On Representing Syntactic Structure

Abstract

In this paper I discuss some diagrammatic representations of syntactic structure. I introduce the concept of syntactic 'distance' as an aid to depict the 'degree of grammatical relatedness' and show that this concept leads to a kind of equivalence among several methods of representation. Though I sometimes speak only of relatedness, I assume that grammatical relatedness and degree of grammatical relatedness are the same thing. Suppose that the concept of relatedness is defined implicitly, at least to the extent that it is possible not only to make statements about which parts of sentences are related to other parts, but also to make judgments about the relative degree of relatedness. If A, B, and C are parts of a sentence we can say, for example, that A is more closely related to B than C is to B. If we assume that such judgments can be made, then associated with each sentence will be a set of order relations concerning the degrees of relatedness between all the possible pairs of constructions in the sentence. Once the order relationships are available, suppose that the words of the sentence are arranged in some space, Euclidian or other, so that all the structures which are most closely grammatically related occur nearest to each other. That is, we let distance be in inverse proportion to relatedness, and we arrange the construction so that the relative distances are preserved. In this way we find a representation of the sentence which explicitly reveals its structure in terms of relatedness. The dimensionality of the representation and its diameter, in the case of distancepreserving representations, are conjectured to be indicators of grammatical complexity. To be specific, we consider the following sentence taken from Nida.' The1 robber was chased by the2 men. We might ask if The1 and robber are more closely related than robber and was. If no judgments are available about strengths of relatedness between words, we may consider relatedness among phrases. For example, suppose that the only judgments are that the mutual grammatical relationships among The robber, was chased, and by the men are all equally strong. In this case, a geometric representation of the structure of the sentence, letting distance be proportional to unrelatedness, is the equilateral triangle in Figure 1. For more refined judgments, we would get more elaborate rankings. Suppose we use three categories of relatedness: nearest, near, and fairly far. By the simplified grouping into three categories we do not imply that all the members of a particular category are equidistant. A possible set of judgments is summarized in Table 1. The key word is the element to which comparisons are made.