Mathematical Institute of Czechoslovak Academy of Sciences^2itnâ 25, Praha 1, Czechoslovakia
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 meaning (the same is told in it) like the given text*
The translation from a natural language into a language L2 is such a function P (in the more general case it is a many-valued function) which assigns to any text T in the language such a text P(T) in the language L2, that f(T) has the same meaning like T0 If we introduce a semantics (or interpretation) M as a function (in general also many-valued) which to any expression e of some language L assigns it3 meaning M £eJ ( compare ), it is possible to say that the function f assigning the texts f(T) from L2 to the text3 T from L-^ i3 the translation only when (1) m[t]= m[f(T)J for any text T from L1.
At the machine (or automatic) translation, the matter is, to define the function f as a mechanizable procedure (i0e, 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 (Do 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<>
The translation F is theoretically - as every function -defined as a set of pairs [t, F(T)] where T runns through all texts in L-p If we really had these pairs practically at disposal, we could use a trivial algorithm of the translation F: we should put in the memory of the computer all the pairs [t,F(T)"' and when being given the starting text T, we should find out in the memory the pair, in the first place of which T would be situated, thus the pair [t, F(T)J , and the demanded translation F(T) would be on the second place of this pair0 This is, of course, not only funny but also impossible.
It seems to be funny because of the fact that to have practically at disposal the pairs [t, F(T)] it would mean to use lively 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)J •
It seems to be impossible because the texts T are too many (it would be possible to admit that infinitely many) and the pairs [_T, F(T)#] could not be included in any computer,, On the other hand, it is necessary to admit that it concerns 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 separated by points, as these parts. Thus, every text T is a sequence
of partial texts, i.e0 sentences S-^, S^.^.S^. so that we may write that T ajjS^, 82,0..,Sk)J o The function of the translation F is, of course, according to the asumption defined for all texts and thereby also for particular sentences S-p S2,...,Sk so that it is possible to construct a somposed text [^(S^) , F(S2),•••»F(Sk)J from the translations of these sentences F(S^), F^), • F^Sk^» that are some partial texts in I^o At the same time, the translations of sentences follow in the same sequence as did the starting sentences in the text T0 It may happen - and we should sure welcome it, if it were always - that it holds
F(S10S2 ..oSk)J = M[(F(S1)oF(S2)..,M(Sk)J .
*'rom (2) there 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, differently than when translating it succeedingly in parts S^, S2 , •.., S^, 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 = (S1oS2o..Sk) in L-^, 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^ was translated, when we want to translate correctly the sentence Sg, becau-
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 as two or more sentences from Lg 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 by 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.
and hence the substantial simplifying of the definition of translation can to be seen. It suffices, namely, to suppose that it is F, that is defined for arbitrary sentences in L1 only (on no account for arbitrary texts when the sentences are a special necessary to define only a partial function F* of the function case of simple texts). Thus, there holds F* (S) = F(S) for every sentence from L, and out of (2) there follows
so that in fact we are able to cope with the function F* when translating the texts.
Similarly, like at the function F, it is possible at the function F* too, to try to give a trivial algorithm making full use of all pairs [_S,F*(S)j • 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 necessary to try to decompose even the sentences in parts, and to translate the sentences in parts, too„
By the decomposition of the translation into sentences there were no difficulties because in printed texs this decomposition into sentences was just ready, and according to the syntanctical means it was possible to decompose its partSo
Of the same simplicity and uniqueness is the decomposition of the sentence S in its single words W-^ W2>0o»,Wk separated by interspaces, so that it is possible to write S = (W^.^W^) like at the te
Besides, the linguists have constructed, a long time ago, a binary translative dictionary from the language L1 into the language Lg» This dictionary is, in fact, defined as a set of the pair of words, the first-one from 1^ and the second-one from L2 having the same meaningolf we denote by f the translation from L, into I*,, where f is again generally many-valued
function (thanks to the homonymy of words) f evidently fulfils the condition (in details see £ 3 j ) (6) I,l[f(W)J= M(W) for every W from Lx .
