PETER KOMMEI, 
AN ALGORITHM OF LIMITED SYNTAX 
BASED ON LANGUAGE UNIVERSALS 
Abstract. 
Hundreds of differentiated syntactic rules as well as all kinds of 
phrase structures and conventions are dispersed over more than fifty 
still existing natural language systems. On the contrary meanings, re- 
presented by nouns, verbs and adjectives are internationally identical. 
Only the way they are carried and expressed by various national lan- 
guages differs. Thus a fundamental division into two parts represents 
the main feature of the ALCO~ITHM OF  IMITED SYNlrAX (A~S). This A~S- 
Division of natural language systems provides two groups of words: 
a) words representing nouns, verbs and adjectives as so called 
~ content words )) or more easily nominated as RADICALS and 
b) words expressing syntactic features and functions, the SYN- 
TAX-PAR TICLES. 
While the human treasure of knowledge in form of meanings 
expressed by content-words is in no way curtailed by ALS-Rules, the 
vast .jungle of still existing syntactical features and syntagms will be 
drastically cooked down to the essentials. Thus the A~s-Rules com- 
prehend several laws to limit syntagms, which are made clear by al- 
gorithms or verbal definitions. Still the limitations enforced by A~S- 
Rules are based on language universals and thus keep all information- 
expressions and -performances in the scope of a natural language 
system. 
1.0. Aims and the unconventional character of approach. 
Significance and necessity to solve the problems concerning Auto- 
matic Translation between different national languages as well as fact 
retrieval, justifies all possible approaches. Worldwide pessimism (M. 
15 
226 PnT~R KOMMI~L 
L. MmsxY, 1968, p. 24 f) relating to this enterprise ten to twenty years 
ago (N. CHOMSXY, 1965, p. 163) has been in no way without foundation 
(3(. BAR-HILL~L, 1940, p. 271 and G. SALTON, 1968, p. 156 f). A Forma- 
lization of natural language systems seems for the ftrst step unavoidable, 
if the three fundamental goals: 
1. AUTOMATIC TRANSLATION 
2. AUTOMATIC FACT I~ETRIEVAL and 
3. ARCHIVAL HARD STORAGE, a once and for good storage of 
human information in form of facts, are aimed at. 
In the thirties L. BLOOMPmLD published a very significant idea 
(1935, p. 208) of dividing natural language systems among others into 
those of 
a) agglutinated morphologies and 
b) those of isolated morphologies. 
While English, French, German and R.milan belong to systems of 
agglutinated morphologies - the morphological structures are glued 
together - Chinese, ideographic-, pictographic- and gesture language 
systems bear an isolated one. When dealing especially with phenomena 
of isolated morphologies, two points become very clear: 
1. The multitude of syntagms i.e. syntactic features and patterns 
coming with agglutinated systems are considerably reduced to the 
very important ones. 
2. The mostly visually to perceive expression units - permanent 
as well as acute - (grams and gestures), are highly content related, 
thus helping to look behind the scenery of language expressions into 
the material of content-phenomena and semantic relations. 
Up to fifty or more existing different language systems can be 
considered as morphologically and syntactically differentiated expres- 
sion - and carrier - systems for only one and the very same information 
treasure, the treasure of human knowledge. So it is necessary to 
unify expression - and syntax - habits. In order to unify and subse- 
quently limit especially the number of existing syntagms, it pays off 
to be very careful when making artificial curtailments. The best way 
still is to lean on natural prototypes, which lead back to the Bloom- 
fieldian division (L. BLOOMn~.LD, 1935, p. 208): 
AN ALGORITHM OF LIMITED SYNTAX 
aggl..~-- 
227 
--~- isolated 
! v g 
• ~ I~' ~. 
Segment: A 
~" ~ ~ ~ ~ 
Segment: B 
Fig. 1. Scale of Language Carrier-Systems: Agglutinative to Isolated 
Consequently it becomes convenient to disregard segment A of 
Fig. 1 entirely and look more into details of segment B. Syntagms, 
limited down by their nature in language expression systems of seg- 
ment B are easier to pinpoint. The vast jungle of syntagms in segment 
A hinders the extraction of those syntagms which are of most signific- 
ance concerning language universals. They are too much covered and 
hidden by conventional balast of low-value syntagms (Fig. 2). 
Segment A 
................. Din. 
..... J 
Segment B 
Dotted 
line :-: syntactical 
universals 
Fig. 2. 
The number of possible syntactic algorithms to construct sentences 
in all existing natural languages is finite, but still at the present state 
"uncontrollable " and thus not computable (G. SALTON, 1968, p. 191). 
