Information Technology Reference
In-Depth Information
FIGURE 1. Ascending hierarchical definition structure for nouns. (Nouns are at
nodes; arrow heads: definiens; arrow tails: definiendum.)
which represent the two kinds of apparitions, namely different nouns for
things distinct in form and shape, and verbs for change and motion.
The structural distinction between nouns (
cl
i
k
) and verbs (
v
i
) becomes
apparent when lexical definitions of these are established. Essentially, a
noun signifies a class (
cl
1
) of objects. When defined, it is shown to be a
member of a more inclusive class (
cl
2
), denoted also by a noun which, in
turn, when defined is shown to be a member of a more inclusive class (
cl
3
),
etc., [pheasant Æ bird Æ animal Æ organism Æ thing]. We have the fol-
lowing scheme for representing the definition paradigm for nouns:
{
{
{
{}
}
}
}
cl
n
=
cl
n
-
1
cl
n
-
2
...
cl
m
(1)
i
i
i
n
-
1
n
-
2
m
where the notation {e
i
} stands for a class of elements e
i
(
i
= 1,2,...,
p
), and
subscripted subscripts are used to associate these subscripts with the appro-
priate superscripts. The highest order
n
in this hierarchy of classes is always
represented by a single undefined term “thing,” “entity,” “act,” etc., which
appeals to basic notions of being able to perceive at all. A graphic repre-
sentation of the hierarchical order of nouns is given in Fig. 1 and a more
detailed discussion of the properties of these (inverted) “noun-chain-trees”
can be found elsewhere (Weston, 1964; Von Foerster, 1967a).
Essentially, a verb (
v
i
) signifies an action, and when defined is given by a
set of synonyms {
v
i
}, by the union or by the intersection of the meaning of
verbs denoting similar actions. [hit Æ {strike, blow, knock} Æ {(hit, blow,
. . .) (stir, move air, sound, soothe, lay eggs,...,boast) (strike, blow, bump,
collide . . .)} Æ etc.]
Â
VV
'
=
{}
vv
v
v
(2)
i
j
k
e
A graphic representation of this basically closed heterarchical structure
is given in Fig. 2, and its corresponding representation in form of finite
matrices is discussed elsewhere (Von Foerster, 1966).
Search WWH ::
Custom Search