Mystery Number Two - Computational Linguistics and Talking Robots - page 36

3.2.3 P ATTERN MATCHING BETWEEN SCHEMA 3.2.2 AND CONTENT 3.2.1

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: α
fnc: β
prn: K

verb: β
arg: αγ
prn: K

noun: γ
fnc: β
prn: K

schema level

inter nal matching

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: Julia
fnc: know
prn: 625

verb: know
arg: Julia John
prn: 625

noun: John
fnc: know
prn: 625

content level

The matching between the schema and the content is successful because the
pattern proplets have the same 6 attributes in the same order as the correspond-
ing content proplets and the variables used as values at the schema level match
the constants at the content level.
The proplet set of a content is order-free in the sense that the storage location
of the proplets does not affect the semantic relations defined between them. 7
This is because the semantic relations between proplets are coded by address
rather than by embedding (as in recursive feature structures). For example, the
three proplets in 3.2.1 may be represented in the order abc, acb, bac, bca, cab,
and cba, and yet maintain their semantic relations intact, as shown below:

3.2.4 M AINTAINING SEMANTIC RELATIONS REGARDLESS OF ORDER

abc acb bac

noun: Julia
fnc: know
prn: 625

noun: Julia
fnc: know
prn: 625

verb: know
arg: Julia John
prn:625

verb: know
arg: Julia John
prn:625

noun: John
fnc: know
prn: 625

noun: Julia
fnc: know
prn: 625

noun: John
fnc: know
prn: 625

verb: know
arg: Julia John
prn:625

noun: John
fnc: know
prn: 625

bca cab cba

verb: know
arg: Julia John
prn:625

noun: John
fnc: know
prn: 625

noun: John
fnc: know
prn: 625

noun: Julia
fnc: know
prn: 625

verb: know
arg: Julia John
prn:625

noun: John
fnc: know
prn: 625

noun: Julia
fnc: know
prn: 625

verb: know
arg: Julia John
prn:625

noun: Julia
fnc: know
prn: 625

6 As defined in NLC'06, 3.2.3, it is sufficient for successful matching if the attributes of the pattern
proplet are a subset of the attributes of the content proplet.
7 This is in contradistinction to a logical formula such as

walk(x)], a phrase structure tree
such as 7.1.2, or a recursive feature structure with unification as shown in NLC'06, 3.4.5, which
change their meaning or lose their well-formedness if the order of their parts is changed. They also
fail to provide a natural primary key (cf. Hausser 2007).

∃ x[man(x) ∧