These two expressions have essentially the same relational meaning. They both
express the relation “on” existing between “a book” and “a table”. However, their
referential meaning is significantly different. Expression 1, as a whole, refers to an
object and is called an object referring expression. In referring to an object, 1 uses
the determiner “the” to specify that the object is salient in the context of use of the
expression (and may have previously been referred to). Expression 1 also uses the
word “book” to indicate the type of object being referred to, with “book” functioning
as the head of the expression. Further, the phrase “on the table” refers to a location
with respect to which the object can be identified and functions as a modifier in the
expression. In referring to a location, the expression “on the table” refers to a second
object “the table” and indicates the location of the first object with respect to the
second object. Within the modifying expression, the relation “on” functions as the
relational head with the object referring expression “the table” functioning as a
complement. In expression 1, the relational meaning of “on” is subordinated to
referential meaning with the modifying function of “on the table” dominating the
relational meaning of “on”. That is, although “on” is the relational head of the
prepositional phrase “on the table”, it is not the head of the overall expression and
does not determine the semantic type of that expression.
Expression 2 refers to a situation and is called a situation referring expression.
The auxiliary “is” provides a temporal specification for the situation, fulfilling a
referential function similar to that of the determiner “the” in “the book” and “the
table”. The relational meaning of 2 is about “being on” and not just “being”, with
“on” functioning as the relational head of the situation referring expression. The
relational head of a situation referring expression is called a predicate—reflecting the
assertional function of the relational head. Note that “on” in 1 is not functioning as a
predicate, since it is presupposed and not asserted. That is, relational heads of
modifying expressions are not predicates, they are (modifying) functions. In
expression 2, the object referring expression “the book” functions as the subject
(argument) of “being on” with “the table” functioning as the object (argument).
Referentially, there is also a reference to a location “on the table”, which competes
with the expression of the relational meaning of “on” as reflected in the difference
between:
3. What is the book on?
4. Where is the book?
where 3 highlights the relation “on” in asking about the object of that relation and 4
highlights the reference to a location using “where” to do so.
The terms specifier, head, modifier and complement are borrowed from X-Bar
Theory [9]. It is acknowledged that X-Bar Theory captures an important grammatical
generalization, with the distinction between specifiers and modifiers representing a
significant advance, but X-Bar theory is in need of semantic motivation, which, when
provided, necessitates certain modifications to the theory [10]. For example, the
combination of a specifier and a head results in a maximal projection which
corresponds to a referring expression. However, the specifier determines the type of
referring expression, not the head, with referential type corresponding most closely to
the syntactic type of a maximal projection in X-Bar Theory. The head, on the other
hand, determines the relational type of the expression (where “relational”
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