Syntax and the single mother

Publisher Website
Google Scholar
Abstract
1.Consider a string s = a1 a2 …an over a finite vocabulary Va, such that s is structured by an asymmetric binary relation R: i.e. there are ordered pairs of elements in the string, ai, and aj, where a, R aj.1 S is a simple structured string if (a) there is a unique element ak such that there is no a1 for which it is true that a1 R ak, and if (b) for all am am, ≠ akit is true that there is a unique a1 such that a1 R am. In graph-theoretic terms these conditions define a tree where a1, a2 …a are paired with nodes in the graph and each a, R a is represented by an arc, and where the tree has a unique root or centre associated with a. Figure i is an instance of such a tree, where k = 3. In Figure a, condition (a) is infringed, in that an arc converges on each node; i.e. for all a, there is an aj such that aj R ai. Figure 3, on the other hand, violates condition (b), in that two arcs converge on a2 i.e. there is not a unique ai for whch it is true that a1 R a2.