Obeying this fact of nature, efforts led to the conclusion, not to operate 
on sentences of natural language as they exist now, but to form a rule 
and a recipe to conceive sentences, which are: 
228 PETER KfiMMEL 
1. natural in character and 
2. easy to formalize and compute. 
Even if limited in syntactic patterns, natural language systems are 
easy to employ because of being available and programmed al- 
ready in the brains of human beings. Interpreting the criteria for natural 
language systems (J. H. GRE~N~ERG, 1968, p. 110 if), it is trivial to rea- 
lize that certain systems, up to now mostly out of regard, deliver con- 
tributions of syntactical features highly valuable for the whole enter- 
prise. Those syntactical features of limited but natural expression 
systems are mainly extracted from language systems of isolated mor- 
phology as shown in Fig. 3, e to m. But the entire operation to limit 
syntagms and form algorithms must be stopped by one certain point, 
which prevents it from crossing the boundaries from natural to artificial 
language systems (Fig. 3). This boundary has been easily pinpointed 
by following the rules of a work published one year ago. In this pub- 
lication a distinct separation between natural and artificial language 
systems has been made per definitionem (P. KOMM~L, p. 86): 
Definition: NATURAL LANGUAGE 
A language is natural in its character, if 
a) the number of using individuals is larger or equals one million 
heads and 
b) the period of use is larger or equals one life span of a using 
individual 
ga C7" ~ 
Natural Languages 
~'o~ ~ 
• ~ .~ 
'~ ' "~O ~.~ " ~ t'rl mb~ t~ m 
• .~.. ~ 
Artificial Languages 
Fig. 3. 
AN ALGORITHM OF LIMITED SYNTAX 229 
The remainder of language systems can be considered artificial. 
Artificial also insofar as a few native language systems, presently only used 
by some thousand individuals, have a too limited number of users and 
thus lack the natural momentum. Within the scope of natural languages 
(Fig. 3, e to m) a rather wide gap exists between d and e. The closer 
a language system is located to the boundary between natural and arti- 
ficial system (Fig. 3, m/n), the easier it becomes to formalize it, as the 
balast of conventional syntactic rules fades away. So it paid off quite 
heavily to analyze language carrier systems especially from e to m 
(Fig. 3). It is a pity that so few linguists have involved themselves with 
language systems of isolated morphologies as shown in e to m in Fig. 
3. This fact explains why the author of this publication has to refer 
to eight of his own publications in the reference literature. 
The language systems in Fig. 3, e to m are natural in character 
and still after the Bloomfieldian definition of isolated morphology. 
Thus they are easier to formalize. They represent: 
e) Children Expression Systems 
f) Adult Foreigner Expression Systems, as found among tourists 
or guest-labourers with a very limited vocabulary treasure and almost 
no knowledge of syntactical patterns. Habits practiced by adults who 
are forced to maintain dialogs in foreign languages without preparatory 
study. Language of people who stay only a limited time in foreign 
countries. 
g) Aviation Control Communication Language as used between 
the pilot and tower personal. 
h) Chinese for the audible perception. 
i) Chinese in written form for the visual perception. 
j) Ideography and ideographic expression systems such as Hiero- 
glyphs, etc. 
k) Gesture Expression Systems as for example deaf-mute, indian 
and nomadic gestures for the acute visual perception. 
1) Pictographic Expression Systems as found in traffic signs, etc. 
In) Japanese KANGO Expression Systems, a form of ideogram 
sequences referring back to Chinese. 
A conglomerate of universals in syntactical features to be found 
especially in the preceding language systems e to m but also among 
those of a to d (Fig. 3) is filtered and concentrated, to retain syntac- 
tic phenomena, characterized by the highest frequency of occurrence 
(Mc. D. NEIr~L, 1971, p. 40). Thus an ALGORITrIM OF LIMITED SYNTAX 
(ALS) in the form of several fundamental syntagms is gained, which pre- 
230 PETER KI3MMEL 
serves a full scale consolidation of the natural momentum and enables 
the user to feel familiar at once. 
The Preceding details led to a somewhat unconventional approach 
characterized by the following three features: 
1. In order to apply a few and most essential syntactical algo- 
rithms for natural languages, the content metric of one meaning is 
enlarged. S~ANNON/W~AWa'S information measurement (entropy/bit) 
has been extended by evaluating eight content criteria or so called 
sub-criteria of one information unit, one meaning or one RADICAL 
(P. KOMMEL, 1972 a, p. 64 if): 1. Identity, 2. Truth, 3. RADICAL- 
Value, 4. Age, 5. Common Frequency, 6. Relative Frequency, 7. 
Priority and 8. the Interlogging Value. 
