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<Paper uid="C69-5401">
  <Title>apos;ules * S ----~AB A -----~ CD A -----.'- D</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Adrian Birb~eeu
4./NTaOOO~ -/'/ ON.
</SectionTitle>
    <Paragraph position="0"> It is an esmontl~, cha~acteristic of nat~al languages that one uox~l oan be concatenated mt~h certain others to form a et~Ing tha~ enters in correct phrases of the language, whale it cannot be eo~atamated ui~h othe~s. The same holds true for e~rlng~ of words. Such eoncatenable elements axe also &amp;quot;mutually eompatible elements&amp;quot; in the sense used b 7 KVAL in a paper doso~ib~n8 an aleori~ for formi~K naxlnum classes of such elements~ Mathematically, a set of ordered pa~s of such &amp;quot;s~tvall~ C/ompatPSble elements&amp;quot; forms a x~latPS~. Ever 7 string Of ~ords belonging to a langua~ can be ~esax~d as being obtained by euoceesive oo~oatenatton of ordered pair8 of mttuall~ oompatPSble elements, i.e. as formed by eueoessive oonoatenation of elements of binary relations be~ to the languase, Some of these string e~e the phrases of the la~ua6e. It is thu possible to define a ~a~ mar of ~elation- and 6ene~ate by it all phrases of the lan~m~.</Paragraph>
    <Paragraph position="1"> If ue tx~ to describe by a ~ this gene~atlon~ the ~aph will be a network desc~Iblz~ the mhole system of lan~uaKe under oonsidex~t ion, The equivalence between a g~am~a~ of relations and an lO-~a~ma~ and the equivalence between a gPS~m~r of ~ela~ions and a oategortal 8x~mmu~ ~ a\]~mst self-evident.</Paragraph>
    <Paragraph position="2"> B~ usi~ the notations for union, interseotion and Oartesiam prod~ct it is imssible to urite one single formula~ however - 2 cumbersome, containinK all phrases belonKinK ~o the ~ under oonsidoratton, This formula wan also bo inte~tareted as dos crlb~m~ an electrical network uhloh will be t~e eleotwlcal analogus of the language, Lot L i and T. 2 be two lan6~ages. Lot N(L I), ~osp N(L2) be the elec~Tlcal networks uslg~d to LI, z~sp L2e It is posslble to devi~e a systel of eleo~ioal oonneotlons between N(~) and N(L 2) such as to obtain eleo~a117 the ~latlon of a phrase belonging to L 2. Let's aall thls method &amp;quot;analogue ~anslation&amp;quot;. Because of the ~oat numbex- of elononts involve4, the oonst1~action of a oomplete ~tom for analogue ~nsla*rlon m~7 be impractioal. Howevert the oo~astr~otPSon of partial neLlorks for simulating translation of a linitod numb~ of phEases mat l~ovo itself useful for delonat~atlonal \];narposos.</Paragraph>
    <Paragraph position="3"> 2. ~SFIN~ION5 i. Let V be a Vooab~LL~WYp that is a set the elementsof whioh a~o words. Assooiste d with the voaabula~ is a operation called oono~tonation which oenmists of writlug one or more words al, a2.,..a k one afte~ another, The resultln~ sequonoe al a2... a k 4- a ~0 By extension we shall call string also a sequence oontainlng one sln~le word.</Paragraph>
    <Paragraph position="4"> The empty word ~ is cbsx~ote~tsed b~ ail = ~ a i = a i fox' ovory ai~ Ve ~me B1;r~lJ U ~33 be oa33edrBontoD~0Be The set of all sentences generated on V is t~ 7 definition the ~ Lo By ~ax~ar G we shall undez~tand a set of rules by which it is possible' to generate the language L.</Paragraph>
    <Paragraph position="5"> Let the set of rules oo~sist of the followln~  - lists elasslf~is~ all words and stria into sets called categories ; - rules of the forn where~,~i ana~/,(~.l...n), are aatesor~s, and ~ o~ared s~r~ aPSj bPSk * We adair that an:v ~i or~/ day contsdn one single word, or even only the empty word ~ ! - a list of the categories which are sentences.</Paragraph>
    <Paragraph position="6"> ~. Z~AMPIJ 1. Let the gzamaar G R be defined by - the voeabula~ v = ~ poor, dear, Jo~-, Ri~=a, sleeps, re.~, ~} , - the eategc~ies - the rules - ~he llst of sentences c~aAz~Iz~ online) deg .</Paragraph>