In whatever way 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, i0e0 if there enters on its input the word W as a sequence of letters 1-^lg • ° which is eventually prolongated by the means of several help-symbols (compare £5 J ) we get on output again the sequence of letters l^l^..,^ , that eventually starts with several help-symbols and simultaneously there holds that (7). f(l1l2o..l(j) = if ^...l* , when W = l-jlg...^, j<k .
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 dictionary..
Taking no account to the fact, in what way the translation of words f is given, one may ask, whether for the sentence S = (W-.W?...W, ) there holds 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 cf words f is the translation of words in basic form only, whereas by the decomposition of the sentence WpWg,o•„7^ are in various word-formso To put it differently : the function f respects only the lexical meaning of words but does not take into consideration morphological questiono«,
However even in the case, the function f could be prolongated 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 in the decomposition of the sentence, yet despite this all - evon under these suppositions - the condition (8) would be fulfilled in the case only, that there are concerned two languages L-^ and Lg that are very strongly cognate, or two dialects of the same language, or in the case and Lg are not cognate, the considered sentence G must be very simple»
The translation fulfilling tho condition analogous to the condition (8) may be called the translation "word by word"0But unfortunately it is known that such a translation is im-
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 end therefore it is necessary to decompose the sentence in another way, at all events in such a way that single parts will contain more than one word (and we suppose, under tacit consent, that the words have full meaning, not only being help-words with the grammer meaning) and that these parts need not be sentenceso 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, where there were no differences between the basic word-form or the mere stem of the word and its various possible formso
4. Syntactical and semantical characteristics of words.
First of all we may suppose that, to every word-form (shape) which appeared in the decomposition of some sentence into words, we are able to define its basic form or stem W (the function f refers just to these basic forms) and its characteristic morphological and eventually even other data referring to the form time, x on mood a.s.o.
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 V/.
Thus, we suppose that there are given functions h and h ~ such that h(W) = (w,c) and h^U^c) = W in each of considered languages (in L-^ and L2 it will be functions h^ and h2).
Although it is well known that the sentence and its translation need not have the same number 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 comment easy) i.e. if it is S = (Wx V/2 ... WK) then
sentence F*(S). The task is, how to get the chain (W^ V/2 ... Y/^-) from the given chain (V/^ V/^ ... V/^) and we know already that it is not possible to get it by means of the translation word by word according to (8) directly.
= (w^, c^) and thus we can oiff erentiate the data (V/-^, W2,..., Wjr) and data (c^, c2, c^).
h2 (W._) = (wi} ci).
Now, it is clear that instead of the condition (8) ought to be the condition because here f is really used for basic forms of words. Then the translation fulfilling (10) 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^O characteristic (c-^, c2, c^). And just here there is impossible except for the most simple example - to find such a function g in order to hold
(11) c. - g(c.) for i = 1,2,..., k.
If it were the case, or in these cases for which the function g could b<3 found, the translation would be easy, because it would evidently hold where, of course, h^(W^) = (w^, c^) for i = 1,2,..., k.
As it is impossible 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 ci in dependence on the sole characteristic ci as it was to be in (11), but in dependence on all characteristics (c^, c2,..., c-^) so that it may be written analogically to (9) where, properly, would be necessary to differentiate functions
Whereas the condition (10) has been fulfilled quite frequently (especially at' simple sentences and above all when we weaken it by admitting the changed the ordering of words in comparison with words 'A'^), i.e. it is often possible to translate word by word as for the meanings of single words, the condition (11) 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 (10), while morphologically and eventually even grammatically single languages differ very strongly and these facts matters in (11).
From this also follows that difficulties of impossibility of the translation word by word according to (8) are - for the differentiation of the meaning and characteristic - due to the characteristic and not to the meanings. This fact has a considerable heuristic import. It is, namely, evident that the suitable parts into which we want to decompose the sentences are to be found with 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 languages by different syntactical an morphological means. It is naturally self-evident that between the significance of considered parts and their syntactical expressions are close connections (see [2.]).
