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:
|
• |
A |
M |
J |
H | |
|
A |
0 |
1 |
1 |
1 | |
|
Eighth = |
M |
. |
0 |
1 |
1 |
|
J |
. |
. |
0 |
1 | |
|
H |
. |
. |
. |
0 |
(14)
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
(15)
This is isosceles but not
X . 0 i+1
YP . . 0
From this the triangle representation is Figure 9.
equilateral.