Graph Theory - Computational Linguistics and Talking Robots - page 179

left side of the NAG in 9.3.3, realizing the verbs and the nouns. On the way
back up, there is nothing left to do except to realize the full stop.
The surface realization 9.3.6 shows that a consecutive numbering is a suf-
ficient, but not a necessary, condition 3 for satisfying continuity (9.1.4). For
example, the combined traversal of arcs 1 and 10 is continuous even though
the arc numbers are not consecutive.
From the software side, the mechanism of multiple visits is easily pro-
grammed. From the cognitive and linguistic sides, however, multiple visits
must be constrained because otherwise there is no limit on complexity. The
constraint applies to connected graphs and comes in two variants.
9.3.7 C ONSTRAINT ON MULTIPLE VISITS , VARIANT I
In content navigation without language realization, a multiple visit is
1. permitted if there are still untraversed arcs in the graph,
2. prohibited if all arcs in the graph have been traversed.
These conditions are based on the possibility of keeping track of how often a
node has been traversed. Constraint I may be relaxed by setting limits on how
often a node may be traversed (traversal counter; cf. FoCL'99, p. 464).
9.3.8 C ONSTRAINT ON MULTIPLE VISITS , VARIANT II
In content navigation with language realization, a multiple visit is
1. permitted if a required function word has not yet been realized,
2. prohibited if there is no value remaining in the current proplet set
which has not already been used exhaustively for realization.
Technically, variant II is based on a language-dependent LA-speak grammar
for mapping content into surfaces.
9.4 Unbounded Dependencies
In the previous section, the same NAG 9.3.3 was used for realizing the surface
(i) of a non-extraposed English relative clause (unmarked order; 9.3.5) and
(ii) of the corresponding extraposed relative clause (marked order; 9.3.6). This
method, based on multiple visits for realizing the marked order, may also be
applied to a construction of English known as unbounded dependency or long
distance dependency .
The unmarked order of this construction is an iteration of object sentences,
as in the following example: