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represented by the
sem
values
indef sg
(indef singular) of the
woman
pro-
plet.
21
The verb's
cat
value
decl
(for declarative) and its
sem
value
pres
(for
present tense) complete the picture. The proplets form an order-free set, and
are held together by a common
prn
value, here
23
.
In summary, predicate calculus uses (i) variables within formulas represent-
ing content and (ii) quantifiers (a) to bind the variables
horizontally
and (b)
to replicate determiners at the same time. DBS, in contrast, (i) replaces the
binding function of quantifiers by a
prn
value, (ii) employs variables solely
for a
vertical
binding between pattern and content proplets, and (iii) codes the
determiner function of quantifiers as values of the
cat
and
sem
attributes.
With the elimination of quantifiers, DBS can restrict the use of all kinds
of variables to the definition of
pattern
proplets. The pattern proplets are
combined into schemata and are used for matching with content by the LA-
grammar rules and for retrieval (activation) in the content-addressable mem-
ory of a Word Bank. Using restricted variables as proplet values is a simple,
powerful method of under-specification,
22
with many uses in DBS.
Up to this point, DBS may be regarded as a modern reconstruction of pred-
icate calculus, though with special emphasis on automatic natural language
interpretation, processing of content, and natural language production - rather
than on truth, satisfiability, consistency, and completeness. The latter are im-
portant, but they are neither intended nor sufficient for building a model of
natural language communication.
Finally, let us consider meaning, which is what semantics is all about. Lo-
gicians take great care to give their formulas a semantic interpretation. It is a
conceptual construction in which “the world” is defined in principle as a set-
theoretical model structure, and the surfaces of the variables and constants of
a formula are defined by hand to refer to these set-theoretical constructs using
a metalanguage. The purpose is inferencing and theorem proving.
Instead of treating concepts in terms of metalanguage definitions, DBS treats
concepts as the basic
procedures
of the agent's recognition and action. Declar-
ative representations of these procedures are reused
23
as the meanings of lan-
guage, with the type/token relation serving in pattern matching (4.3.3). This
procedural approach to concepts and meanings demands the switch from a
21
The values
exh, sel, def, indef, sg,
and
pl
are defined set-theoretically in NLC'06, 6.2.9.
22
Restricted variables are inherently open-ended. When used for matching, variables may be bound
tentatively to values not in their restriction set. Also, when new selectional constellations (Chap. 8)
have been found, these must be added to the relevant restriction sets.
23
Cf. Roy 2005 for a similar approach.
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