Ultrametric Distance in Syntax

must

jump high.

Figure 5: The 4-ary tree for “Alf must jump high”

Alf

and finally there is one 4-ary tree (compare Haegeman (1994) p.142 [13] dia-
gram 84f) with diagram Figure 5 and matrix:

2.2 Triangle representation of the proceeding

All ultrametric triangles are isosceles with small base, but only some are equi-
lateral. The previous subsection 2.1 suggests that binary branching implies that
there are no equilateral triangles in ultrametric models of syntax. For example
from matrix (13), d(A, M) = 1, d(A, J) = 2, d(M, J) = 2 has the triangle repre-
sentation Figure 6, and from matrix 14, d(A, M) = 1, d(A, J) = 1, d(M, J) = 1
giving in the triangle representation Figure 7. In the next section it is proved
that JX structure implies that there are no equilateral triangles.

__ -ZT- ___

2.3 The X Template

The JX template Figure 8 is the form that nodes take in syntax. The matrix
representation of this is:

• Spec X Y P

Spec   0   i + 2 i + 2

X     .     0   i+1

YP .       .      0

From this the triangle representation is Figure 9.

equilateral.

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