    <Paragraph position="7">  In this simple case, the rules are of form (~), with i=l. Now, stax~ln~ froa ~, by successive substitutions we obtain .-, . (~: The sOt ~iS thus oomposod of 12 ordered pai~s and triplets. Wrttt~ down ~he strlngs associated ~o these paJ~s an~ triplets we enwaerate the sentences of the language L(~) generated by  ~ion a binary relatinn on V.Sinilarly, if V 2 is the set of all strings obtained by the ,on,arena, ion of two words (&amp;quot;etrlnge of 2&amp;quot;), then ~ is a blna~ relation ~ ViU V. These relations have d~eot lAub~istlo in~e~p~e~atlonm, for ~ aa~ be ~e~Waz~d as the ~elatPSon be~leen adjective and nom~ 0 whale is the relation be~een nmm ~oup and verb. Of course, these simple inte~-~tationm a~e valid within the flailed exposed above.</Paragraph>
    <Paragraph position="8"> For convenAenee of des,rip, ion, in what follows we shall c~ll a g~a~ma~ of the type 4eflned in 2p o.K, (~R in example I, a ~A-a~ of relations, Sets lAMe ~ and Y in example i are sots of ordered pai~s of strlnss whose oonoatenation leads ~o o~her e%Tinss that can belon8 to sentences of the language under oonsideEatlone Conc~tenable elements are also oomDatible elements, by oompatibili~y underetandln6 a eimmet~io nontEansitlve relation. P~gardsd as such 0 these elements can be olassifled into olasseeo one of whioh is aaxiaal, by means of an algoPSitha developed by KARI~REN ~1~ . We are Interested to classify ooncatenable eleaents by laposln~ the restriction, that follows.</Paragraph>
    <Paragraph position="9">  5. DEFINITION 2. Two categories ~, d~ 2 are called dlfferent if there is at least one third catesoz~ such that, a) either - 5 alb is a stx.ing contained in a~ leaat one sentence of lan~ap, i.e. alb belongs to a categor7 of the langu~e, fox eve~ al~ 1 0 b ~ ~ , while a2b is contained in no sentence of ~he l~e. which ever would be a 2 , b , b) me a2b Is a stri.~g oontalned in at least one sentence of the la~. for evex 7 a2~ ~, b~ ~ . while alb is oon~alned in no sentence of the language, which ever would be 6. EXAMPLB Re Let's oonsider ~ follceing relations  atlnts, e e e~ Ac~rding tO definition 21 ~4and ~ are of different cateKoriee since them exist in English catesories ~.t= I sees..ants, coaes, reeds, sleeps. &amp;quot;''3 ~= { see. ,ant. coae. read. sleep....</Paragraph>
    <Paragraph position="10"> such ~hat the Engllsh language, while be a x~tlon belon~m~ to the ~%~h gx~mm~.</Paragraph>
    <Paragraph position="11"> 7. ~OR~. F~ every ~a~a~ of relatic~s we ~ find an e~aivalen~ lC-~a~a~ (i~ediate-constit~en~ ~am~ar) and conve~asl~.</Paragraph>
    <Paragraph position="12"> - 6 - null The proof followl iemediatel~v f~a ~ observation that a~ rule of the fona (1), PS.o.</Paragraph>
    <Paragraph position="13"> can be substtbuted by the followlag set of ~Krsmns~ rules  and convorsol~.</Paragraph>
    <Paragraph position="14"> in a grammar of relations, eorresponds a termiaal of the equivalent I~-~ and oonversoly.</Paragraph>
    <Paragraph position="15"> 8. REMARK 2. From %he equivalence beCween a K~amma~ of relations and an IC-~-amma~ i~ folloues also the equivalenoe between a ~auma~ of relations and a oateKorial Kz~um8~. The . nocessax'y proofs can be found in BAR-HILLEL, ~AIFHAN and SHAMIR  b) In the oquPSvalent oategor:Lal grammar t - poo~ t dea~ a~e of oategox 7 n/n - John~ Rl~ha~d are of cateKor 7 n - Sleeps, reade are of catessry ~\~ - S is the sentence oateKory.</Paragraph>
    <Paragraph position="16"> Io. GRAPH\]EAL REI~ESENTATION. We shall associate to each gEaRma~ of relations a graph, obselwing the following conventions! - each path must be followed from the extreme left to the extreme ~tght, along the arrows ; - a sentence is a sequence of words found along a path.  Thus, the ~aph correspondlng to g~ammar ~ in example i</Paragraph>
    <Paragraph position="18"> An example given by the author for the ~reneh language i-\[4j ie</Paragraph>
