Mystery Number Five - Computational Linguistics and Talking Robots - page 101

6.4.1 U SE OF PROPOSITIONAL CALCULUS IN PREDICATE CALCULUS

[p circle(x)]

The unanalyzed propositions p and q preceding the arrow are replaced by
red(x) and circle(x) in the formula of predicate calculus following the arrow. 19
The quantifier

∧ q] = ⇒∃ x[red(x) ∧

x horizontally binds the two instances of the variable x. The
formula of predicate calculus inherits from the formula of propositional cal-
culus the connective

∃

∧ (including its truth table) and the bracketing structure

surrounding it.
DBS, in contrast, accommodates the extension to functor-argument within
the structural means of the proplet format, as shown below:

6.4.2 I NTEGRATING FUNCTOR - ARGUMENT IN DBS

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦

adj: red
cat: adn
mdd: circle
nc:
pc:
prn: 62

noun: circle
cat: sn
mdr: red
nc:
pc:
prn: 62

⎡
⎣

⎤
⎦

⎡
⎣

⎤
⎦ = ⇒

rec: red
next: circle
prev:
prn: 62

rec: circle
next:
prev: red
prn: 62

The two proplets preceding the arrow treat red and circle as elementary recog-
nitions, 20 indicated by the core attribute rec . They are connected by the values
of the continuation attributes next and prev .
In the two proplets following the arrow, the core attributes rec are revised
into the more differentiated attributes adj and noun , characterizing the parts of
speech. The continuation attributes prev and next reappear as nc (for next con-
junct) and pc (for previous conjunct). They are used for the intrapropositional
coordination of adjectives, as in beautiful, young, intelligent (9.6.6, 9.6.7),
and nouns, as in the man, the woman, and the child (cf. 9.2.5; NLC'06,
Sect. 8.2).
The common prn value of the red and circle proplets, here 62 , indicates
their belonging to the same proposition, and assumes the binding function of
the quantifier in 6.4.1. The kind of semantic relation between the two proplets
is established by the continuation attributes, here mdd and mdr , and specified
further by their values, circle and red , respectively.

18 In machine learning, CIN and CIP would be examples of learning from experience .
19 Even though red circle is linguistically a phrasal noun and not a sentence, it is treated in 6.4.1 as a
proposition insofar as red(x) and circle(x) each denote a truth value.
20 We refrain from calling an elementary recognition or action a “proposition.” A set of proplets with
a common prn value is called a proposition only if it contains a verb - which presupposes functor-
argument.