2. A conglomerate of syntactic universals found especially in 
content-related natural language systems is cooked down to the es- 
sentials in form of a few syntactical algorithms with highest frequency 
of occurrence. This conglomerate in cooperation with the newly con- 
ceived content evaluation (1) is called: ALGOraTaM Or LIMITED SYNTAx 
3. The amalgamation of the preceding features (1) and (2) in 
form of the very .~LS serves for a case study. This case study involves 
an execution of Archival Hard Storage, Automatic Fact Retrieval and 
Automatic Translation of Natural Languages. It covers a small mole- 
cular scope of human knowledge centered around the meaning " Sand 
Glass" and the "father - son - relation ". Those artificial question 
answering systems on structural and functional phenomena of the 
domain " Sand-Glass" as well as the "father - son - relation " can be 
considered a recipe for automated handling of the remaining human 
knowledge treasure on earth. Concessions to be made appear in the form 
of stereotype syntactical patterns, which affect the esthetic momentum 
but not the transmission flux of information. A natural text to be com- 
puted is conceived after application of the easy to learn and easy to 
limit ALS-kules, which makes it natural in character. Present day used 
texts of Natural Languages must be rewritten. 
2.0. A RADICAL, the newly conceived content unit and its sub-criteria 
in the ALS-system. 
In 1928 Hartley originated the idea of demonstrating the canal capa- 
city of a system mathematically. He put the logarithm of the sum 
AN ALGORITHM OF LIMITED SYNTAX 231 
concerning all possible situations equal to the information capacity 
(R. v. L. HARTLEV, 1928, p. 535 f). Later this was reversed by Shannon 
and Weaver. In respect to the probability of choice Weaver stated: 
"The actual expression for information is " (W. W~AVER, 1964, p. 14) : 
H = - loe p, 
Expressed by the logarithm dualis in bits Shannon declared the proba- 
bility of occurrence to be high, if the information value is small. In 
case the probability of occurrence reaches 1 the information equals O. 
t (a,) = - ld = 0 bit 
Consequently if p = 0, it will cause the information to become inde- 
finite (C. E. SHANNON, 1964, p. 63): 
I (a~)=-ldO=oo bit 
This calculation, which is analogous to the entropy evaluation of 
thermostatisfical data was used (1963) by Beer to express the dimensions 
of information values by bits. He associates several different inscrip- 
tions on train windows with the corresponding information value 
(S. BEER, 1963, p. 65): 
Do not lean out of the window 137.75 bits 
E perieoloso sporgersi 104.50 " 
Lisfarligt art luta sig ut 128.25 " 
Ne pas se pencher aus dehors 128.25 " 
Nicht hinauslehnen 85.50 " 
Since that time, developments have shown that a strict limitation to 
only this kind of content evaluation might lead into a blind alley. 
Bit evaluations are sufficient under certain circumstances to measure 
carrier systems and signs as their units, but they fall absolutely short 
in the determination of contents in the form of information. A newly 
born scientific fact or an invention represents one meaning and can be 
named with one sentence, one word or even one sign. This meaning 
stands for an information unit and is criticized by more than the value 
"improbability of occurrence ", which might come close only to No 
6 of the eight content criteria. 
232 PETER KUMMEL 
An information unit, represented by an abbreviated noun, verb, or 
adjective in lemma- or better said stem - form, is called RADICAL. 
A RADICAL is the main and only component in ALS - sentences be- 
sides the particles. The PARTICLES carry exclusively syntactical 
functions. A RADICAL can be subdivided into eight further sub- 
criteria, which also are to be enumerated. 
Quite well known among Orientalists and about 1 billion asiatic 
people are the so called RADICALS, after which composed Chinese 
Characters can be classified (P. Kt~MM~L, 1966, p. 110 f). The system 
of RADICALS delivers for the information theory as well as Semantics 
of natural languages a highly valued contribution to form sub-criteria 
of one meaning. In other words they represent the interlacing-, entan- 
gling- or involving-value of one meaning to others. With the aid of 
RADICALS several sub-criteria of one meaning can be formalized 
and enumerated to a 100% degree of precision. Below, five examples 
of Chinese RADICALS are given in connection with several composi- 
tive characters, in which the RADICAL represents one component: 
RADICALS: Composed Characters: 
l'~ ,HIssel----- ~. to re.t, wage, 
~ to b.y, ~ I~'e'"ber/l'ers°" 
There are already existing expression systems in Natural Languages, 
¢ saddle, ~'f~ whfp 
Go-Stone (a game) 
.~,~ to continue, 
• '~%" to seg ~:~ receive, i~. 
which come close to Ars-habits. Besides the Chinese expression system 
for example the Japanese KANGO-System is known. ~ 
means literally " Chinese words ". In a Japanese text theoretically all 
particles have to be eliminated, in order to generate a KANGO- 
Text. For example: The sentence: The car runs fast can be written: 
t 2 3 
AN ALGORITHM OF LIMITED SYNTAX 233 
If 1 the nominative particle, 2 the adjective particle and 3 the verl~- 
suffix are oMtted, it results in ~,~'-, ,¢~, out of which still tile 
same meaning is understood. Examples for used KANGO-Expres- 
sions in Japanese are: ,,,,~. \]~ d!~c.lt to park,, or: ")~")__~, x~ "~ 
an electrical express train. Both KANGO-Expressions were conceived 
after the fifties. 
