5 
1965 International Conference on Computational Linguistics 
MACIIINE TRANSLATION AND CONNECTEDNESS BETWEEN PHRASES 
Karel ~ U L ~ K 
Mathematical Institute of Czechoslovak Academy 
of Sciences~itn~ 25, Praha l, Czechoslovakia 
• ~.. ~ .~.~ _~ \] 
~ulik i 
I. Machine Translation. 
To translate a special text from one language into another 
means to construct to the given text in the first language, such 
a text in the second-one that has the same ~ (the same is 
told in it) like the given text. 
The t_ranslation from a ~tu~al language L I into a language 
is such a function F (in the more general case it is a many- 
valued function) which assigns to any text T in the language 
L I such a text F(T) in the language L2, that F(T) has the same 
meaning like To If we introduce a semantics (or interpretation) 
M as a function (in general also man~-valued) which to any ex~res- 
sio____~n E of some language L assigns its meaning M\[E~(compare\[~\]), 
it is possible to say that the function F assigning the texts 
F(T) from L 2 to the texts T from L 1 is the translation only when 
(1) M\[TJ= M\[F(T)J for any text T from L I. 
At the machine (or automatic) translation, the matter is, 
to define the function F as a mechanizable procedure (ioe. 
algorithm) according to which an arbitrary starting text T in L 
is being succedingly modified till we get the translated text 
F(T) fulfilling naturally (I)o The corresponding algorithm can 
be finally programmed for a suitable computer.With respect to the 
used computer, the programme of the algorithm must not be too 
long, not even the wide range of memories must not be emploied 
and at last the translation must not take up too much of time. 
Usually it is required for the algorithm of a translation, to 
be the most effective. 
~ul~k 2 
2oTranslation_"Sentence bu sentence"= 
The translation F is theoretically - as every function - 
defined 
texts in L 1. If we really had these pairs practically at dis- 
posal, we could use a trivial algorithm of the translation F~ 
should put in the memory of the computer all the pairs~T,F(T)\] we 
and when being Riven the starting text T, we should find out in 
the memory the pair, in the first place of which T would be si- 
tuated, thus the pair IT, F(T).\] , and the demanded translation 
F(T) would be on the second place of this pair° Thic is, of course, 
not only funny but also impossible. 
It seems to be funny because of the fact that to have prac- 
tically at disposal the pairs IT, F(T) 7 it would mean to use live- 
ly translation and thus to translate all possible texts in advance. 
But the automation of translation signifies to exclude as much as 
possible the direct intervention of man out of the proceeding of 
the translation and thus to sustitute a man by a machine. On that 
score, we do not possess practically the pairs ~T,F(T)\] . 
It seems to be impossible because the texts T are too manu 
(it would be possible to admit that infinitely many) and the pairs 
IT, F(T)J could not be included in any computer° On the other hand, 
it is necessary to admit that it concerus the algorithm, which 
is very simple (only to look up in the memory would take up too 
much of time). 
The trivial algorithm being practically impossible, it is 
necessary to try to decompose long texts into parts and then to 
translata part by part. Naturally, it seems to be profitable, 
to treat sentences, that are in printed texts distinctly separa- 
ted by points, as these Darts. Thus, every text T is a sequence 
~ulik 3 
of partial texts, i.eo sentences Sl, $2,...~S k so that we 
~Tite that T =/SI, S2,o..,Sk) J ° The function of the may 
translation F is, of course, according to the asumption 
defined for all texts and thereby also for particular sen- 
tences SI, S2t...,S k so that it is possible to construct 
a somposed text LF(SI) , F(S2),...~F(Sk) / from the transla- 
tions of these sentences F(SI) , F(~), ..., F(Sk) , that ere 
some partial texts in L2° At the same time, the translations of 
sentences follow in the same sequence as did the starting s~nten- 
ces in the text To It may happen - and we should sure welcome it, 
if it were always - that it holds 
(2) F( slos2 o..s k) -IF( s l) °F( s 2 )o..F(s k) .I 
or at least the weaker condition 
(3) • 
From (2) ther~ follows (3) but in no way the contrary° 
For the translation the condition (3) is sufficient. It might, 
namely, happen that we translate the text T, as a whole, different- 
ly than when translating it succeedingly in parts S1,S2,...,Sk, 
so that (2) does not hold, but despite this (3) holds. 
In the condition (2) and similarly the condition (3) were 
fulfilled for any text T = (SloS2o..S k) in L1, it would signify 
that it was always possible to translate single sentences of the 
text quite independently each of another. It is probably not true. 
