Graph Theory - Computational Linguistics and Talking Robots - page 175

In short, extrapropositional coordination requires a treatment which is some-
what different from that of the other three grammatical structures. The basic
choice is between the following graph-theoretical options:

9.2.7 G RAPH - THEORETICAL ALTERNATIVES FOR COORDINATION

1. unidirectional

0

NAG−1 NAG−2 NAG−3

2. bidirectional, symmetric

0

NAG−1 NAG−2 NAG−3

3. bidirectional, asymmetric

0

NAG−1 NAG−2 NAG−3

The unidirectional variant 1 has the advantage of not cluttering the represen-
tation with too many arcs. It is suitable for extrapropositional NAGs like 9.2.3
and 9.2.4, but not for intrapropositional coordination (9.2.5), and does not re-
flect adequately the concatenation structure of the associated proplets (9.2.2).
The bidirectional symmetric variant 2 reflects the possible backward naviga-
tion provided by the proplet representation. In 9.2.3 and 9.2.4 it may be added
as an arc 10, defined as the inverse of the respective arc 5. Apart from arc 10
not being traversed in an extrapropositional navigation, variant 2 is equally
suitable for intra- and extrapropositional coordination, and is like the other
NAG structures by being symmetric as well.
The asymmetric bidirectional variant 3 is motivated by intrapropositional
coordination. Consider the empty traversals of arcs 4 and 5 in 9.2.5: because
there is no limit on the length of a coordination, the empty traversals on the
return from an intrapropositional coordination require linear time. The alter-
native to variant 3 is to connect the backward arcs to the initial rather than
the previous item. 6 This has the effect of reducing the cost of empty backward
traversal from linear to constant. Variants 2 and 3 may be combined.

6 In the proplet representation, this may be reflected by using an ic (for initial conjunct) rather than a
pc (for previous conjunct) attribute. In a hear mode derivation, the value of the ic attribute is passed
along incrementally, from conjunct n to conjunct n+1 , making for simple rule patterns.