Mystery Number Five - Computational Linguistics and Talking Robots - page 105

In this example, all core and prn values of the content are simultaneously
substituted with variables in the schema (method one) and all variables are
restricted to the value they replace (method two). In this way, strict equivalence
between the content and the schema representation in 6.5.1 is obtained.
The yield of a schema may be enlarged by adding values to the restriction set
of variables. Consider the following example of a schema matching the content
corresponding to Every child slept , but with extended variable restrictions.

6.5.2 C ONVERTING A SCHEMA INTO EQUIVALENT CONTENTS

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: α

cat: snp
sem: pl exh
fnc: β
mdr:
nc:
pc:
prn: K

verb: β

cat: decl
sem: past
arg: α
mdr:
nc:
pc:
prn: K

where α {man, woman, child}, β {sleep, sing, dream}
and K N

schema

⇐⇒

Every man dreamed.
Every woman dreamed.
Every child dreamed.
The contents are generated from the schema by systematically replacing the
variables

Every man slept.
Every woman slept.
Every child slept.

Every man sang.
Every woman sang.
Every child sang.

content

with elements of their restriction sets. Even if no restriction
set is specified, the yield of a schema relative to an actual Word Bank will be
finite.
A schema may be derived automatically from any set of partially overlapping
contents. Consider the following example:

α and β

6.5.3 S ET OF CONTENTS WITH PARTIAL OVERLAP
Julia eats an apple John eats an apple Suzy eats an apple Bill eats an apple
Julia eats a pear John eats a pear Suzy eats a pear Bill eats a pear
Julia eats a salad John eats a salad Suzy eats a salad Bill eats a salad
Julia eats a steak John eats a steak Suzy eats a steak Bill eats a steak
Of these 16 propositions, each contains the proplet eat , while the proplets
Julia, John, Suzy ,and Bill occur four times as subject and the proplets apple,
pear, salad ,and steak occur four times as object. Based on these repetitions,
the propositions may be summarized as the following schema:

6.5.4 S UMMARIZING THE SET 6.5.3 AS A SCHEMA
⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: α
fnc: eat
prn: K

verb: eat
arg: αβ
prn: K

noun: β
fnc: eat
prn: K