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The derivation is based on the same navigation as 3.3.2, wherebby the surfaces
are realized from the goal proplet of each navigation step, using mainly the
core value. In NLC'06, the DBS cycle of communication has been worked out
in detail for more than 100 constructions of English.
3.4 Algorithm of LA-Grammar
Having shown informally how the data structure of proplets may be used (i)
for mapping surfaces into content (3.3.1), (ii) for activating content selectively
(3.3.2), and (iii) for mapping activated content into surfaces (3.3.3) let us turn
to the formal rules performing these procedures. Given that the three phases of
the cycle of natural language communication are each time-linear, i.e., linear
like time and in the direction of time, they may all three be handled by the
same algorithm, namely time-linear LA-grammar. 9
The rules of an LA-hear grammar combine a “sentence start” ( ss ) with a
“next word” ( nw ) into a new “sentence start” ( ss ). Furthermore, the ss ,the
nw ,andthe ss are defined as pattern proplets which are applied to content
proplets by means of pattern matching (as in 3.2.3).
Consider, for example, the definition of N+FV (for nominative plus finite
verb). The rule is shown as it applies to a matching language input, corre-
sponding to the first derivation step of 3.3.1 (explanations in italics):
3.4.1 LA- HEAR RULE APPLICATION
i. rule name
ii. rule package
N+FV
{FV+N}
v. resulting ss -pattern
iii. ss-pattern
iv. nw-pattern
noun: α
cat: NP
fnc:
verb: β
cat: NP XVT
arg:
noun: α
cat: NP
fnc: β
verb: β
cat: X VT
arg: α
rule
level
matching and binding of variables
output
noun: Julia
cat: nm
fnc:
prn: 1
verb: know
cat: s3' a' v
arg:
prn:
noun: Julia
cat: nm
fnc: know
prn: 1
verb: know
cat: a' v
arg: Julia
prn:1
language
level
9 LA-grammar is of lower complexity compared to Phrase Structure Grammar regarding relevant lan-
guage classes (TCS'92). The LA-grammar algorithm for the lowest class C1 has more expressive
power than a finite state algorithm (cf. CoL'89, Sect. 8.2). Time-linear applications range from de-
scribing the evolution of the universe and the development of an embryo all the way to the control of
production lines, the disassembly of old ships, the stages of a soap opera, and organizing a team of
workman as to when which task has to be finished for the next tema to appear, for all eventualities.
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