Sometimes, it is necessary to know, how the sentence S 1 was trans- 
lated, when we want to translate correctly the sentence ~, becau- 
~ullk 4 
se regularly both sentences are connected as to the contents, 
and not always this connection is expressed by syntactical 
means. In addition, sometimes it is necessary to translate 
too long sentences from L I as two or more sentences from 
and then not even the sequence is possible to be defined in 
advance. 
In spite of this, the condition (2) or at least (3) is the 
basic asumption for Any translation "sentence b~ sentence" and 
most part of translation belongs to such a type of contemporary 
translations. To be competent to accept the asumption (2) or 
(3) it sufficies to confine oneself to some texts only, and the 
texts not fulfilling this assumption are necessary to be adapted 
before the translation in order to make them able to fulfill it. 
It is not clear, of course, how to find it out at the given text, 
before starting the translation. 
£he asumption (3) stands for nothing else than 
(4) 
and hence the substantial simplifying of the definition of trans- 
lation can to be seen. It suffices, namely, to suppose that it is 
necessary to define only a partial function F ~ of the function 
F, that is defined for arbitrary sentences in L I only (on no 
account for arbitrary texts when the sentences are a special 
case of simple texts). Thus, there holds F ~ (S) = F(S) for every 
sentence from L I and out of (2) there follows 
(5) sl.s2...s k) :IF'( s I ~.~(s 2).. .F~(s~ ~jv 
F( 
~ulfk 5 
so that in fact we are able to cope with the function F ~ when trans- 
lating the texts. 
Similarly, like at the function F, it is possible at the 
function ~ too, to try to give a trivial algorithm making 
full use of all pairs \[S,F~(S)~ o But the situation improves 
only a little. It wold be again necessary to translate all the 
sentences in advance and even these are still too many, so that 
all preceding reasons remain valid, what means, that it is necessar~ 
to try to decompose even the sentences in parts, and to trans- 
late the sentences in parts, too° 
3o Translation "word by word"_° 
By the decomposition of the translation into sentences 
there were no difficulties because in printed texs this de- 
composition into sentences was just ready, and according to 
the syntanctical means it was possible to decompose its parts@ 
Of the same simplicity and uniqueness is the decomposition 
of the sentence S in its single words WI, W2,ooo,W k separated 
by interspaces, so that it is possible to write S = (WIW2..oW k) 
like at the text. 
Besides, the linguists have constructed, a long time ago, 
a binary translative dictionary from the language L 1 into the 
language L~o This dictionary is, in fact, defined as a set of 
the pair of words, the first-one from L 1 and the second-one 
from L 2 having the same meaningoif we denote by f the trans- 
lation from L 1 into ~, where f is again generally many-valued 
~ulfk 6 
function (thanks to the homonymy of words) f 
the condition (in details se-. L 3 .i ~) 
evidently fulfils 
W from L 1 . 
In whatever wmy the trivial algorithm of the translation 
of texts and sentences was funny and impossible, this algorithm 
is in case of the translation of words not only possible, but 
also it is used from time to time by living translators. At most 
machine translations, there is really choosen for the algorithm 
of the translation f the just mentioned trivial algorithm, i.e. 
into the memory of a computer there are input all pairs W, f(W) 
and the most tedious procedure is - how it was said- to look up 
in the memory and to compare. 
But it is not necessary to use this trivial algorithm° 
It is possible to construct a sequential automaton and thus 
to construct also a corresponding technical apparatus which 
will realize the function f, ioeo if there enters on its input 
the word W as a sequence of letters ll12.oolk, which is even- 
tually prolongated by the means of several help-symbols (compare 
\[5 \] ) we get on output again the sequence of letters Ii12...i k D 
that eventually starts with several help-symbols and simultane- 
ously there holds that 
i W ~ when W = 1112 .lj j<k (7) f(ll12o..l j) = i i i...Ik , .. , _ • 
There is a question, whether there is not possible, when using 
this automaton, to shorten the time necessary for translating~ 
when evidently all lost times can be excluded at looking up in 
the input dictionaryo 
~ulfk 7 
Taking no account to the fact, in what way the translation 
of words f is given, one may ask, whether for the sentence 
S = (WIW2...W k) there holds 
(s) z (s) = \[few l) f(w 2) f(W2)ooof(Wk> , 
which is the similar condition to the condition (2) for the 
translation of texts. 
