Ultrametric Distance in Syntax



Figure 12: Illustration of dominates

5.1 Definition of dominates.

Definition [13] p.85

Node A dominates node B iff:

i) h(A) is higher up or at the same height on the tree as h(B) i.e.h(A) ≥ h(B)
ii) it is possible to trace a line from A to B going only downward,

or at most going to one higher node.

Remarks

The first requirement is that A is at a greater height than B. The second re-
quirement restricts the possible downward route from A to B so that it contains
at most one upward segment.

Example (compare [13] p.83)The phrase tree Figure 12 gives the ‘dominates’
matrix:

S

NP (S)

N(S)

AUX

VP

V

NP (E)

Det

N(e)

S

1

1

1

1

1

1

1

1

1

NP (S)

0

1

1

0

0

0

0

0

0

N(S)

0

0

1

0

0

0

0

0

0

AUX

0

0

0

1

0

0

0

0

0

D = AVUPX

0

0

0

0

1

1

1

1

1    (23)

V

0

0

0

0

0

1

1

1

1

NP(E)

0

0

0

0

0

0

1

1

1

Det

0

0

0

0

0

0

0

1

0

N(E)

0

0

0

0

0

0

0

0

1

where 1 indicates “A dominates B”

and 0 indicates that it does not.

14



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