Because of this, it is necessary to introduce, besides the mentioned characteristics some others more, namely, logical and semantical that will be common for all languages and will be quite independent of the syntax of languages. And just this condition is fulfilled by the logical and semantical- questions.
Under the logical characteristics of words we understand data on the fact whether and what logical conductions or other logical means (as quantors or negations) are by these words expressed. These facts are known from the logical analysis of sentences worked out by H. Carnap.
By the senmantical characteristics of words we understand data on the fact whether the given word (we suppose word with full meaning in no way grammatical or logical words) plays the role of individual constant, or variable i.e. whether it defines a certain object (here the term object is used in the wide sense of the term) or an arbitrary-one with certain propertied, or plays the role of one-placed prédicat, i.e. denotes some property, or of two-placed prédicat, i.e. denotes two-member relation, or in general n-placed prédicat, 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 prédicats 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 quite distinctly defined data referring to the conditions under which the situation is being described (here belong some adverbial modifier).
Thus, we suppose that we know the function k (analogously like h) which to any word-form W assigns its logical and semantical characteristic d, thus, k(W) = d, while again whether the word :'■/ is predicate and how many-placed, yJa datum of what kind the predicate is, y^ whether there is in W the definition of time and of what kind, yy whether W is the definition of place and of what type, y^ a datum on the special definition of the condition a.s.o.
5* Primitive phrases.
With respect tc the semantical characteristics of words it is possible and quite natural - similarly as in the predicate-logic -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 predicate - in this phrase (while phrases contain n+1 words) and the other words (just in the number n) pluy the role of individual constants or variables being placed on single places (positions) of the considered predicate. In accordance with the mentioned it referrs, in this phrase, to the denotation of the n-membered relation and to the denotation of all n objects that are mutual in this relation. Thus, every such phrase is, in fact, a certain statement or a.definition on the situation. As it is the analogy, of the primitive formula in the mathematical logic (e.g. P(an, a^, a-,) is the primitive formula when we know that ? is a three-figured predicate, that x^, x2, y~- are individual constants placed on their three places, and that the mentioned record says that the objects denoted by these constants are in relation denoted by the predicate P ) we call such a phrase the primitive phrase.
Simultaneously, it is immediately evident that the primitive phrase need'not have the grammatical form of a sentence, and in most cases it really does not have it. It has the form of a sentence just when its predicate is a verb and when this verb has not the grammatical form of a gerodnd or a participle.. For instance „a man reads a book" is the primitive phrase in the form of a grammatical sentence (here evidently „reads" plays the role of two-figured predicate), but the primitive phrase „a man reading book" or „a man who 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.
From these examples there follows that primitive phrases correspond with primitive formulas in the predicate logic of higher order. In the phrase „man is mortal" there is evidently concealed the universal quantor „every" so that this phrase has the same meaning 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 (c^, c2, c^) where c^, c2, Cj are such that c-^ denotes a substantive in the first case, c2 denotes a transitive verb, c-^ and c2simultaneously coinciding in their components as for the gender and number, and at last c^ signifies that it referrs to a substantive in the fourth case, when, in addition, the range of characteristics' 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 always to the word suceeding it immediately). If we, namely, made full use of the function h we would get h £a man} = [ man, c^l, h [reads} = [ read, cR] and h [a-book"} = [ book, Cg j , and simultaneously it couls sure hold c^ = c^, cR = c2 and Cg = c^ .
The considered language is, besides its word-store put down •in the dictionary, characterized also by the list of all characteristics 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 man reads a book" the function k, we get some semantical word-characteristics dir, d- and d-., and one of them will be especially distin-guished as a basic predicate of the considered type of the primitive phrase. In our case it is d^ and for illustration we shall come to an agreement that this basic predicate and other semantical characteristics will be put down in the same way like it is done •in the predicate logic, namely d^(dT., dg). Let us call this entry the semantical characteristic of the considered phrase and also the semantical characteristic corresponding with the syntactical characteristic (c,., c-o, c,- ) of the considered phrase. Analogous agreements are to be made even with respect to other components of the semantical characteristic, particularly for the definition of time, place and other conditions.
