Graph Theory - Computational Linguistics and Talking Robots - page 181

The semantic relations and signature graphs of the iterated object sentence
construction 9.4.1 and the corresponding unbounded dependency 9.4.2 are the
same; both have the degree sequence 2221111 (disregarding the start line). The
only difference between the respective NAGs is in the object of the final object
sentence, i.e., To m or WH . The dependency in 9.4.2 is between the surface-
initial WH and the object of the final object sentence; it is unbounded because
there is no limit on the number of intervening iterated object sentences.
The order of proplets in the following content representation of 9.4.2 follows
the NAG. Given that proplets are inherently order-free, they could just as well
be shown in the alphabetical order of the core values or in the surface order:

9.4.3 P ROPLET REPRESENTATION OF 9.4.2
⎡
⎣

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

verb: believe
arg: Bill (love 8)
fnc: (say 6)
prn: 7

verb: love
arg: Mary WH
fnc: (believe 7)
prn: 8

verb: say
arg: John (believe 7)
prn: 6

noun: John
fnc: say
prn: 6

noun: Bill
fnc: believe
prn: 7

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: Mary
fnc: love
prn: 8

noun: WH
fnc: love
prn: 8

The verb proplet say has the arguments John and (believe 7) , the verb proplet
believe has the arguments Bill and (love 8) , and the verb proplet love has the
arguments Mary and WH .
The verb proplets believe and love of the object sentences are opaque (Sect.
7.5) because they have an additional fnc attribute to serve as an argument of
their higher clauses. The values of these fnc attributes are addresses, specified
as the core and the prn value of the preceding higher verb, just as the arg
attributes of the higher verbs specify the following subclause as an address
(bidirectional pointering).
Finally consider the surface realization of the unbounded dependency con-
struction based on the NAG in 9.4.2. The WH word is accessed and realized
by traversing arcs 3-6-9. This navigation is continuous, in line with 9.1.4, 3,
despite the nonconsecutive numbering. Then the auxiliary did is realized by
returning to say via arcs 10-11-12, relying on the usual do-support of English
WH constructions. From there, the realization from arc 1 to arc 8 resembles
that of the iterated object sentence construction 9.4.1. Omitting arcs 9 and 10,
the navigation returns to say via 11-12 to realize the fullstop. 8

8 Superficially, the signature in 9.4.1 may seem to resemble a Nativist Phrase Structure tree. However,
as explained in Sect. 7.1, the lines in a Phrase Structure tree indicate dominance and precedence,
whereas the lines in a DBS graph indicate the subject

/ verb, the object \ verb, the modifier | modified,

and the conjunct − conjunct relations.