Conclusion - Computational Linguistics and Talking Robots - page 242

replacing Montague's quasi-mechanical interpretation method with the com-
putational automation provided by efficiently running software.
These two completions, however, have necessitated many solutions differ-
ent from Montague grammar in particular and Symbolic Logic in general. For
example, predicate calculus uses the logical elements to construct a syntac-
tic exoskeleton, while DBS integrates the logical and the contingent elements
into flat feature structures with ordered attributes (proplets) which code inter-
proplet relations solely by addresses, and are therefore order-free (3.2.4).
The difference between DBS and predicate calculus, in particular regarding
the role of quantifiers, may be shown in more detail with the following exam-
ple from Montague (1974, PTQ):

12.4.1 P REDICATE CALCULUS ANALYSIS OF Every man loves a woman.

x[man (x) y[woman (y) & love (x, y)]] reading 1: ∀ →∃

y[woman (y) & [ x[man (x) love (x, y)]] reading 2: ∃ ∀ →

This standard 19 analysis of predicate calculus treats the English surface as syn-
tactically ambiguous. The reason is a scope ambiguity suggested by the creak-
ing hinges of its quasi-mechanical exoskeleton. The contingent elements are
man , woman , and love .
In DBS the ambiguity alleged in 12.4.1 is not syntactic-semantic, but at best
pragmatic. 20 The content of the sentence is shown as a set of proplets:

12.4.2 DBS ANALYSIS OF Every man loves a woman.
⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

noun: man
cat: snp
sem: exh pl
fnc: love
prn: 23

verb: love
cat: decl
sem: pres
arg: man woman
prn: 23

woman
cat: snp
sem: indef sg
fnc: love
prn: 23

In DBS, the logical quantifier x is represented alternatively by the sem val-

ues exh pl (exhaustive plural) of the man proplet, while the quantifier

∀

∃ yis

18 When writing SCG'84 we had to learn the hard way that a typed calculus is not very practical. Even
worse, the small fragment we had managed to define in SCG'84 turned out to be unprogrammable.
The solution, published as NEWCAT'86, is a strictly time-linear derivation order.
19 Montague's main contribution is the quasi-mechanical translation of the English surface into formulas
of predicate calculus. The number of grammatical constructions is rather small, and motivated in part
by concerns of analytic philosophy, such as de dicto and de re .
20 The distinction between syntactic, semantic, and pragmatic ambiguities is explained in FoCL'99,
Sect. 12.5. Only syntactic ambiguities are of complexity-theoretic relevance. The syntactic ambiguity
of the example 12.4.1 seems to originate mostly in classes on predicate calculus.