Contains research objectives and reports on three research projects.National Science Foundation (Grant GP-2495)National Institutes of Health (Grant MH-04737-04)National Aeronautics and Space Administration (Grant NsG-496)U. S. Air Force (Electronic Systems Division) under Contract AF19(628)-248

Halle, Morris

Lightner, T. M.

Stanley, R. J.

DSpace@MIT

XXIII. LINGUISTICSProf. R. Jakobson T. G. Bever T. M. LightnerProf. J. Kurylowicz J. L. Fidelholtz P. S. Peters, Jr.Prof. M. Halle R. S. Glantz C. B. QuallsProf. G. H. Matthews J. S. Gruber J. R. RossProf. P. M. Postal Barbara C. Hall S. A. SchaneProf. P. Colaclides T. J. Kinzer III R. J. StanleyDr. Paula Menyuk R. P. V. Kiparsky J. J. ViertelDr. W. A. O'Neill S.-Y. Kuroda A. M. Zwicky, Jr.RESEARCH OBJECTIVESThe research of the linguistics groups aims to develop a general theory of languagewhich encompasses all that can be known about language. This theory attempts to revealthe lawful inter-relations existing among the structural properties of different languagesand among the different levels of a given language. As regards subject matter, there-fore, all aspects of language are of interest to our group. Work now in progress dealswith the phonology, morphology, and syntax of a score of different languages and theabstract features of these linguistic levels, with language learning, language disturb-ances and speech perception, with linguistic change (syntactic as well as phonological),with semantics, the philosophy of language and the history of ideas concerning the natureof language, with the poetic use of language and the structure of literary works, with themathematical and logical foundations of linguistic theory, as well as with the abstractstudy of symbolic systems similar to natural languages.Since many of the problems of language lie in the area in which several disciplinesoverlap, an adequate and exhaustive treatment of language demands close cooperationof linguistics with other sciences. The inquiry into the structural principles of humanlanguage suggests a comparison of these principles with those of other sign systems,which, in turn, leads naturally to the elaboration of a general theory of signs, semiotics.Here linguistics touches upon problems that have been studied by philosophy. Otherproblems of interest to logicians - and also to mathematicians - are touched upon in thestudies devoted to the formal features of a general theory of language. The study oflanguage in its poetic function brings linguistics into contact with the theory and historyof literature. The social function of language cannot be properly illuminated withoutthe help of anthropologists and sociologists. The problems that are common to lin-guistics and the theory of communication, the psychology of language, the acoustics andphysiology of speech, and the study of language disturbances are too well known to needfurther comment here. The exploration of these interdisciplinary problems, a majorobjective of this group, will be of benefit not only to linguistics; it is certain to provideworkers in the other fields with stimulating insight and new methods of attack, as wellas to suggest to them new problems for investigation and fruitful reformulations ofquestions that have been asked for a long time.M. HalleA. NOTE ON THE MOTIVATION FOR USING TRANSFORMATIONALRULES IN PHONOLOGYIn the development of liquid diphthongs in South- and East-Slavic,l one can accountfor the insertion of vowels by application of any of the three rules given below:This work was supported in part by the National Science Foundation (Grant GP-2495),the National Institutes of Health (Grant MH-04737-04), and the National Aeronautics andSpace Administration (Grant NsG-496); and in part by the U. S. Air Force (ElectronicSystems Division) under Contract AF19(628)-2487.QPR No. 76 271(XXIII. LINGUISTICS)(1) - + vocal in env: + vocal L C- cons - cons-tense -tense- diff - diffa grave La grave(2) -- + [ vocal in env: vocal LC- cons - cons-tense - tense- diff - diffa grave a grave(3) Struct. Descr: V L C1 2Struct. Change: 12 - 112In these rules we used the following abbreviations:V for any F voc segment-cons-tense- diffL for any + voc segmentS+ consC for any [+ cons] segmentRules (1) and (2) are context-sensitive rewriting rules, whereas rule (3) is an ele-mentary transformational rule. Since all three rules derive doorg from dorg, beergfrom berg etc., the question arises as to whether the context-sensitive rewriting methodor the transformational method of describing this phenomenon is correct.It is clear that rule (3) expresses the linguistic fact of reduplication in a more naturalway than either rule (1) or rule (2) does. Thus the facts are that lax, nondiffuse vowelsare reduplicated in position before liquid followed by consonant. In rules (1) and (2),however, it is necessary to make an additional specification for the feature gravity. 