It is known that this condition holds nearly never for 
most natural languages, because the translation of words f 
is the translation of words in basic form only, whereas by 
the decomposition of the sentence WI, W2,o.oW k are in va- 
rious word-formso To put it 8ifferently:the function f res- 
pects only the lexical meaning of words but does not take 
into consideration morphological questions° 
However even in the case~ the f1~nction f could be pro- 
longated from basic forms on other form of words-what, of 
course, need not be possible-or on the contrary, if we adapted 
to the basic form single words W i in the decomposition of the 
sentcnce~ yet despite this all - even under these suppositions 
- the condition 48)would be fulfilled in the case only, that 
there are concerned two languages L 1 and L 2 that are very strongly 
cognate, or two dialects of the same lamguagej or in the case 
L 1 and L 2 are not cognate, the considered sentence S must be 
very simpleo 
The translation fulfilling the condition analogous to 
the condition (8) may be called the translation "word b3; word"° 
But unfortunately it is known that such a translation is im- 
~ulfk 8 
possible in natural languages, although it would be very 
advantageous and simple° 
It does not mean, of course, that the decomposition of 
the sentence into words cannot be used; it is too fine and 
therefore it is necessary to decompose the sentence in another 
w~y, at all events in such a way that single parts will con- 
tain more than one word (and we suppose, under tacit consent, 
that the words have full meaning, not only being help-wor~s 
with the ~rammer meaning) and that these parts need not be 
sentences° Before introducing these parts~ it is necessary 
to take into consideration various necessary morphological 
and grammatical statements, and thereby to adapt properly 
the condition (8), too, wher~ there were no differences between 
the basic word-form or the mere stem of the word and its va- 
rious possible forms° 
~ullk 9 
4. Syntactical and semantical characteristics of words. 
First of all we may suppose that, to avery word-form (shape) 
which appeared in the decomposition of some sentence into words, we 
are able to define its basic fo~n or stem W (the function f 
'refers just to these basic forms) and its charaqteristic ' 
c = (x I, x 2, ... , xn), where n is according to the need a 
sufficiently great integer and single x j are some gran~matical 
morphological and eventually even other data referring to the form 
W. For example x I can be the datum on word-kind, x 2 the datum 
on case, 
time, x 7 
x 3 on gender, 
on mood a.s.o. 
x 4 on number, x 5 on person, x 6 on 
Naturally we also assume that on the contrary, if it is 
given the basic form w and prescribed (of course admissible) the 
characteristic c, it is easy to define the starting form ~$. 
-\] 
Thus, we suppose that there are given functions h and h - such 
that h(W) = (w,c) and 
T guages (in L I and ~2 
h-!(w,c) : W in each of considered fan- 
it will be functions h I and h2). 
Although it is well known that the sentence and its trans- 
lation need not have the same nLnnber of words, this demand is not 
far from truth when we pay attention only to the full-meaning 
words. Let us consider, however, such sentences S which fulfil 
this demand (this is the supposition for making the conm~ent easy) 
i.e. if it is S = (W I W 2 ... W K) then 
(9) F#(W 1 W 2 ... = "'" WX ) , 
~ullk I0 
T 
where evidently ~i are the words of the decomposition of the 
- - ~K sentence F~(S). The task is, how to get the chain (W 1 W 2 ... ) 
from the given chain (W 1 W 2 ... W E ) and we know already that it 
is not possible to get it by means of the translation word by word 
according to (8) directly. 
When we use a function 
its basic form 
: (wi, c i) 
and data 
w i and characteristic ci, namely, 
and thus we can differentiate the data 
(c I, c 2, ..., cK). 
h I we get from any word-form W i 
h.(W. ) : J- l 
(W I, W 2,'.-, W K) 
It is similar with the translated sentence 
when one uses the function 
h2 (~i) = (~i' ~i )" 
(w I w 2 ... w E) 
h 2. Again we are able to discern data 
(~l' ~2' "'" ~K ) when evidently 
Now, it is clear that instead of the condition (8) ought 
to be the condition 
(I0) ~i = f(wi) for i = 1,2,..., k 
because here f is really used for basic for~s of words. Then 
the translation fulfilling (i0) is in fact the translation ,,word 
by word" but only in the respect of the meaning of word, being 
far from complete translation. There is missing the proceeding, 
how to get from the starting characteristic (c!, c2, ..., c K) 
characteristic (~i' ~2' "'" cK )" And just here there is impossible - 
except for the most simple example - to find such a function g ~n 
order to hold 
(!i) c i = g(ci) for i - 1,2,..., k. 
~ullk II. 
tlon 
it would evidently hold 
If it were the case, or in tl~ese cases for which the func- 
g Could b~ found, the translation would be easy, because 
0 k, g(c i) for i = 1,~,..., 
(13) G(C l, c2,..., c K) : cx)' 
as it was to be in (Ii), 
(c I, c2,..., c K) 
where, properly, would be necessary to differentiate functions 
- c K) ~ ~ k. G1, G2, GI< and put c i = G i (c l, c2,.,., ~o~ i = 1,2,... 
Whereas the condition (lO) has been fulfilled quite frequently 
# ~especially at I simple sentences and above all when we weaken it by 
admitting the changed the orderir~ of words W i in comparison with 
words ~i ), i.e. it is often possible to translate word by word as 
for the meani~s of single ~ords, the condition (ll) has nearly never 
been fulfilled. It can be understood, because in the respect of 
meaning the languages do not differ as a matter of fact and this 
matters in (lO), while morphologically and eventually even gran~ati- 
cally sidle languages differ very stro~ly and these facts matters 
in (ll). 
so that 
dependence on the sole characteristic c i 
but in dependence on all characteristics 
it may be written analogically to (9) 
where, of course, hl(W I) = (wi, c i) for i = 1,2,..., k. 
As it is impos~ibie to translate one characteristic after 
another, it is necessary to use instead of the supposed (but in 
general not existing) function g, the more complicated function 
G. This function will not define single characteristics ~i in 
~ul/k 12 
From this also follows that difficulties of impossibility 
of the translation wo~'d by word accordi~ to (8) are - for the 
differentiation of the meaning=- and characteristic - due to the 
characteristic and not to the meahings. This fact has a conside- 
rable heuristic import. It is, ne~mel}', evident that the suitable 
parts into vJhich %re want to decompose the sentences are to be found 
v~ith respect to their significance and not with respect to their 
syntactical or even morphological properties, in this case, namely, 
these parts will be found at the same time in all languages even 
if having been expressed in different lang~uages by different syn- 
tactical an morphological means. It is naturally self-evident that 
between the significance of considered parts and their syntactical 
expressions are close connections (see \[~ 3). 
Because of this, it is necessar3: to introduce, besides ~ 
mentioned characteristics some others more, namely, logical and 
semantical that will be co~uuon for all !ang~uages and will be ojaite 
independent of the syntax of la~uages. And just this condition is 
fulfilled by the logical and semantical questions. 
Under the logical characteristics of v,~ords we understand 
data on the fact ,~vhether and vzhat logical conjuctions or other logi- 
cal means (as quantors or negations) are by these vlords expressed. 
These facts are known from the logical analysis of sentences vJorked 
"% fh -v~ °- 
out by ~. ~a~p. 
By the ser~antical characteristics of ~,~ords ',re understand data 
on the fact ~vhether the given word (v~c suppose v~,ord v,,ith full meaning, 
in no way gra~mmatical or logical v,,ords) plays the role of individual 
constant, or variable i.e. v,'hether it defines a certain otject 
~ullk ,,13 
(here the te~n object is used in the wide sense of the term) or 
ce~ ~a~n propertied, or plays the role of an arbitrary-one with ~-~ 
one-placed predicat, i.e. denotes some property, or of two-placed 
predicat, i.e. denotes two-member relation, or in general n-placed 
predicat, i.e. denotes n-figured relation. 
The situation is not so hopelessly complicated as it would 
seem at the first sight. For instance, the individual constants 
even the variables are only substantives while verbs are always 
predicats one-. two- three- even more placed, according to the 
smaller or greater number of their objects. Adjectives are always 
one-placed predicate a.s.o. 
Besides the mentioned - and in the logic current - it is 
necessary to consider as semantical characteristics data On time 
and place and probably not yet c uite distinctly defined data 
referring to the conditions under which the situation is beir~g 
described (here belong some adverbial modifier). 
Thus, we suppose that We know the function k (analogously 
like h) which to any ~;ord-form W assigns its logical and 
semantical characteristic d, thus, k(W) = d, while again 
d = (yl y2 X 1 , , , ..., y ) where e.g. y is a datum, whether the 
2 word W is the logical functor and of what kind~ y is a datum 
3 wh~ther the word ~i is predicate and how many-placed, y 
a datum of what kind the predicate is, y4 whether there is in ~:l 
the definition of time and of what kind, 
ac.~inl~zon of place and of what type, y 
d,~i..nltion of the condition a.s.o. 
y5 whether W is the 
6 a datum on the special 
~ulik 14 
5- Primitive phrases. 
With respect to the semantical characteristics of v:ords it 
~.L - -- ~ • ,. • is possible and quite n~ural similarly as in the prec~c~te-logle - 
to take as important in a sentence such phrases (i.e. their parts) 
that include always one word playing the role of n-placed predicate - 
so called basic oredicate - in this ~raso (while phrases contain 
n+l v~'ords) and the other words (just in the number n) play the 
role of individual constants or var.a~ies bei~g placed on single 
places (positions) of the considered predicate. In accordance with 
the mentioned it referrs~ in this nhrase, to the denotation of the 
n-membered relation and to the de~o~_on of all n objects that 
are mutual in this relation. Thus, every such phrase is, in fact, 
a c~r~a..~ statement or a definition on the situation, as ~÷ is the 
analogy of the primitive fo~u!a in the mathemazical logic (e.g. 
o~uz~ when we Kno~v that P is P(a!, a2, a 3) is the primitive f ~- ~'~ • 
a three-figured predicate, that Xl, x2, x 3 are individual constants 
placed on their three places, and that the mentione5 record sa~,s that 
the objects denoted by these constants are in relation denoted by 
the predicate P ) we ca 7~ such a phrase the primitive ~h ~,' 
S'~"7'-~_~aneou~!jo ,', -"~ ~s irz~~edmatel~," evident " ~ ~' ~n~ ~ne primitive J.b -- 
phrase need not nave the grcmm~atica! for~ of a sentence, and in 
most cases it really does not ~ have it it ~ .... '~~ ~ ° . ~os ~ morn o~ a sentence 
just when its predicate is a verb and v:hen this verb has not the 
gra~z:atica! -~ ~ ~.o~m of a gerodnd or a participle. For instance ,,a man 
reads a book" is the i~:rimitive phrase in the form of a jr~m~atical 
sentence (here evid~,nt!y ,,reads" plays the role of two-figured predi- 
cat~)~ but ~," ~..u primitive phrase ,,a man reading book" or ,,a man who 
~ullk 15 
is reading a book" has not the form of a sentence even if having 
the same meaning like'the preceeding phrase, because both express 
the same fact. Some other types of primitive phrases are e.g. these 
,,very good" wh~re ,,very" is a one-placed predicate and on the place 
of it stands ,,good" (although in another primitive phrase ,,good 
book" is good itself a one-placed predicate), or ,,reads quickly", 
where a one-placed predicate is quickly a.s.o. 
From these examples there follows that primitive phrases 
correspond with primitive formulas in the predicate logic of higl~er 
order. In the phrase ,,man is mortal" there is evidently concealed 
the universal quantor ,,every" so that this phrase has the same 
meani~ like ,,every man is mortal" and thereby to not a primitive 
phrase but a composed-one. 
With regard to the syntactical side, the primitive phrases 
differentiate on the basis of the characteristics of single words. 
For instance, the sequence of word-characteristics (el, c2, c$) 
where Cl, c2, c~ are such that c I denotes a substantive in 
the first case, c 2 denotes a transitive verb, c I and c 2 
simultaneously coinciding in their components as for the gender 
and nur~ber, and at last c 3 signifies that it referrs to a substan- 
tive in the fourth case, when, in addition, the rar~e of characte- 
ristics sets the future word-order, is the characteristic of the 
primitive phrase ,,a man reads a book" (when an indefinite article 
is a considered not to be self-contained word\] and we assign it 
al~ays to the wol~ suceeding it i~m~ediately). If we, namely, made 
full use of the function h we would get h \[a man\] : \[ man, ci~i\] , 
h \[reads\] = \[ read, cR\] and h \[a book3 = \[ book, CB\] , and 
~ul/k 16 
simultaneousl7 it couls sure hold c~r~:~ = c l, c R = c 2 and c B = c 3 . 
The considered language is, besides its word-store put down 
in the dictionary, characterized also by the list of all charac- 
teristics of primitive phrases. That is what we shall suppose at 
any of the considered languages. 
If we use for the considered primitive phrases. That is 
what we shall suppose at any of the considered languages. 
if we use for the considered primitive phrase ,,a nan reads 
a book" the function k, we get some semantical word-characteris- 
tics d~\[, dy~ and dB, and one of them will be especially distin- 
~ul~n~a as a basic predicate of the considered type of the orimitive 
phrase. In our case it is d R and for illustration we s~all come 
to an agreement that this basic predicate and other sem~ntical 
characteristics will be put down in the same way like it is done 
• in the predicate logic, namely dR(d~,~, dB). Let us call this entry 
the semantical ch~racteristic of the considered phrase and also 
the semantical characteristic correspondi~ with the syntactical 
characteristic (c~ji, CR, c 5) of the considered phrase..~n~lo~ous 
agreements are to be made even with respect to other components 
of th~ semantical characteristic, particularly for the definition 
of time, place and other conditions. 
~;~t the same time, the semantical characteristic comprises 
these facts: d R a dat~n that it refe=rs to the two-figured 
predicate (eventually specialized by ~" ~e denotat~.on of some acti- 
vity), on the first place of which is just the word, with the seman- 
~ica! characteristic d~ i (e.g. ~vith a shpplement ,,agens") and 
~ul!k 17 
he second place of w.~!ch corresponds with the semantical characte- 
o 
ristic d B (eventually with supplement ,,patiens"). Simultaneously, 
the semantical characteristics may be eventually complemented 
with further data, when it turns out to be suitable. It is important 
only, that there are to be data (as it is mentioned in the paren- 
theses) that referr to the meanir~ and that are common for all 
languages. 
Q By the semantival characteristic 
dR(dN, d B) there is put 
down, in the basic semantical categories, just what we want to 
express (By that time the basic forms Read, ~an, Book are fai!ir~; 
~ • these are possible to be chosen differently) whmle the corresponalng 
syntactical characteristic (c~{, cR, c.)~ puts down how to expr@ss 
it. 
Now, the way is evident, how to translate primitive phrases 
from the language L 1 into L 2. There is important that ',~e suppose 
that whatever can be expressed in LI, can be expressed even in 
L 2 what is the basic supposition on the possibility of translating. 
From this there follows for the function of the translation ofl 
words f that for every basic form W from L there exists 
f(W) in L2, and that for ev.ery semantical characteristic 
dl(d2, d3, ..., d n) corresponding with the syntactical characte- 
ristic(cil' ci2' "'" Cin ) in L I there exists the syntactical 
characteristic, correspondil~ with it (Cjl , c j2 , ..., Cjn) in 
L 2 and just this-one (of course they may be several) will be 
declared to b~ the trabslation of the corresponding syntactical 
characteristic from L I. Thereby a further function ~ is defined 
~eventually a many-valued) for which there holds that 
~ul/k 18 
(!4) ~ (Cil, ci2 , ..., Cin)l : (Cjl, cj2 , ..., c. )2 ~n ~ 
wh e (. , )I, ( ..... )~ • . • - have the s~e semantical characteristic. 
: \[w i, ci\] for i : !,2,.., n, 
(c l, c 2,.'., Cn) ! characteristic 
Now, if it is given a or~aitive phrase 
L I we use first t~he function h and we get h \[ (Wi)\] = 
and thus its syntactical 
but now 
(W !, W 2,.-., Wn )I 
(c I, c 2,.-., Cn)! = 
= (Cjl, c j2, ..., Cjn)2 so that 
(15) F~'(WIW 2 ... W n) = (h21~f (W.ol)' Cjl\] h21 \[f(wj2)' cj2\] "'" 
. cj \] ) 
and this is, in fact the needed weakeni~ of the condition ~!~). 
It is evident that the primitive phrase from L 2 on the 
righthand side of the equation (15) has really the same meaning 
as the primit~e phrase on the left-hand of the equation. As for 
~ne meaning of single words~ this is guaranteed by the function ~ 
and as for the meaning o£ the whole phrase, it is guaranteed by the 
function ~ , that luhll-s (14) that here in a special case plays 
the role of the function G, because (!4) and (13) are identical. 
~ulfk 19 
6. Compound phrases. 
The composing of two or more primitive phrases in com- 
pound phrases can be performed by the usual logical means (e.g. 
by means of logical conjunctions "even" or "if,...theno.." even- 
tually of other analogous conjunctions like "but" and similar, 
or by mo~ns of negation and quantors) in a v~ll-known way, or c~n 
be perfomed by the pure linguistic expressive means. Both these 
kind~ may be arbitrarily interchanged by the successive compo- 
sing. 
Similtaneously, it is decisive that the composing of single 
primitive phrases corresponds with the composing of their syn- 
tactical and, of course, semantical chsrac~eristicso Besides, 
there are mostly composed such two phrases that have some word 
in common, or where some word is repeated. This fact is necessa- 
ry to be distinguished especially by composing the corresponding 
rharacteristics, or - what is in substance the sam~- it is necesse- 
r~ ~ to join to ar~ word-characteristic c the symbol express~.ng a va- 
" l riable for the basic for.ms of word, so that we shall write X,c 1 
v,,here we can put for X the real basic forms of words. 
The composing of primitive phroses in compound phrases 
belong to the field of the synthesis of phrases° If we, for 
instance~ want to say that some man reads s book and simulta- 
neously that he reads quickly and~ in addition, that this book 
is good ~nd even very good, we can express it in the following 
cnmound phrases P = (which is zramm~tically the form of the 
sentence) "m~n reads quickly a very good book"° The syntax 
of this phrn~e is n~t evidently ewpress~d b$" the logical means° 
In the considered case the following primitive phrases are 
P1 "Po = " reads quickly", concerned: = " a ma reads a book, 
P~ = "good book" and P4 = "very good"o From these phrases 
the compound phrase is put togethcro If we use the function 
h fcr single words of the considered phrase, we get successively 
h\[a man\]=~man, Cl\] , h\[quicklyl=Lquick, c2.7 , hEreads I =L-read, C3~o.. ' 
,,,,h\[a book\]=~book,, cJ~where Cl, C2,ooo , 0 6 are the correapon- 
dine syntactical characteristics° Analogously when we use the fun - 
ction k we get the semantical characteristics of single words° 
The syntactical characteristics of single (separate) 
primitive phrases PI' P2' P3' P4 are successively CI,C2,C3,C4, 
, , , , , , ,L"3, e3, ) 
C3 = (D?5,C 51 ~ ~W6, c6. I) and C4 = ~:;4' c4.~ '\[WS' c5.~ )° At the 
same time, there is very important that some variables W i occur 
simultaneously in two primitive phrases° Thereby is, namely, 
expressed the circumstance that by these two phraes is told so- 
mething of the same fact and just this circumstance plays the 
decisive role at stating the constents-connection among more phrases° 
If we started from the given phrase " a man quic1~ly reads 
a very good book" we would find the mentioned four primitive 
phrases as follows: first we would use for single words the functi- 
on h and k and then we would find for every word of the mentioned 
phrase, which can be the basic predicate of some primitive phrase 
(it can be found out of its semnatical characteristics and by the 
semantical characteristics of the primitive phraes) further 
words belonging to it in a certain primitive phrase, ioeo which 
take places of the considered predicate and this occurs only 
~ulfk 21 
in comparison of the syntactical characteristics of words 
frcm the given phrase with the syntactical characteristics 
of a certain investigated primitive phrase° 
For instance, in our case~ if we have found out according 
to the semnatical characteristic that the word "reads" is two- 
placed predicate, we would find out the syntactical characteris- 
tics cf such primitive phraes, the basic word of which was 
just the two-placed predicate. Then we have kncwn what syntac- 
tical characteristics of words and - as far as the word-order 
is concerned - where there are to be found, so that we find out 
whether the investigated primitive phrases are in the given phra- 
se included° When finishing it for all these words, we shall find 
it successively for all primitive phrases that in the given 
phrase are comprised° 
In such a way is, namely, depicted the analysis of the 
compound phrase, not composed by the logical means. If there are 
used the logical means, then the given phrase is decomposed 
like in the logic° 
Rut it is necessary to mention in addition, that for the 
economy-reasons and for saving the number of syntactical charac- 
teristics of the primitive phrases, it is convenient to work 
often with incomplete characteristics onlyo The question 
is, whether we shall include two primitive phrases" a man reads 
a book" And "the man read a book" into one (incomplete) 
syntactical characteristic, or into two different and naturally 
complete -ones. The incompleteness wi\]l consist in the failing 
fact on number (and si~ni\]arly it woula be in other phraes with 
data on gender and case), but naturally there would not fail 
~ulik 22 
the datum on coincidence in number between ,,a man" and ,,reads 
or ,,the man" and ,,read" because this fact will be ~.~st decisive 
for the incomplete characteristics. 
The possibility of the use of incomplete syntactical cha- 
racteristics by the synthesis is, of course, also evident. If we 
want to make the whole synthesis of the compound phrase indepen- 
dent on proper meanings of single words, then we can givG in the 
syntactical characteristics neither the gender nor the number, 
because both of them are defined differently no sooner than by 
the choice of the basic form (because in many cases genders are 
steadily fixed). But even here it is not the matter of principle 
but the matter of effectivity. 
