textit{round}_{pred}, (λx.\ct{round}(x))⟩ ⊢ ap$

Non-intersective adjectives

Because they have a distribution similar to that of intersective adjectives—that is, they may modify nouns attributively—non-intersective adjectives should also have syntactic type $(n/n)$ and semantic type $((e → t) → (e → t))$. We can assign a lexical entry like (5) to the adjective short.

$⟨\textit{short}, (λf.(λx.\ct{short}(f)(x) ∧ f(x)))⟩$

Thus when short combines with the noun basketball player,

$⟨\textit{basketball player}, (λx.\ct{bbp}(x))⟩ ⊢ n$

it will produce:

\[⟨\textit{short basketball player}, (λx.\ct{short}((λx.\ct{bbp}(x)))(x) ∧ \ct{bbp}(x))⟩ ⊢ n\]

This result helps us explain the entailment that arises from the sentence Jo is a short basketball player—that is, that Jo is a basketball player.

--- title: "Subsective adjectives" bibliography: ../../semantics.bib format: html: css: ../styles.css html-math-method: mathjax mathjax-config: loader: {load: ['[tex]/bussproofs','[tex]/bbox','[tex]/colorbox']} tex: packages: {'[+]': ['bussproofs','bbox','colorbox']} --- ::: {.hidden} $$ \newcommand{\expr}[3]{\begin{array}{c} #1 \\ \bbox[lightblue,5px]{#2} \end{array} ⊢ #3} \newcommand{\ct}[1]{\bbox[font-size: 0.8em]{\mathsf{#1}}} \newcommand{\abbr}[1]{\bbox[transform: scale(0.95)]{\mathtt{#1}}} \def\true{\ct{T}} \def\false{\ct{F}} $$ ::: How should we analyze attributive adjectives, in general? Well, first, we should assign nouns like *linguist* a syntactic category---call it $n$. Further, if we take nouns to denote properties (i.e., sets of entities---those to which the noun applies), then we can say that the semantic type associated with the syntactic category $n$ is the type $(e → t)$ of characteristic functions of entities. Thus for example *ant* can be given the lexical entry in (@ex-ant). (@ex-ant) $⟨\textit{ant}, (λx.\ct{ant}(x))⟩ ⊢ n$ Because attributive adjectives modify nouns---and can apparently do so recursively (*silly fake purple... ant*)---we should give them a category that allows them to take a noun on their right and give back something of the same category. Thus they should have the syntactic category $(n/n)$. As a result, they must have the semantic type $((e → t) → (e → t))$. ### Intersective adjectives Since we would like intersective adjectives to contribute both the entailment that the noun they modify is true of the predicated-of entity, *and* the entailment that they themselves are true of the predicated-of entity when they occur predicatively, we can assign them lexical entries like in (@ex-round-lex) (for *round*). (@ex-round-lex) $⟨\textit{round}_{attr}, (λf.(λx.\ct{round}(x) ∧ f(x)))⟩ ⊢ (n/n)$ Note that, here, I'm using the abbreviation $$p ∧ q$$ for $$p = q = \true$$ In addition to this lexical entry, we should ensure that we also have a lexical entry for *round* when it occurs in predicative position, as in (@ex-round-predicative). (@ex-round-predicative) The chair is round. Crucially, (@ex-round-predicative) is entailed by the sentence *the chair is a round stool*. To account for the predicative use, we can assign *round* the additional lexical entry in (@ex-round-predicative-lex), according to which its syntactic category is $ap$ and its semantic type is thus $(e → t)$ (instead of $((e → t) → (e → t))$). (@ex-round-predicative-lex) $⟨\textit{round}_{pred}, (λx.\ct{round}(x))⟩ ⊢ ap$ ### Non-intersective adjectives Because they have a distribution similar to that of intersective adjectives---that is, they may modify nouns attributively---non-intersective adjectives should also have syntactic type $(n/n)$ and semantic type $((e → t) → (e → t))$. We can assign a lexical entry like (@ex-short-lex) to the adjective *short*. (@ex-short-lex) $⟨\textit{short}, (λf.(λx.\ct{short}(f)(x) ∧ f(x)))⟩$ Thus when *short* combines with the noun *basketball player*, (@ex-bbp-lex) $⟨\textit{basketball player}, (λx.\ct{bbp}(x))⟩ ⊢ n$ it will produce: $$⟨\textit{short basketball player}, (λx.\ct{short}((λx.\ct{bbp}(x)))(x) ∧ \ct{bbp}(x))⟩ ⊢ n$$ This result helps us explain the entailment that arises from the sentence *Jo is a short basketball player*---that is, that Jo is a basketball player.