At the same time, the semantical characteristic comprises these facts: d^ a datum that it referrs to the two-figured predicate (eventually specialized by the denotation of some activity), on the first place of which is just the word, with the semantical characteristic d,.r (e.g. with a supplement „agens") and "he second place of which corresponds with the semantical characteristic dg (eventually with supplement „patiens").
By the semantival characteristic d^Cd^, dß) there is put down, in the basic semantical categories, just what we want to express (By that time the basic forms Read, Man, Book are failing; these are possible to be chosen differently) while the corresponding syntactical characteristic (c... Cr>, a-.) puts down how to express • it.
Now,-the way is evident, how to translate primitive phrases from the language into L^. There is important that we suppose that whatever can be expressed in L^, can be expressed even in 1>2 what is the basic supposition on the possibility of translating. From this there follows for the function of the translation of. words f that for every basic form W from L there exists, f (V/) in L2, and that for every semantical characteristic d-^dg, d-j, dn) corresponding with the syntactical characte-
Jl J2 Jn L2 and just this-one (of course they may be several) will be declared to be the trabslation of the corresponding syntactical characteristic from L^. Thereby a further function is defined
v/hen (.....) , (.....)** have the saine semantical characteristic.
(15) F*(W,W? ... W ) = (h^ff (w, ), c, 1 hi
and this is, in fact the needed weakening of the condition (12).
It is evident that the primitive phrase from L2 on the righthand side of the equation (15) has really the same meaning as the primiti/e phrase on the left-hand of the equation. As for the meaning of single words, this is guaranteed by the function f and as for the meaning of the whole phrase, it is guaranteed by the function y , that fulfills (14) that here in a special case plays the role of the function G, because (14)' and (13) are identical.
6. Compound phrases.
The composing of two or more primitive phrases in compound phrases can be performed by the usual logical means (e.g. by means of logical conjunctions "even" or "if,...then0.." eventually of other analogous conjunctions like "but" and similar, or by means of negation and quantors) in a weLl-kncwn way, or con be perfomed by the pure linguistic expressive means. Both these kir.de may be arbitrarily interchanged by the successive composing.
Similtaneously, it is decisive that the composing of single primitive phrases corresponds with the composing of their syntactical and, of course, semantical characteristics. Besides, there are mostly composed such two phrases that have some word in common, or where some word is repeated. This fact is necessary to be distinguished especially by composing the corresponding rharacteristics, or - what is in substance the same- it is necessary to join to any word-characteristic c the symbol expressing a variable for the basic forms of word, so that we shall write X,c-^J where we can put for X the real basic forms of words.
The composing of primitive phrases in compound phrases belong to the field of the synthesis of phrases. If we, for instance, want to say that some man reads a book and simultaneously that he reads quickly and, in addition, that this book is good and even very good, we can express it in the following compund phrases P = (which is grammatically the form of the sentence) "man reads quickly a very good book"0 The syntax of thin phrase is n^t evidently expressed by the logical meanse
In the considered case the following primitive phrases are
h for single words of the considered phrase, we get successively ding syntactical characteristics,. Analogously when we use the fun -ction k we get the semantical characteristics of single words0
The syntactical characteristics of single (separate) primitive phrases P^, P2 , p_, P. are successively C,,C2,C-,CA, same time, there is very important that some variables 77^ occur simultaneously in two primitive phrases <, Thereby is, namely, expressed the circumstance that by these two phraes is told something of the same fact and ju3t this circumstance plays the decisive role at stating the constents-connection among more phrase
If we started from the given phrase " a man quickly reads a very good book" we would find the mentioned four primitive phrases as follows: first we would use for single words the function 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, i0e0 which take places of the considered predicate and this occurs only 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 characteristics cf such primitive phraes, the basic word of which was just the two-placed predicate. Then we have known what syntactical 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 phrase includedo TA"hen 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.
But it is necessary to mention in addition, that for the economy-reasons and for saving the number of syntactical characteristics of the primitive phrases, it is convenient to work often with incomplete characteristics only., 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 will consist in the failing fact on number (and similarly it would be in other phraes with data on gender and case), but naturally there would not fail
the datum on coincidence in number between „a man" and „reads or „the man" and „read" because this fact will be just decisive for the incomplete characteristics.
