Axioms for Metonymy

Both varieties of metonymic transfer can be easily captured in the present framework by means of transformation axioms. The coercion from X to F(X) is a matter of substituting for the leading argument (or eventuality) variable in the Syn predication another variable representing a functionally related entity.

(1)	$Syn(w,e,f,x,a,y,b) \& rel(e_{0},e) \, \supset \,Syn(w,e_{0},f,x,a,y,b)$

Here, e plays the role of X and e plays the role of F(X). Viewed from the perspective of interpretation, this says that the phrase w is being used in the embedding context as though it referred to or described one entity or eventuality e₀ but in fact w, by itself, refers to or describes a related entity or eventuality e. From the perspective of generation, it says that if you want to refer to or describe an entity or eventuality e₀ you can do so by refering to or describing a related entity or eventuality e.

The coercion from P to $P \circ F$ is a matter of substituting for one of the x or y arguments in the Syn predication another variable representing a functionally related entity. Two axioms are required, one for each argument position. The first is

(2)	$Syn(w,e,f,x_{0},a,y,b) \& rel(x_{0},x) \, \supset \,Syn(w,e,f,x,a,y,b)$

The effect of this axiom in interpretation is as follows: The axiom is applied to the predicate or head word w in the proof graph below the point at which it links up with its argument x. Above the application of this axiom, the argument is the variable x and refers to the explicit, uncoerced argument. The axiom introduces the coercion relation rel(x₀,x). Below the application of the axiom, the argument is x₀, the implicit, coerced argument. It is this that becomes the argument of the predication associated with w and to which the selectional constraints are applied. The NP describing x then really does refer to x and is thus available for subsequent pronominalization.

The other ``predicate transfer'' axiom is

(3)	$Syn(w,e,f,x,a,y_{0},b) \& rel(y_{0},y) \, \supset \,Syn(w,e,f,x,a,y,b)$

Figure 2 illustrates the use of Axiom (3) on the sentence

John read Proust.

in conjunction with axioms that say that Proust wrote novels, which are texts, and that the writing relation is a possible coercion.

  

Figure 2: Parse of ``John read Proust'' using Axiom (3).

The coercion occurs on the word ``read'', changing its logical object from Proust to the novels of Proust. This in effect ``transfers'' the predicate ``read'' into the predicate ``read the novels of''. Note that the phrase ``Proust'' is still and only an NP refering to the man Proust and not his works. This is what restricts the possibilities for subsequent pronominal reference.

By contrast, if this example were to be handled with Axiom (1), as a coercion from Proust to the novels of Proust, the interpretation would be as illustrated in Figure 3.

  

Figure 3: Parse of ``John read Proust'' using Axiom (1).

In this chapter, Nunberg's lead will be followed, and cases of metonymy will be treated as instances of predicate transfer, thus involving axioms (2) and (3).

I will not attempt here to determine possible constraints on metonymic coercions. Here the coercion relation rel will be axiomatized in the loosest possible way. It is symmetric and transitive:

$(\forall \,x,y) rel(x,y) \, \supset \,rel(y,x)$
$(\forall \,x,y,z) rel(x,y) \& rel(y,z) \, \supset \,rel(x,z)$

For the purposes of this chapter any relation will be taken to be a possible coercion relation. This is captured by the axiom schema

(4)	$(\forall \,\ldots,x,\ldots,y,\ldots)[p'(\ldots,x,\ldots,y,\ldots) \, \supset \,rel(x,y)]$

That is, any two arguments of the same predication are related to each other. Any predication can function as a coercion relation between any two of its arguments, including its eventuality argument.

Of the possible coercion relations, the most salient will be selected by the abductive interpretation process. Among the most salient relations between entities are those conveyed explicitly in the text itself. A number of seemingly disparate phenomena that are normally thought of as syntactic can be analyzed as examples of metonymy, where the coercion relation is provided by the explicit content of the sentence itself. Six such cases will be examined here--extraposed modifiers of the subject, ataxis, container nouns, distributive readings, small clauses in disguise, and the assertion of grammatically subordinated information.