Finally, the use of RADICALS with a limited number of PAR- 
TICLES comes not only close to CHINESE and Japanese KANGO- 
Texts, but also offers the opportunity to subdivide one RADICAL- 
into several content-criteria. 
The eight sub-criteria of a RADICAL: 
1. IDENTITY 
A new information unit can be interpreted and integrated here and 
there. It can be filed here and there. The identity is implemented by 
the RADICAL-Number (Deuterziffer) (P. KOMM~r,, 1972 b, p. 483 f). 
The first meaning in the human treasure of knowledge receives the 
number 1. The RADICAL-Number is implemented at a graph's 
vertex (Fig. 4) in the way of decimal fractures used for decimal classi- 
fications. The RADICAL represents a vertex 
to the origill 
-~ i i i ..~.~ J ill i,i 
II 
m 
Fig. 4. 
in a graph which also can be shown as a loop with connection strings 
like a cable-tree. 
/ 
234 P~T~R KUMMEL 
2. TR UTH 
If a new information represents a perpetuum-mobile or a product 
of fantasy, it has to be marked false. The truth is implemented into 
the treasure of knowledge graph by even numbers making use of the 
IDENTITY-Numbers under 1. If the truth is not existing and an 
implementation has to be done, odd RADICAL-Numbers are pro- 
vided. 
3. RADICA1,-VALUE 
It is more or less related to existing information, which makes it 
attached as a green bud to thicker or thinner branches of the informa- 
tion graph (Fig. 5). The RADICAL-VALUE is also to compare 
with the 
Fig. 5. 
distribution ability of a vertex (P. K/JMMI%, 1969, p, 64 if) and thus is 
identical to the number of strings in the vertex loop (Fig. 6). The 
RADICAL-VALUE is written in brackets at the RADICAL-Loop or 
the vertex. For more detail see P. KOMra~L (1972 b, p. 481 f) and 
P. KOMMEL (1972a, p. 36 f). 
{5) 
j,,,, 
0) 
Fig. 6. 
AN ALGORITHM OF LIMITED SYNTAX 235 
4. AGE 
If an information unit or RADICAL turns out to be not new, the 
exact age has to be determined. The implementation of age is done by 
chronological numbers, starting with 1 for the oldest and furnishing 
the highest in use for the latest RADICAL. Secondly the age of a 
RADICAL may be determined in relation to a known time-calendar. 
So it receives a birth-date. 
5. COMMON FREQ UENC Y 
Ifa RADICAL is already known, it can be classified by its common 
frequency since its birth. The COMMON FREQUENCY is imple- 
mented by numbers indicating the occurrences of counts (P. Ki)M~L, 
1968 b, p. 242 if). 
6. RELATIVE FREQUENCY 
In comparison to others, one information occurs for practical use 
oftener or not. The information unit with the highest relative occur- 
rence is designated with the number one (1). Another of half of that 
rate by 1/2 and so on (P. KOMMEL, 1968 b, p. 242 if). The Relative 
frequency substitutes more or less Shannon/Weaver's Bit-Metric. 
7. PRIORITY 
A larger or smaller importance compared to other meanings is 
indicated by a number which states the surface tension of a RADICAL- 
Graph in those places, where the surface is grown unregular (Fig. 7). 
The vertex A is located close to a surface area where high tension 
exists (see arrows !). It owns a higher PRIORITY-Value than the knots 
B and C. The PRIORITY-Value is measured in percent. If the tension 
on the RADICAL-Cluster 
236 P~T~R ~OMMEL 
Fig. 7. 
(see arrows !) is strong enough, the PRIORITY-Value can reach up to 
100% (P. K/~MSfEL, 1972 b, p. 483). 
8. INTERLOGGING-VALUE 
An individual associates with a certain meaning (RADICAL) another 
meaning, which lies far away from the Cluster-Branches of the first 
concern (Fig. 8). Thus this association cannot run along neighbouring 
branches, but jumps to a RADICAL-Loop far away via the dotted lines 
{H: - ...... 
| q . , 
j s 
| # 
Fig. 8. 
