Graph Theory - Computational Linguistics and Talking Robots - page 173

9.2.1 E XTRAPROPOSITIONAL COORDINATION OF TWO PROPOSITIONS

leave cross

John house John street

The corresponding proplet representation of this content connects the verb
proplets leave and cross bidirectionally via their nc and pc slots:

9.2.2 B IDIRECTIONAL POINTERING IN THE PROPLET REPRESENTATION
⎡
⎣

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

verb: leave
arg: John house
nc: (cross 2)
pc:
prn: 1

verb: cross
arg: John street
nc:
pc: (leave 1)
prn: 2

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: John
fnc: leave
prn: 1

noun: house
fnc: leave
prn: 1

noun: John
fnc: cross
prn: 2

noun: street
fnc: cross
prn: 2

The bidirectional connection at the proplet level (reflecting the corresponding
signature) allows two kinds of traversal, forward and backward.
Forward navigation is based on the following NAG. It may be used for real-
izing the surface John left the house. Then he crossed the street. :

9.2.3 NAG FOR FORWARD NAVIGATION THROUGH 9.2.1

5

0

leave cross

1 6

4

78 9

3

2

John house John street

The corresponding backward navigation is based on the following NAG,
which may be used for realizing the English surface John crossed the street.
Before that he left the house. :

9.2.4 NAG FOR BACKWARD NAVIGATION THROUGH 9.2.1

leave cross

5 0

6 9 1 4

3

8 2

7

John house John street

The point is that within a given traversal, e.g., 9.2.3 or 9.2.4, only one direction
is used for the extrapropositional relation, i.e., the respective version of arc 5.
This is different from the other semantic relations of structure, i.e., (i) intra-
and (ii) extrapropositional functor-arguments as well as (iii) intrapropositional
coordination, in which a complete traversal requires the use of both directions.
Compare, for example, the extrapropositional coordination 9.2.3 with the fol-
lowing intrapropositional coordination: