Mystery Number Five - Computational Linguistics and Talking Robots - page 104

6.5 Schema Derivation and Hierarchy Inferencing

By using (i) a common prn value in lieu of the variable-binding function of
the logical quantifiers and (ii) sem values in lieu of the determiner function
of x, the use of variables in DBS may be limited to pattern proplets ,

in contradistinction to content proplets , which by definition may not contain
any variables. Pattern proplets are combined into schemata for the purpose of
matching corresponding contents.
A schema may be derived from a content by replacing constants with vari-
ables (simultaneous substitution). The set of content proplets matched by a
schema is called its yield . The yield of a schema relative to a given Word Bank
may be controlled precisely by two complementary methods. One is by the
choice and number of constants in a content which are replaced by variables.
The other is by variable restrictions.
The use of restricted variables allows us to convert any content into strictly
equivalent schemata and any schema into strictly equivalent contents. As an
example of the content-schema conversion consider the content corresponding
to Every child slept. Fido snored. , i.e., the coordination of two propositions,
each with a subject-verb construction, one with a phrasal noun, the other with
a proper name as subject. 21

∃ xand ∀

6.5.1 C ONVERTING A CONTENT INTO AN EQUIVALENT SCHEMA

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: child
cat: snp
sem: pl exh
fnc: sleep
mdr:
nc:
pc:
prn: 26

verb: sleep
cat: decl
sem: past
arg: child
mdr:
nc: (snore 27)
pc:
prn: 26

noun: Fido
cat: nm
sem: animal
fnc: snore
mdr:
nc:
pc:
prn: 27

verb: snore
cat: decl
sem: past
arg: Fido
mdr:
nc:
pc: (sleep 26)
prn: 27

content

⇐⇒

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: α
cat: snp
sem: pl exh
fnc:

verb: β
cat: decl
sem: past
arg: α
mdr:
nc: (

noun: γ
cat: nm
sem: animal
fnc: δ
mdr:
nc:
pc:
prn: K+1

verb: δ
cat: decl
sem: past
arg: γ
mdr:
nc:
pc: (

where α {child}, β {sleep},
γ {Fido}, δ {snore}, and
K {26}

β

schema

mdr:
nc:
pc:
prn: K

δ K+1)

pc:
prn: K

K)
prn: K+1

β

21 The fact that every takes a singular noun but refers to a plural set is expressed by the cat value
snp , for singular noun phrase, and the sem values pl exh . The phrasal noun and the proper name
proplet have the same attribute structure, but are distinguished by means of different cat and sem
values. This way of treating phrasal nouns and proper names alike is much simpler than type raising
in lambda calculus (Montague 1974, PTQ).