2In terms of reduplication, then, we prefer the formulation of rule (3). It is possible,however, that in terms of the remaining rules of the grammar, one might find reasonto prefer either rule (1) or rule (2) to rule (3), and it is this question that we examinehere.The question will concern the exact place of insertion: in rule (1), the inserted vowelis placed before the original vowel; in rule (2), after the original vowel; in rule (3),the original vowel is reduplicated without specification of position.In arguing for the context-sensitive rewriting rules (1) and (2), one can bring thefollowing facts to bear: Slavic liquid diphthongs with acute accent develop into Russianforms that show stress after the liquid (dorg - dorog); grave accent, however, developsinto Russian forms that show stress before the liquid (birg - b6reg).QPR No. 76 272(XXIII. LINGUISTICS)If one interprets acute accented vowels as being marked [+ accent], and graveaccented vowels as being marked [- accent], then one can propose that rule (1) is cor-rect, and that it must be modified in the following manner:(1') + vocal in env: + vocal LC- cons - cons-tense -tense- diff - diffa grave a grave- accentJThe derivations of Russian dor6g, b6reg are now the following:dorg -1'- do6rg -metathesis- dor6gberg -1'- beerg --metathesis-- beregWe now require a rule that places stress on the first vowel of forms none of whosevowels are accented:bereg - b~regApplication of this initial stress rule will correctly derive stress in forms liken~ bereg (from na bereg). Derivation of forms like za bireg, however, will require usto formulate an additional rule because the underlying form za bereg would giveza bereg. If we postulate that the initial stress rule places stress on the first vowelafter # if the form in question contains no accented vowel, then the underlying form#za#bereg# will give #zi#b6reg#. The additional rule that we propose is that in formswith more than one accented vowel, only the final accented vowel is stressed:#za#b6reg# - za beregIn order to derive na bereg, we mark the root berg for the idiosyncratic feature ofdropping # after the preposition na:#na#bereg# - #na bereg# - ni beregAcceptance of rule (1') has forced us into the position of postulating two additionalrules:(4) Place stress on first vowel after # if the form in question contains no accentedvowels.(5) Place stress on the last accented vowel of any form.The argument in favor of using rule (1) has now disappeared, for, given rules (4) and(5), the correct results can be obtained either from application of a modified form ofrule (2) or from application of rule (3). The modified form of rule (2) is the following:QPR No. 76 273(XXIII. LINGUISTICS)(2') - + voc a l  in env: + vocalcons LC- cons - cons- tense - tense- diff - diffa grave a gravep accent p accentThe derivations of dorog, b6reg, ni bereg and za b6reg resulting from applicationof rule (2') are:dorg -2'-0 doorg -metathesis- dorog -5- dorogberg -2'- beerg -'metathesis- bereg -4- b6regna#berg -2'- na#beerg -metathesis- na#bereg -# deletion-na bereg -- 4- n beregza#berg -2'- za#beerg -metathesis- za#bereg -4-za#b~reg -5- za b6regThe derivations with rule (3) used are identical to those given directly above. Sincethere is no external reason to prefer (1') or (2') to (3), we choose (3) for the reason out-lined at the beginning of this report. Additional confirmation for the correctness of ourdecision can be drawn from the arbitrariness of the formulation of rules (1') and (2'). Ifone restricts the rules of the phonological component to simple rewriting rules, thenthere is no way to choose whether V should be inserted after V followed by L C orbefore V followed by L C - either formulation will derive correct representations. Inthe transformational description, however, there is no question as to whether the insertedvowel precedes or follows the original vowel.T. M. LightnerReferences1. In this paper we assume familiarity with M. Halle and T. M. Lightner, On thephonology of tort, tolt, tert, telt in Old Church Slavonic and Russian, Quarterly Prog-ress Report No. 75, Research Laboratory of Electronics, M. I. T., October 15, 1964,pp. 121-123.2. There is reason to believe that in Russian, all lax vowels - regardless of theirdiffuseness - are reduplicated before liquid followed by consonant. In this case, then,the formulation of rules (1) and (2) requires two additional, unnecessary specifications,one for gravity and one for diffuseness.B. ON THE DEVELOPMENT OF turt tirt tult tilt IN RUSSIANIt is well known that Proto-Slavic turt tirt tult tilt developed into Modern Russiantort tert tolt tolt, respectively. In this report we shall examine evidence indicatingQPR No. 76 274(XXIII. LINGUISTICS)that this historical development did not involve a simple lowering of lax vowels beforeliquid followed by consonant.Any discussion of the development of turt tirt, etc. in Modern Russian is complicatedat the outset by the problem of those forms which have undergone secondary polnoglasie:Vsumerecnyj (cf. sumerki), dolog, polon, bestoloc (cf. tolk), verevka (cf. very'), zolovkaetc. We shall not consider this problem here, but will confine our discussion to clearcases like torg, xolm, tverdyj, pervyj, etc. Also, we shall omit from discussion theChurch Slavic element in Russian.Our proposal is that our earlier analysis of tort tolt tert telt be generalized toinclude all lax vowels.1 Thus we propose the following set of rules:(1) Struct. Descr: V L V1 2Struct. Change: 12 - 112(2) SD: V L C1 2 3SC: 123 - 213In these rules we used the following abbreviations:V for any + tenvocal segment- cons- tensejL for any + vocal segmentC for any [+ cons] segmentFollowing are sample derivations:torg: turg -1- tuurg -2- turugcerkov': cirk -1-- ciirk -2- cirikmerznut': mirz -1- miirz -2- mirizThe later development included the following rules:(3) Sharping of consonants before acute nonconsonantal segments.(4) Desharping of c.(5) Loss of jers. In particular, to strengthen jers before liquid-jer clusters, and weakenjers after jer-liquid clusters. We shall not make this rule precise as it involvesobvious problems. Note, however, that a relaxation of the restrictions of this rulewill permit us to account for the forms with secondary polnoglasie.(6) Desharping of r before dentals.QPR No. 76 275(XXIII. LINGUISTICS)(7) Replacement of e by e before nonsharp consonants and in certain categories, suchas loc. sg. (b, er, ez, e < b, er, ez, e), short form adj. (t, em, en < t, em, en), and in2 pl. pres. (n, es, et, e < n, es, et, e).Following are sample derivations:merznut': miriz -3- m, ir, iz -5- m, er, z -6- m, erz -7- m, erzcerkov': cirik -3- c, ir, ik -4- cir, ik -5- cer, k3T. M. LightnerReferences1. See M. Halle and T. M. Lightner, On the phonology of tort, tolt, tert, telt inOld Church Slavonic and Russian, Quarterly Progress Report No. 75, Research Labor-atory of Electronics, M.I. T., October 15, 1964, pp. 121-123.2. In the development given here we do not make any provision for stages of devel-opment intermediate between Proto-East-Slavic and Modern Russian. Thus, for example,it seems reasonable to assume that at some stage in the development of Old Russian thejer-liquid clusters were pronounced as syllabic liquids; for convincing argument in sup-port of this position, see V. S. Golysenko, K voprosu o kacestve plavnogo v kornjax,vosxodjascix k turt, tirt, tult v drevnerusskom jazyke XII-XIII vv., Istoriceskajagrammatika i leksikologija russkogo jazyka (Moscow, 1962), pp. 20-28. Note also thatthe rules of development given here do not reflect chronological order. Thus, forexample, sharping of consonants (rule (3)) is clearly a chronologically earlier phenom-enon than reduplication of vowels (rule (1)) or metathesis (rule (2)).3. For discussion of the pronunciation of sharp [r,] in forms like cerkov', pervyj,etc., see L. A. Bulaxovskij, Istoriceskij kommentarij k russkomu literaturnomu jazyku(Kiev, 1958), p. 98.C. FINITE STATE REPRESENTATIONS OF CONTEXT-FREE LANGUAGES1. We shall show the existence of a class C of regular (finite state) languages with theproperty that(i) There is a fixed finite alphabet Vo from which each language in C is constructed;(ii) Given any context-free (CF) language L there is a member RL of C such thatRL is equivalent, in some sense, to L. More precisely, there is a single CF languageK and a fixed homomorphic operation p (i.e., a one-state finite transducer 4) such thatfor each CF language LL = (K nR L).The language K and the operation 4 have a very simple and natural interpretation. Thus,while CF languages are a richer class than regular languages, each CF language L stillhas a simple and natural representation in terms of a regular language RL.We have referred implicitly above to "the class of all CF languages"; it is crucialthat we be explicit about the vocabularies from which the terminal and nonterminalQPR No. 76 276(XXIII. LINGUISTICS)symbols for these CF languages are drawn. Let VT be the universal vocabulary fromwhich we pick the terminal symbols of each CF language. The case for which VT isfinite is of most interest, and involves no real loss in generality. We thus assume inthe following discussion that V T is fixed and finite. If, however, VN is the universalvocabulary from which we pick the nonterminal symbols of each CF language, it isapparent that we do lose generality if we let VN be finite; for example, if VN were finite,then the union of two CF languages need not be CF. Thus we shall assume that V N isfixed and infinite.Given this framework, we show the existence of the class C. Our method of doingthis is essentially that of Chomsky, 1 i.e., we associate with each CF language L (moreprecisely, with some CF grammar generating L) a finite transducer TL which takesfinite strings over VT as input. For any given input x, the output TL(x) of TL is thestring x together with a bracketing of x. The set of all outputs TL(x) is a language that,as we will show, has all of the desired properties of RL given above. We cannot, however,use Chomsky's method of constructing