Mystery Number Two - Computational Linguistics and Talking Robots - page 37

The six possible proplet orders are arranged vertically. The bidirectional se-
mantic relations within each triple are indicated by lines, which are like rub-
ber bands adjusting to the varying arrangements of the proplets. For a better
drawing of these lines, the proplet in the middle is moved one step to the right.
The coding method illustrated in 3.2.1-3.2.4 with an example of intrapropo-
sitional functor-argument works equally well for extrapropositional coordina-
tion (or any other construction of natural language):

3.2.5 C OORDINATION STRUCTURE OF Julia sang. Sue slept. John read.

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

verb: sing
arg: Julia
nc: (sleep 11)
pc:
prn: 10

verb: sleep
arg: Sue
nc: (read 12)
pc: (sing 10)
prn: 11

verb: read
arg: John
nc:
pc: (sleep 11)
prn: 12

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: Julia
fnc: sing
prn: 10

noun: Sue
fnc: sleep
prn: 11

noun: John
fnc: read
prn: 12

The propositions with the prn values 10, 11 ,and 12 are concatenated by the
pc (for previous conjunct) and nc (for next conjunct) values of the respective
verbs. For example, the nc value of the second proplet sing is (sleep 11) ,
while the pc value of the fourth proplet sleep is (sing 10) . 8
The proplets in the extrapropositional coordination 3.2.5 are order-free in
the same sense as shown in 3.2.4 for the intrapropositional functor-argument
3.2.1. They may likewise be turned into a schema by replacing the constants
with variables:

3.2.6 T URNING 3.2.5 INTO A SCHEMA
⎡
⎣

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

verb: β
arg: α
nc: ( δ K+1)
pc:
prn: K

verb: δ
arg: γ
nc: ( ψ K+2)
pc: ( β K)
prn: K+1

verb: ψ
arg: φ
nc:
pc: ( δ K+1)
prn: K+2

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: α
fnc: β
prn: K

noun: γ
fnc: δ
prn: K+1

noun: φ
fnc: ψ
prn: K+2

The schema matches the content 3.2.5 from which it was derived as well as an
open number of similar contents. The computational simplicity of the match-
ing procedure depends crucially on the definition of proplets as non-recursive
feature structures, with the order of attributes fixed within proplets.
The order-free coding of semantic relations is produced by a time-linear
mapping from ordered surfaces to an order-free set of connected proplets in
the hear mode (3.3.1, 3.4.1). It is essential for the following functions:

3.2.7 F UNCTIONS BASED ON THE ORDER - FREE NATURE OF PROPLETS

1. Hear mode: storage of proplets in the content-addressable database of a
Word Bank (4.1.1).