The possibility of the use of incomplete syntactical characteristics by the synthesis is, of course, also evident. If we want to make the whole synthesis of the compound phrase independent on proper meanings of single words, then we can give 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. Semantical dependence and connectedness.
As, according 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 defin the semantical dependence among the words of the primitive phrase by the demand that the basic predicate always depends on all other words that occur in the phrase, i.e. on its arguments (e.g. Q depends on x and on y). Just so justified would be the defi nition that, on the contrary, all arguments depend on the basic predicate.
If we demonstrate this semantical dependence on a diagramm ■"c always draw the connecting line, provided with/an arrow-head, directing from an argument to a basic predicate. At the same time of course, according to the position of separate words - if they are more to the left or to the right -we discern always the word-order.
We say that the semantical dependence is concerned because this relation among 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 referring evidently to the reality. The semantical dependence does not refer to anything else than to 'the fact of telling something of something (on the mathematical level the fact of telling Q(x,y) 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 0.* and puts down
We say further that in the primitive phrase the basic predicate is directly connected with any of its arguments, i.e. two words of the primitive phrase cohere together when either the first depends on the second, or the second on the first. When illustrating the direct connectedness we can use the same diagramm like when illustrating the dependence, but we do not pay attention to arrow-heads. Thus, evidently in. P "man" is directly connected (x,y ) ).
with "reads" but is not connected with "books" a.s.o.
But if there is given the phrase and if we have found all .its primitive phrase's, then it often happens that some word of the given phrase, will occur (come up) in several primitive phrases. This evidently signifies that we are justified to identify the repeated words (naturally not always)occurring in different primitive phrases of the same sentence, and that is what we do by illustrating it on diagramm. In the considered case of the sentence "a man reads quickly a very good book" we get on to the diagram:
In this way, there are defined the semantical dependences among single words of the given sentence. The connectedness (no more direct) among single words of the sentence will be introduced in the way, common in the theory of graphes, namely, the words x is connected with the word y in the phrase P when there exists a finite sequence of the words of the sentence P, z^, z^j zy such that = x, z^ = y and that z^ and zj_+]_ immediately cohere together for any i = 1,2,..., k-1.
Finally, if there is given the whole text consisting of single phrases, to which we have found their diagramms of the semantical dependence or connectedness, then often would happen that in the succecing phrases the same objects are spoken of, like in the preceeding-ones. Sometimes, this fact is distinctly expressed by the referrin means (there are e.g. pronouns, definite articles and-similar), but sometimes these are concealed and in this case it v/ill be necessary to complete the text (or not to admit such a text at all).
In the case of the whole-text-diagramm two cases are possible: either there is a connected graph and then we say that the connected text is concernée, 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.
.sentences and we remind that the condition (2) resp.(5) is not allways satisfied, because e.g. sometimes it is necessary to know, how the sentence S-^ was translated, when we want to translate correctly the sentence S2? But now it is simple to see that there is exactely one word W in S1 and \\ in S2 such that V/
In other words these informations concerning V/ are the necessary context, when we want to translate conectly S2 » It is similar in other caseso
What concerns the translation of the particular sentences which are decomposed into the primitive phrases the main principales are described in J*4 ~] , because it is easy to indtroduced to each primitive phrase a corresponding rule as in a phrase structer grammarjl |„
LITERATURE
Chomsky II,On certain formal properties of grammars. Information and Control 2(19^9),137-167 Culik K., Some problems in theory of languages (Czech), Proceedings of 1.conference on cybernetics 1962 (in print) Culik K., Application of abstract semantics and theory of graphs to polyglot dictionaries (Russian), A'roblems of Cybernetics (in print) Cullk K., Semantics and Translation of Crammars and ALGOL-like languages,Kybernetika 1(196?),47-49
Glushkoff V.l.'., Synthesis of digital automata (Russian), Iwoscow 1962