    <Paragraph position="20"> Such graphs are called networks. An earlier example is to be found in MARCUS ~53 , Taking into @onsideratioa what has already been written at ~ (ie. in remark 4 ) , the above graphs oan be remarried as networks of binar~relatioms. Th~ desoribe not only sentence structures, but also the whole system of the language, Now we shall simplify the graph (~) without altering i~  ii. ELECTRICAL ANAIDGUES. If ~ g~aph like (6) or (7) is considered to be aa electrical diagram where oath word is substitut~ by a contact, and each arrow by an electrical conductor (wire), the result is u electrical analogue of the grammar. In this analogue if ome cIsses all comtee~8 correspomdlng to a semtemce, a contimuous electrical path is established and the curremt flows from ome extremity to the other. The detectiom of thim eurran@ is a proof of &amp;quot;grammaticality&amp;quot; for the word sequence under consideration. Electrical analogues can be designed also algebraically. For this it is necessary to proceed ~S ~o//Q~/~ from the list of sentences ~, ~2, .... ~/~ 8tarttng</Paragraph>
    <Paragraph position="22"> - replace each~/and esch~iby the corresponding rules of type (1),and so on until the ~lght member of the formula contains only the words of the vocabulary. Such a formula is (2) in example 1' We have now at our disposal a formula enumerating the ordered n~ples associated to all sentences of the language L. This formula is to be interpreted in terms of switching algebra as follows s - an n-#~ple (Sl,a2,..degs r) correspon~to a series connection of the elements al,s2,...ar ! - the union 6 ~/ correspond~ to s paralel connection of the</Paragraph>
    <Paragraph position="24"> In \[#\] is presented an electrical analogue of the grammar described by graph (7).</Paragraph>
    <Paragraph position="25"> 12. GRAPHS OF TRANSIA TIONS~ This chapter and the following are intended as su~ested applications of the above discussion, to the understanding of the process of translatlon. No attempt is ma@f to start from more rigorous definitions, 85 may be found for e~pie in /6\] or \[7\] * Here the process of translation of a simple sentence from language L I , into language ~, is regaz~led as consi% ring of the following operations s a) seek the given sentence in the d/ctionsry ~-~ | i b) if the whole sentence is found in the d/otionary, write e~ down the translation found there and ~ the process | c) if tBe sentence is not found in the dictionary, divide it into two subst~i~gs admitted by the gra-..sr (in fact, immediate constituents) ! d) seek each of the substr/ngs in ~he dictionary | - 11 e) if one substrlag is found in the dictionar~, write down its translation as given in the ~ctto.ar~ ! f) if one substring is not found in the dictionar~, divide it again into two further substr~ngs and then proceed again as indicated under d) ! 6) the prooess stop~ when a strin6 is obtained which contains only words belonging to the vocabulary of the language L2. A difficulty rises currently during the process of translation, and this is due to the fact that many words, or strings composed of more than one wo~d , admit two or mo~e translations.Such is the case with homonyms. Special subroutines have been developed to solve t~e problem of homonyms in digital translation of language. Suoh subroutines are based on successive step, of conditioned decisi~ To quote only a few very simple examples, MARCUS , in \[8J ,gives ske~ ohes of algorithms for translating into Roumanian &amp;quot;example&amp;quot; and &amp;quot;this &amp;quot;and for solving the homonymy of the French &amp;quot;pas&amp;quot; or ~he English &amp;quot;this&amp;quot;deg The problem is related to that of sequential unde1~standing of s sentence, as described by ZIEREH \[9\] * Let us put the DEoblem somewhat differently. To choose the writs word (or subst~i.