According to traditional grammar, the predicate is the part of a sentence that modifies the subject, i.e., the sentence can be divided into two parts: the subject and the predicate. For example, in the sentence The kids may have started the game, the NP (the kids) is the subject and the VP (may have started the game) is the predicate. I know that the term predicate identifies elements in the language system and predicator identifies the semantic roles. The former is related to syntax/grammar while the latter is related to semantics (argument structure). However, inspired by predicate calculus, modern theories of syntax and grammar see predicates as relations between or functions over arguments. Predicates assign a property to a single argument or relate two or more arguments to one other, e.g., Sam helped you (help is a predicate, while Sam and you are arguments). Up to this point it's clear.
Now, Hurford (2007) defines predicator and predicate as follows:
The predicator of a simple declarative sentence is the word (sometimes a (partial) group of words) which does not belong to any of the referring expressions and which, of the remainder, makes the most specific contribution to the meaning of the sentence. Intuitively speaking, the predicator describes the state or process in which the referring expressions are involved.
Predicate is any word (or sequence of words) which (in a given single sense) can function as the predicator of a sentence.
The problem arises with the following example:
A tall, handsome stranger entered the saloon.
This sentence only contains one predicator (enter) but the sentence also contains the words tall, handsome, stranger and saloon, all of which are predicates, and can function as predicators in other sentences, e.g. John is tall, He is handsome, He is a stranger and That ramshackle building is a saloon.
Now, some people illustrate this specific example as:
A tall, handsome stranger (predicate) and entered (predicator)
While others, on the basis of traditional grammar, argue that since A handsome stranger is the subject of the sentence, it cannot be a predicate. According to them:
A tall, handsome stranger (subject), entered the saloon (predicate) and entered (predicator)
In my view, the sentence can be illustrated as follows:
A tall, handsome stranger (argument of predicate) entered (matrix predicate/predicator) the saloon (argument of predicate)
A tall, handsome stranger (as a subject) may not necessarily be acting as a predicate in this specific sentence, but the illustration given in Hurford (2007) may simply mean that these words can act as predicator or predicate in other sentences e.g. He is tall, He is handsome and He is a stranger. In all these sentences, the VP (is tall, is handsome, is a stranger) is a predicate and the words tall, handsome and stranger are predicators. Is this correct?
The question is about the first group who label the sentence according to traditional grammar and are confused when they interpret A tall handsome stranger as the predicate in the sentence A tall, handsome stranger entered the saloon.