7. Sementica! dependence and connectedness. 
As, sccording to the supposition, there is denoted in 
every primitve phrase its basic predicate which always stands in 
front of parantheses in its semantical characteristic (for instan- 
ce at Q(x,y) Q is the basic predicate) it is possible to define 
the semantical dependence among the words of the primitive phrase 
by the demand that the basic predicate a!v~ays depends on all 
other v;ords that occur in ti~e phrase, i.e. on its arguments (e.g. 
Q deoends on x and on y) Just so Ous~ii-ed v~'ould be the defi- 
nition that, on the con~.~r$~° 7, ell argtm~ents depend on the basic 
predicate. 
If we demonstrate this semantical dependence on a diorama, 
_ =~.,~ drav: the connectin C !in~, provided },~ith, an arrow-head, 
directir~ from an argument to a basic predicate• At the same time, 
~ul~k 23 
of course, accordi~ to the position of separate words - if 
they are more to the left or to the right -we discern always 
the word-order. Four primitive phrases from the preceeding 
paragraph are deomstrated in the following diagramm: 
We say that the sem~tical dependence is concerned because this 
relation ~o~ the basic predicate and its arguments, expressed 
just by the theorem that objects denoted by the arguments are 
in relation defined by the basic predicate, is quite initial 
definition referri~ evidently to the reality. The semantical 
dependence does not refer to a~thing else than to the fact of 
te!li~ somethi~ of somethi~ (on the mathematical level the 
fact of telli~ ~l.~ ~ ~,~) can be transferred only on the basic 
relation of the adherence to the set) when one passes from the 
predicate Q to the binary relation Q~ and puts down 
(x,y)@Q~). 
We say further that in the primitive phrase the basic pre- 
dicate is directly connected with any of its arguments, i.e. two 
words of the primitive phrase cohere together when either the 
first depe~s on the second, or the second on the first. ~hen 
illustrating the direct connectedness we can use the s~e diagrmr~ 
like when il!ustrati~ the dependence, but we do not pay attention 
to arrow-heads. Thus, evidently in P "man" is directly connected 

~ulik 25 
by the referrin means (there are e.g. pronouns, definite articles 
and si~:~!ar), but sometimes these are concealed and in this case 
it will be necessary to complete the text (or not to admit such 
a text at all). If there are everywhere the referring means 
expressed, they are possible to be used for further identification 
of the v~ords of single diagran~Is for separate p~ras~s ~analogously 
as it was mentioned at the primitive phrases), and thereby to get 
the diagramms of the semantical dependence, eventually even the 
dependence for the whole text. 
In the case of the whoie-text-diagr&v~ two cases are possible: 
either there is a com~ected graph and then we say that the connec- 
ted text is concerned, or this graph is disconnected and then we 
say that the text is disconnected. But, any disconnected text 
splits, in a natural way, into its connected components and it 
is evident that it will be possible to translate these components 
independently on themselves (because they do not cohere together 
semantically). 
Therefore we can concern only a connected context T. 
According to the section 2 T = (SI.S 2. ...Sk), where S i are 
sentences and we remind that the condition (2) resp.(5) is 
not al!ways satisfied, because e.g. sometimes it is necessary 
to know 3 how the sentence S I was translated, when we want to 
translate correctly the sentence $2~ But now it is simple to see 
that there is exactely one word WI in S I and ~2 in S 2 such that 
W I and W 2 are directly connected° Therefore we may express a hy- 
pothesis that it is sufficient to store same informations con- 
oerning the single word W I instead of the whole translation of S I. 
~ulik 26 
In other words these informations concerning W I are the 
necessary context, when we want to translate conectly $2o 
It is similar in other cases° 
'~at concerns the translation of the particular sen- 
tences which are decomposed into the primitive phrases the 
main principales are described in \[4.\] , because it is easy 
to indtroduced to each primitive phrase a corresponding 
as in a phrase structer grammar il\]o rule 
bullk 2 7 

References

Chomsky ~,On certain formal properties of grammars. 
In o .... ~\]on nnd Control 2(19~9),137-167 

~ulfk K., Some problems in theory of langusg~s (Czech), 
Proceedizgs of 1.conference on cybernetics 1962 (in print) 

~ul/k K., Applicst~on of abstract semantics and theory 
of graphs to polyFlot dictionsries (Russian), ~roblems 
of Cybernetics (in print) 

~ul!k ~ Semantics and Translation of Crantmars snd ALGOL- 
-like lan~u~es,~,ybernetika 1(196~) ,47-49 

Glushkoff V '" SyntLe~is of d~gital ~utomata (R~Jssian), 
~F ~,.os cow 1962 