~ between more than one possible variants, we need some supplementary condition, or conditions. A first and most important condition is that the right word (substT~g) must match grammatically the other words (subst~ings) in the string. That is to say that the right word (string) must form with another word ~subet~iag) in the string an ordered pair belonging to a certain rela. tion accepted by the grammar of the language ~. In the graphical representation suggested above, the right word (subst~,ng) must find itself on a continuous path with the other words (substr~gs) contained in the translation of the sentence under consideration, For example, let L I be the Englis~language and ~ the French. Let the sentence in L I be &amp;quot;we see the bo~'. It must be - 12 divided into (we see) (the boy). Putting side by side the correaponding parts of the English and French graphs, and marking by do~ ted lines the mapping defined in the dictionary, we can draw for the first substr/ng the graph  There are cases when the condition of gra~latioality is. not sufficient. Then a human translator,uses supplementary information, like general knowledge of the subject treated in the text, style used etc. Graphically, such information may be taken into account, for example, by assigning different colours to different types of subject Then the diagram must close through paths of different colour.</Paragraph>
    <Paragraph position="26"> - 13 13. ELECTRICAL TRANSLATION. Let us assume now that we have at our disposal an electrical analogue N(L I) of the language ~, and an electrical analogue N(~) of the language L 2. We can further immaglne such an electrical connexion between the two analo~-ues that when a contact &amp;quot;ai&amp;quot; closes in N(LI) ~ all contacts corresponJding to the different possible translations of &amp;quot;ai&amp;quot; indicated by the dictionary ~-~2 are closed in N(L2). Then, when a continuous path of contacts is closed in N(L I) , its translation can be only a continuous path resulted in N(L2). For the selection pf ~he type of subject or of the style used, we can devise a switch that makes only the corresponding connections between N(L I) and N(~), or in N(~) and N(L 2) themselves. Such a mwitch may have, for ex~nple, positions marked * literature, mechanics, electricity, electronics, chemistry, medicine etc.</Paragraph>
    <Paragraph position="27"> Some texts may contain sufficient information to enable the above switch to find automatically its right position. This idea ~serves an entirely separate discussion.</Paragraph>
    <Paragraph position="28"> 14. CONCLUDING R~ARKS. What was suggested under 13 and 1@ are in fact examples of cabled logic. The implementation of these ideas for an entire language may encounter tremenduous technical difficulties. Designing graphs and electrical analogues for limited parts of language may prove however useful for demonstrational purposes. Thus it would be possible to achieve other models of language understanding and translation than those provided by digital programs and cunputers. The author feels that this is indeed interesting, far as explained by ZIERE~ \[9~ ~ the process of understanding must not be actually as divided into elementary steps as in an algox~thm -- &amp;quot;Dazu kommt noch dass beim Verstehen der gesprochenen Sprache dutch den Menschen auch der soziale Kontext und das Erlebnisverm~en des Menschen zum Abbau der angebotenen Information bei~gt. - 14 Hierin ist der, Computer dem Menschen unterle~en&amp;quot;.</Paragraph>
    <Paragraph position="29"> Another author, SAUVAN \[lo~ , disoussing other subjects, believes that a Sequential computer cannot treat adequately a combJ~atc rial problem for it has no possibilities of global perceptions &amp;quot;L'auteur est persuad6 que lee recherehes doivent s'orienter vers le~ logiques o~bl6es semblables aux structures e@~brales&amp;quot;.</Paragraph>
    <Paragraph position="30"> - 15 -</Paragraph>
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