(Fig. 8). The extent of the INTERLOGGING-Value is given by the 
distance of the dotted line, to be measured by the differences of the Iden- 
tity-Value in the l~adical-Cluster. Secondly the INTERLOGGING- 
Value depends on the number of interlogging- and distance-jumps via 
dotted lines, in other words by the number of dotted lines. 
AN ALGORITHM OF LIMITED SYNTAX 237 
Definition: RADICAL 
A RADICAL represents a meaning, which can be subdivided into 
so called sub-criteria or RADICAL-Criteria. The RADICAL repre- 
sents the counter-part to the PARTICLE in ALs-Texts. It carries the 
meanings of nouns, verbs and adjectives. For automatic translation 
purposes a RADICAL is translated exclusively into different national 
languages. 
3.0. The PARTICLES, a limited number of syntagms permitted in the 
ALS-System. 
The human knowledge is to be considered as a huge cluster of now- 
adays not less than several million RADICALS. But a language, funct- 
ioning as a carrier system for information and thus single RADICALS, 
is always composed of syntagms too. These syntagms finally combine 
sequences of RADICALS to sentences of Natural Language Systems. 
They can be reduced to a minimum of units, but may not be neglected 
entirely. A very carefully done and delicate process of limiting down 
the syntagms resulted in a concentrated stockpile of abbreviated 
PARTICLES integrated into the ALS-I~ules. The PARTICLES are 
abstract in their character and each embodies a motion in the branches 
of the RADICAL-Cluster. Consequently the use of a PARTICLE 
releases an electrical process within an associative hardware storage. 
The PARTICLES in isolated form do not supply much information. 
They become useful only when appearing in connection with RADI- 
CALS. As some examples of elementary PARTICLES can be consi- 
dered: 
1. /(quest.)/for question and 
2. /(pret.)/for preteritum or past tense. 
Definition: PAR TICLE 
In ALs-Texts the PARTICLE represents the counterpart to the 
RADICAL. A PARTICLE serves as a fundamental syntagm exclu- 
sively syntactical functions. The PARTICLE is considered a concen- 
trate of internationally universal syntactic rules. For automatic transla- 
tion purposes the PARTICLE is not translated, thus appearing in 
internationally understood abbreviated forms of Latin or Greek. 
238 p~.T~.a ~OMM~.L 
4.0. Fundamental rules of the algorithm of limited syntax divided into 
single paragraphs. 
In order to use ALS, conventional sentences must be transformed to 
heteronoms with the maximum size of a fivefold-heteronom. Different 
from other approaches to the same project, where at least 172 syntac- 
tic features must be taken into consideration (T. WINOG AD, 1972, 
p. 173 f), AtS limits the formalism by permitting only stereotype pat- 
terns. These patterns include contextual rules within the nominal- 
sequences of up to five nouns. Only a restricted number of PARTI- 
CLES within the fivefold-heteronom is permissible. ALs-Formalisms 
are based on the " Grundregeln der Formalgrammatik" (P. KOMM~L, 
1972b, p. 485) as well as on details described in the "Deuterfolgen- 
Grammatik" (P. KOMlVmL, 1972a, p. 76 ff and 83 f). The main rules 
of ALS are classified in paragraphs: 
1 All expressions of Natural Language must be divided into RADI- 
CALS embodying meanings and PARTICLES representing syntacti- 
cal function. 
2 Each RADICAL has to appear in sentences with an abbreviated morpho- 
logy, in stem-pattern or lemma-form. 
3 All expressions must be cast into sequences of RADICALS similar 
to heteronoms. Example: glove = mononom, Handschuh = binom 
in form of a heteronom. 
4 Each of these heteronoms may not exceed the size of a fivefoldnomen. 
In other words, a sentence may not include more than five RADI- 
CALS. Example of a maximum: /train/terminal/station-master/office 
/telephone/. 
5 Each of these heteronoms according to ~ 4 is to carry one meaning 
in form of an information unit. 
6 The meaning of a sentence in the form of a heteronom is always to be 
taken out of the last RADICAL, while the preceding ones only serve 
for more detailed specifications. Example: /information/bank/means 
bank or accumulation place. But/bank/information/means news from 
or about banks. 
7 Each meaning according to ~ 5 has to be analyzed by the eight con- 
tent criteria (P. KOMMEL, 1972a, p. 69 f) and (P. KOMM~L, 1973b, 
p. 482 if). 
Additionally they must be translatable into all existing natural languages. 
8 Each meaning or RADICAL according to \] 7 must be furnished with 
a national language identification number for example 1-10 belonging 
AN ALGORITHM OF LIMITED SYNTAX 239 
59 
5 10 
511 
12 
5 13 
5,4 
5 is 
36 
5 17 
~8 
19 
5 20 
to the most relevant national language systems on earth (see 5.3 below !). 
