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Adjectives: A Uniform Semantic Approach - University of Windsor

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336 N. Abdullah and R.A. Frost<br />

Guitarist = {j: guitarist,…} : guitarist<br />

Musician = {j: musician, …}: musician<br />

Veteran = {j: musician}: veteran<br />

Where j = ||John||<br />

From this representation, it is clear that the statement John is a veteran guitarist<br />

cannot be affirmed. This is because j is not in the intersection <strong>of</strong> Veteran and<br />

Guitarist.<br />

Maria is a former teacher<br />

Maria is a programmer<br />

---------------------------<br />

Therefore, Maria is a former programmer (Invalid)<br />

Set representation:<br />

Human = {m: human,…} : human<br />

Teacher= {m: teacher,…} : teacher<br />

Former= {m: teacher,…} :former<br />

Programmer={m: programmer,…} : programmer<br />

Inference examples:<br />

(6)<br />

├ m ∈ (Former ∩ Programmer) Expected answer: false<br />

├ m ∈ (Former ∩ Human) Expected answer: false<br />

3.3 Multiple-<strong>Adjectives</strong>-One-Head-Noun Combinations<br />

In the previous section, we presented an intersective treatment <strong>of</strong> adjective-noun<br />

combinations. In this section, we extend this treatment to include adjectival phrases<br />

with multiple adjectives and a head noun.<br />

3.3.1 An Analysis<br />

Providing an intersective account for expressions with multiple adjectives and a head<br />

noun is a more challenging task than single-adjective-noun combinations. This is<br />

because an adjective in a combination can have different scopes. To illustrate,<br />

consider examples (7).<br />

a) Oceania is a deep blue ocean<br />

b) Companies favour intelligent, aggressive people<br />

c) Jane is an attractive blond woman<br />

In (7-a), deep may have wide scope, i.e. modifies blue ocean, or narrow-scope, i.e.<br />

modifies blue. (7-b) is not ambiguous, because <strong>of</strong> the comma. (7-c) is ambiguous, due<br />

to wide and narrow scope readings.<br />

An at-face-value, set-theoretic representation for the examples in (7) is not<br />

possible, with the exception <strong>of</strong> example (7-b). This is due to the associative law <strong>of</strong> set<br />

theory, stated below:<br />

∀ Sets A, B, and C A∩ (B ∩C) = (A ∩B) ∩C<br />

Thus, for instance, mapping example (7) to set intersections would fail to capture the<br />

different possible readings. In particular, consider the wide-scope reading <strong>of</strong><br />

attractive in (7-c). This reading can be expressed as follows:<br />

(7)

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