Adjectives: A Uniform Semantic Approach - University of Windsor

Adjectives: A Uniform Semantic Approach 337
Jane is an [attractive [blond woman]] (8)
And, the set-theoretic representation of the adjectival phrase might look something like:
Attractive ∩ (Blond ∩Woman) (9)
However, this representation does not capture the intended meaning. That is,
attractive in (8) modifies the expression blond woman as a whole. In other words, for
someone who utters (8), blond is essential to the extent that if the denotation of Jane
were not blond, the utterance (8) might not have taken place.
3.3.2 A Solution
In order to accommodate adjective phrases, we need to do two things. First, expand
our ontology to include properties—assuming that adjectives denote properties. This
will enable us to form new property types from the more basic ones. Second, we need
a rigorous typing system, whereby every set has a type. The typing system we are
proposing shortly will enable us to generate new types from the basic ones.
The type system must correspond to the grammar’s production rules. Grammar
rules for adjective phrases might look like the following:
AP ::= AN
N::= AN | man |woman |man |dancer| surgeon|…
A::= good | red |attractive| fragrant|…
The rules in (10) will recursively generate adjective phrases such as good man,
fragrant red roses, etc. The grammar in (10) generates noun phrases by means of a
string concatenation function. A typing system should parallel the grammar and be
able to recursively define new types from existing ones. Such a system is inductively
defined as follows:
a) The basic types are the nodes of the taxonomy of Figure 1, e.g.
Nat(ural) Kind, Kind, Properties, Role, Implement, and ┬.
b) If a is a property type and b is a basic type, then a: b is a type, see the
example regarding the wide-scope reading.
c) If a and b are property types then a-b is a property type, see the
example regarding the narrow-scope reading.
d) If a is a type and b is a non-property type, then a: b is a type.
e) Nothing else is a type.
(11-a) states the basic types assumed. In a full-fledged system, the set of
admissible basic types must be larger than this. However, this set suffices to
demonstrate our approach.
(11-b) states that the first basic type of a resulting set is a property type. This is
because here we are only treating adjective-noun—not noun-noun—combinations, for
example. (11-c) generates property types. This is necessary for dealing with narrowscope
readings, i.e. when an adjective modifies another adjective and both modify a
noun or an adjective phrase. Both (11-b) and (11-d) ensure that the resulting type is
that of the head noun.
(10)
(11)