Ultrametric Distance in Syntax

The man                 ate a dog.

Figure 10: The Correct Tree for the Example in the Introduction.

3 The minimum ultrametric distance between
lexical categories

3.1 The minimum distance principle

We assume that it is the minimum distance between lexical categories that is
important, and refer to this as the minimum distance principle. In part
this is motivated by the discussion in subsection 1.4. A current psycholinguistic
model of sentence production is the garden path model, see for example Fra-
zier (1987) [12] and Roberts (2004) [32]§5.4. Part of this model requires the
minimal attachment principle, which is “do not postulate unnecessary nodes.”:
this can be thought of as a minimum principle. The minimum distance prin-
ciple implies that the correct tree for equation (6) illustrated by figure 1 is
Figure 10, so that all entries occur at the lowest possible height. Thus in
particular tree A is preferred to tree B. This assumption does not effect the
matrix U (16) given and described below, but will have an effect when the anal-
ysis is extended to θ-theory, see Haegeman (1995) §3.2.3 [13]. From the above
d(N, D) = 1, d(N, V ) = d(D, V ) = 2. Similarly from Figure 11, d(V, A) = 4.

11

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