Thus for translation purposes the adequate expression sequences belong- 
ing to each identification number can be provided. 
The heteronoms according to ~ 4 exist of conventional nouns, as well 
as substantivated verbs and substantivated adjectives as nouns. Exam- 
ple: ... gives the money =/moneytransfer/ or sunny day =/sunday/ 
etc. 
All RADICALS according to 1 and 3 should be possibly limited to 
their lemma patterns respectively shortest understandable form. Exam- 
ple: Automobile = auto or television set = TV- set. 
Each RADICAL in lemma-pattern should not surpass the length of 
a certain sequence number of letters, which is stated here with 20 let- 
ters. 
Each RADICAL within a heteronomic sentence must be written 
within vertical lines. Example:/father/. 
Longer sentences of conventional text can be reduced to several hete- 
ronoms by rewriting. As an example see the text of Newsweek 
below: 
According to the chainstitch-method (P. KOMM~r, 1972a, p. 77 and 85) 
as well as recursive functions (P. KOMMEL, 1972b, p. 485, ~ 4) one RA- 
DICAL of the preceding heteronom is chained into the following one. 
Example: The father living in London gives the son studying in Paris money. 
1. A threefold heteronom:/father/London/living/, 2. A threefold hete- 
ronom: /father/son/moneytransfer/ and 3. Another threefold hetero- 
nom: /son/Paris/study/. 
Heteronoms of concrete value end with a concrete noun or RADI- 
CAL. Example: /motor-car/door/. Heteronoms with an abstract 
value end with an abstract noun. Example: /motor-car/delivery/. 
Necessary PARTICLES expressing for example time, questions, etc., 
must not be placed behind the last RADICAL of the heteronom. Exam- 
ple: The father gave the money: =/father/(pret.)/moneytransfer/. 2. 
Does the train leave at 12 : 30 h? --/train/12 : 20 h/(quest.)/depart/. 
PARTICLES have to be written in brackets. Example see ~ 16! 
Serving the purpose of automatic translation all PARTICLES must 
be expressed in Latin, Greek or an internationally known abbreviated 
letter sequence, because PARTICLES will not be translatable in the 
^Ls-System. 
The pronoun, which normally represents a noun, always has to be re- 
placed by the originally substituted noun. Example: Little Joe does 
not say: "I want to eat ", but:/Joe/want/eat/. Or, the pilot does not say: 
ledg " /C I / / / / "yes" or "I acknow e , but: essna niner three victor affirmative. 
For each RADICAL to be used with ALs-Systems a fully content- 
related expression unit in form of a pictogram has to be furnished. 
240 PBT~R KUMMEL 
This must be available in an adjacent archive. Thus ambiguity by 
carrier functions of different languages as well as homo-and syno- 
nymities can be eliminated. Even for the conception of content related 
abstracts pictograms are possible, see (P. KiJMlVI~L, 1972a, p. 53 if). 
The meanings stay constant in time (P. KOM/CmL, 1967b, p. 42 if) and (P. 
Ki~lvil~L, 1968a, p. 52 f). Pictograms of abstracts must be conceived 
with the fourth dimension "time" in them, realized by an arrow or a 
dotted line for deplacements and movements. For example in China 
and Japan the character carrying the meaning " to gather" or " assem- 
ble " is still presently in use. The sign-etymology reveals the following 
development of morphological structures: 
1. "~- ,2. ,3. ,4. 
21 
22 
§ 23 
1. A bird flies into the direction of the arrow on top of a tree. Numbers 
2, 3 and 4 represent abbreviations within several thousand years of use. 
4. expresses the present da~ used form in China and Japan. 
For each RADICAL the equivalent lemma or stem-word of at least 
ten National Language Systems has to be provided and implemented. 
Context sensitivity is limited down to a sequence law: Subject-Object- 
Predicate. Example: /fatherlson/moneytransfer/. 
RADICALS written in vertical strokes and PARTICLES written in 
brakes and vertical strokes are expressed by letter sequences without 
capital letters. 
Example of rewriting conventional text into ALS-TEXT: 
Text to be rewritten: Newsweek, February 5, 1973, page 1, top of the 
week, second column above: MACAO BOOMING OUTPOST, Page 23.: 
Portugals pint-size colony of Macao is a geopolitical anachronism per- 
ched precariously on the flank of China. Newsweek correspondent 
Tony Clifton reports how Macao, once known as the world's wickedest 
city, is flourishing against all odds- and changing in the process. The 
preceding text is reduced to sequences of heteronoms or sentences 
according to ALS-Rules: Caution: This states an example of ALs-R.ules 
and is not implemented for case study purposes! 
