Non-subsective adjectives

Non-subsective adjectives can be fit into the same mold. Thus let’s assume that they also have syntactic category \((n/n)\) and semantic type \(((e → t) → (e → t))\).

Vanilla non-subsective adjectives

Non-subsective adjectives which aren’t privative—e.g., alleged—can be given lexical entries like (1).

\(⟨\textit{alleged}, (λf.(λx.\ct{alleged}(f)(x)))⟩ ⊢ (n/n)\)

This lexical entry helps get at the fact that we don’t observe an entailment concerning Bo’s anthood from the sentence Bo is an alleged ant; in particular, (1) helps explain this fact by not including ‘\(∧ f(x)\)’ after ‘\(\ct{alleged}(f)(x)\)’.

Privative adjectives

Privative adjectives contribute the entailment that the modified noun does not hold of an entity of which the whole noun phrase is predicated. To account for this fact, we can give a privative adjective like fake the lexical entry in (2).

\(⟨\textit{fake}, (λf.(λx.\ct{fake}(f)(x) ∧ ¬f(x)))⟩ ⊢ (n/n)\)

Now if we combine fake with basketball player, we get:

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

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title: "Non-subsective adjectives"
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Non-subsective adjectives can be fit into the same mold.
Thus let's assume that they also have syntactic category $(n/n)$ and semantic type $((e → t) → (e → t))$.

### Vanilla non-subsective adjectives

Non-subsective adjectives which aren't privative---e.g., *alleged*---can be given lexical entries like (@ex-alleged-lex).

(@ex-alleged-lex) $⟨\textit{alleged}, (λf.(λx.\ct{alleged}(f)(x)))⟩ ⊢ (n/n)$

This lexical entry helps get at the fact that we don't observe an entailment concerning Bo's anthood from the sentence *Bo is an alleged ant*;
in particular, (@ex-alleged-lex) helps explain this fact by not including '$∧ f(x)$' after '$\ct{alleged}(f)(x)$'.

### Privative adjectives

Privative adjectives contribute the entailment that the modified noun does *not* hold of an entity of which the whole noun phrase is predicated.
To account for this fact, we can give a privative adjective like *fake* the lexical entry in (@ex-fake-lex).

(@ex-fake-lex) $⟨\textit{fake}, (λf.(λx.\ct{fake}(f)(x) ∧ ¬f(x)))⟩ ⊢ (n/n)$

Now if we combine *fake* with basketball player, we get:

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