TL from L as it stands. The reason is that inhis construction we need, for each nonterminal symbol "A" used in the grammar for theCF language L, two bracket symbols "A[" and " A" in the output vocabulary of TL. Thusthe output vocabulary (call it V ) of the whole class of transducers T L for all CF lan-guages L must be infinite, since VN is infinite. It is crucial, however, in showing thatK is context-free that V be finite. We avoid this difficulty by showing that, notwith-ostanding the fact that V N is infinite, Vo can be made to be finite. We do this by showingthat there is a finite set S of bracket symbols (in fact, a set of 8 bracket symbols) suchthat each single symbol "A[1' or ]A"' for A E V N, can be represented as a (finite)sequence of symbols of S in such a way that the desired properties of the output lan-guages of the transducers TL still hold.Our task, then, is to define a particular CF language K, a homomorphism 4, andan algorithm for associating with each CF language L a transducer TL such that therelation above holds. We proceed in two steps. First, we construct a normalized gram-mar for each CF language. Second, we show how this normalized grammar can be usedto define the instructions for the desired transducer. Except for the above-mentionedmodification our proof is exactly that of Chomsky.The details of the proof may be found in Stanley 2 and in Chomsky.1 In this reportwe describe only the form of the normalized grammar, which is of interest in itself.2. Consider a context-free grammar G that meets the following conditions.(I) Every nonterminating rule of G is of the form A - BC, where B and C aresingle symbols of VN.(II) Every terminating rule of G is of the form A - a, where a is a single symbolof VT.QPR No. 76 277(XXIII. LINGUISTICS)(III) G has no rules of the form A - BB.(IV) If A - BC is a rule of G, then D - CE is not a rule of G for any D, E.Conditions (I)-(IV) allow us to adopt the following notational convention in writingrules of G. Let the members of VN be represented as L 1, L 3 , L 5 , L 7, .. ., andR 2 , R 4 , R 6 , R 8 . .. called L-symbols and R-symbols, respectively, where L. * R.1 jfor all i, j. Then we can write each rule of G in one of the four following forms:L.- LkR R. --L RL. - a R.- a.1 J(V) G contains no pairs of rules of the formLj L.R R - L.R n.j ik m inThat is, an L-symbol L. cannot be dominated in G by both an L-symbol (Lj) and anR-symbol (R ).(VI) G contains no pairs of rules of the formL "- L.R, Rm - L R kj ik m nkThis is simply the analog of (V) for R-symbols.Conditions (V) and (VI) say that any given symbol in G is dominated either byL-symbols or by R-symbols, but never by both.(VII) If G contains the pair of rulesL i. - L.R k L - L.R s ,Spthen, whenever G has a rule L. - L R , G also has the rule L - L R , and con-1 mn p mnversely. Similarly, if G contains the pair of rulesRi - L.Rk ,  R - L.R ,3 p j sthen, whenever G has a rule R. - L R , G also has the rule R - L R , and con-1 mn p mnversely. That is, any symbol that dominates a given L-symbol L. in G dominatesexactly the same pairs as any other symbol dominating L.. (Note that we do not attemptto impose on G a condition on R-symbols analogous to this one on L-symbols.)A context-free grammar meeting conditions (I)-(VII) will be called an a-normalizedgrammar. We can show, by means of a long but fairly straightforward proof, that everycontent-free language can be generated by an a-normalized grammar. Chomsky haspointed out that there is a mistake in his article 3 and that when he refers to a modifiedQPR No. 76 278(XXIII. LINGUISTICS)normal grammar he actually needs a stronger form of normalization. This strongerform is precisely what I have called a-normalization.3. The relation L = .(K n RL) is an important result in the theory of CF languages. Itnot only shows that CF languages can represent aspects of symmetry which cannot berepresented in regular languages (which, perhaps, is intuitively clear), but it alsoshows that this symmetry property is the only property that CF languages have andregular languages do not. This follows from our relation which shows that every CFlanguage L is homomorphic to just those members of some regular language which pos-sess certain properties of symmetry. The properties of symmetry are precisely whatcharacterizes sentences of K, a fact that becomes clear in a complete proof of ourrelation.R. J. StanleyReferences1. N. Chomsky, Formal Properties of Grammars, in R. R. Bush, E. H. Galanter,and R. D. Luce (eds.), Handbook of Mathematical Psychology (John Wiley and Sons, Inc.,New York, 1963); see especially Sections 1. 6 and 4. 2.2. R. Stanley, Finite State Representations of Context-free Languages (submittedfor publication to Information and Control).3. N. Chomsky, Formal Properties of Grammars, op. cit., see p. 374.QPR No. 76 279

Linguistics

http://dspace.mit.edu/bitstream/1721.1/54066/1/RLE_QPR_076_XXIII.pdf

Linguistics

Abstract

Similar works

Full text

Available Versions

DSpace@MIT