1. /macao/outpost/boom abstract, all ALs-Sentences or heteronoms 
2. \[macao/23/page exist of abstracts; with the exception 
3. ~portugal/macao/pint-size/colony/ of No. 7 
4. ~macao/geopolitical/anachronism/ 
5. /macaolchina/flanklunsafelsitting I 
AN ALGORITHM OF LIMITED SYNTAX 241 
6./newsweeklcorrespondentltonycliftonlmacao/report/ 
7. /macao/ (pret.)/£1rst/wicked/world/city/ 
8. /macao/ (against/s~/odd/flouri~h/ 
9. /macao/process~change/. 
5.0. A case study within a molecular scope of human knowledge 
5.1. Archival Hard Storage by the ALS-System. 
The whole human knowledge is to compare with an immense 
Cluster of RADICALS. Each RADICAL represents one meaning. All 
of them are connected to each other following the graphic rules of a 
directed graph. The number of meanings is finite. Each day new mean- 
ings are added, because inventions and scientific detections are made. 
Thus the cluster grows daily. In order to obtain a 100% precise record 
of the Cluster, each RADICAL should be evalt~ated after its eight 
content- or subcriteria. These data of the criteria have to be imple- 
mented into a storage system. For reasons of rationality primarily 
facts should be stored and expressions with untrue contents omitted. 
One molecular scope of the human treasure of knowledge is shown 
in Fig. 9. This RADICAL-CLUSTER in form of a directed graph 
explains the single connections between the RADICALS. If a Cluster 
in form of a cable-tree is given (P. KOMmEL, 1972a, p. 65), compare 
also the loops in figures 4, 5 and 6 above, at each RADICAL the 
DISTRIBUTION- or RADICAL-VALUE is indicated by counting 
the number of cables in the loop. 
Satzd-Glass 
S. G. Struct.,, S.G. Glass, S, G. llousil~g, S.G. Frame, S.G. Sam\[ 
7 
X~°" G. Function ~ S.G. Hand Movement,\] Wall. l*ang, p0s~ti0n Dir. Time 
........ 
Mcasurh\]g __ ~ ~ J , ~, G. mcch l 4 
Device - ., nlovemmC " ~S. 
/ puttiqg top down pos. | G. time Meas. 
| 
Omamcnt, F. ~ = ' - 
Fig. 9. 
In Fig. 9 five concreta and eight abstracta are listed. The way they 
are implemented can be considered ripe for eternal implementation. 
16 
242 PraTER gfdM~r 
But for each RADICAL the enumerated sub-criteria must be given 
(compare 4.0!). 
5.2. ALS-fact retrieval in natural language. 
The procedure of Fact Retrieval is in this case not simulated with 
the help of a model but executed in realistic practice. The naturally 
grown graph in Fig. 9 as a "directed graph" allows questions and 
precise answers, The precision comes close to that demanded by patent 
office examiners. The operation of Fact Retrieval in the RADICAL- 
CLUSTER is compared to the function of a beetle, crawling up and 
down the branches of a bush, a cluster or a tree. 
Possible questions and answers: 
Thirteen meanings are cut off from the knowledge treasure and put 
into the system including their relations. The user might 
. ask about one meaning: He delivers his question in natural AT S- 
Text. For instance: /existence/(quest.)/sand-glass/function/. "/exi- 
stence/ \](quest.)/" alone represents the ALs - equivalent for "what 
is a ...?", or, "what about a ...? ". This constituent of a query 
"/existence/ \](quest)/" triggers immediately a ftrst order retrieve 
circuit (Fig. 10), which is programmed to print all content criteria 
of one RADICAL in ALs-Text. The other constituent of "/sand- 
glass/function/" guides the ftrst order retrieve circuit to its cor- 
responding loop or RADICAL in the information graph. The 
content criteria of the heteronom /sand-glass/function/ are taken 
from the storage and are printed, 
d~,~ ' ~'~ "~ a p • s 
-:. ~ 
Query RADICAL Query RADICAL 
Fig. 10. Fig. 11. Fig. 12. 
(first ord. R.C.) (second ord. R.C.) (third ord. R. C.) 
AN ALGORITHM OF LIMITED SYNTAX 243 
. 
. 
ask, what does a meaning belong to? For instance in ALs-Text: 
/depend/(quest.)/sand-glass/function/. This triggers a "second order 
retrieve circuit" (Fig. 11). For the purpose of an answer all content 
criteria of the next upward loop or RADICAL (in this case "/sand- 
glass/" are printed in ALS-Text, 
ask, what does a concrete meaning consist of, respectively what 
subfunctions an abstract meaning can be divided in? This reads 
for instance in ALs-Text: /consist/(quest)/sand-glass/structure/. By 
"/consist/(quest)/" or "/divisible/(quest/" a third order retrieve 
circuit (Fig. 12) is triggered. All content criteria of the neigh- 
bouring ramificated RADICALS from the " Query - RADICAL" 
are printed in succession according to the decimal fracture of the 
RADICAL-Numbers. 
For the procedttres so far three questions different in function were 
possible: 
clear text: ALs-Text: implemented procedure: 
1. what is a ...? / existence \[ (quest) \[ 1st order retrieve circuit 
2. to what belongs a ...? / dependent / (quest) / 2nd order retrieve circuit 
3 a. of what consists a? / consist / (quest) / 3rd order retrieve circuit 
3 b. into what funaions 
divisible is a ...? / divisible / (quest) / 3rd order retrieve circuit 
If the preceding microscopic scope of human knowledge is extended, 
or further scopes including human relations are added, surely other 
questions must be available or made available as for instance: who?, 
by who?, etc. Also the RADICALS of many concreta must be subdi- 
vided and ramificated into concreta as well as abstracta. 
5.3. ALS-Automatic translation in natural language. 
In order to make use of the INTERLOGGING-VALUE of one 
RADICAL, the following jump has been made from the RADICAL 
/sand-glass/: A person associates with Sand-Glass an uncle in London, 
who, in former times, helped to construct a working model of a Sand- 
Glass. This uncle has a son studying in Paris who spends lots of money 
from his father. The interlogging string ends at the RADICAL: 
/father/ (Fig. 13). 
244 WT~.R K~JMMEL 
/f~thed Ir:<hc£/sonl /fatherlsonlmoneytransfer\] 
/£=a~e~/1o,,do,~/ /raa, cr/lonao,qliving/ 
w 
/son/ /son/paris/ /son/paris/study\] 
L v : O .... IL 
Fig. 13. 
A second interlogging jump is made, when the sentence: The 
father who lives in London, gives his son studying in Paris money. Three 
6Ls-Sentences are conceived: 
1. Ifather lsonlmoneytransfer / 
2. /father/London/living/ 
3. /son/Paris/study/ 
The procedure of Automatic Translation demands that each RADICAL 
to be translated must be implemented into the RADICAL-CLUSTER 
as in Fig. 13. All sub-criteria of a RADICAL have to be implemented 
by numbers too. Corresponding to the Fact Retrieval above in 5.2., 
each meaning or information unit implemented as a RADICAL into 
the system is additionally related to a set of numbers. These related 
identification numbers each point to a repertoire of nouns belonging 
to national languages. If, for instance, the system is furnished with ten 
different national languages, every single RADICAL handled must 
be numbered with a national identification number (P. Kf3MM~L, 1972b, 
p. 486). From 1 to 10 for example the following national language 
systems might be put in sequence corresponding to their frequency of 
occurrence and importance by the user's per capita rate: 
1. English 2. Chinese 3, Indian 
4. Russian 5. Spanish 6. French 
7. Portuguese 8. Japanese 9. German 
10. Dutch 
and 
Each meaning represented in the system by a RADICAL or loop 
with its eight content criteria, is international in character. Only the 
RADICALS can carry expressions of several national languages, not 
the PARTICLES. To obey this rule, words for question input can be 
AN ALGORITHM OF LIMITED SYNTAX 245 
of ten different national origins. The system is programmed to mark 
each word with an additional national number, corresponding to the 
very nationality. Thus, ten different words link to one implemented 
meaning of one RADICAL and are connected to it. 
The demand to translate into one of the ten above listed languages 
triggers a corresponding number between 1 and 10. Consequently 
ALs-Texts can be printed for answers in 10 different national languages. 
Because of internationally known syntactic patterns exclusively ap- 
plicated in the ALs-Sequence of heteronoms, the nationality of each 
RADICAL in use does not affect the syntactical momentum involved. 
This leads to a simplification of the whole act of AUTOMATIC 
TRANSLATION. The entire procedure is solved by exclusively 
translating the RADICAL-Expressions for the whole information in 
form of heteronoms. If needed, the number of different national lan- 
guages implemented into the system can be extended voluntarily above 
ten. 
Automatic Translation of different national languages according to 
the ALs-System is only possible if all information units (meanings or 
RADICALS) concerned are implemented in the very patterns of the 
Automatic Fact Retrieval under ~ 2 and after the ALS-R~ules. All texts 
to be handled must follow stereotype syntactical features obeying 
strict eliminations of syntagms with low frequencies of occurrence as 
described in the ALGORITHM OF LIMITED SYNTAX (ALS). 

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