Contains research objectives and reports on one research project.National Science Foundation (Grant G-7364)National Science Foundation (Grant G-13903

Chomsky, A. Noam

Halle, Morris

Jakobson, Roman

Postal, P. M.

Contains research objectives and reports on one research project.National Science Foundatio

Chomsky, Avram Noam

Parikh, R. J.

DSpace@MIT

Linguistics

XXV. LINGUISTICS*Prof. R. Jakobson Dr. Paula Menyuk D. T. LangendoenProf. A. N. Chomsky A. R. Carlson T. M. LightnerProf. M. Halle J. A. Fodor Krystyna PomorskaProf. L. M. Kampf C. Fraser P. M. PostalProf. A. L. Lipson Barbara C. Hall J. ReitzesDr. G. H. Matthews J. J. Katz D. E. WalkerS. J. KeyserRESEARCH OBJECTIVESThis group sees as its central task the development of a general theory of language.The theory will attempt to integrate all that is known about language and to reveal thelawful interrelations among the structural properties of different languages as well asof the separate aspects of a given language, such as its syntax, morphology, and pho-nology. The search for linguistic universals and the development of a comprehensivetypology of languages are primary research objectives.Work now in progress deals with specific problems in phonology, morphology, syn-tax, language learning and language disturbances, linguistic change, semantics, as wellas with the logical foundations of the general theory of language. The development ofthe theory influences the various special studies and, at the same time, is influencedby the results of these studies. Several of the studies are parts of complete linguisticdescriptions of particular languages (English, Russian, Siouan) that are now in prepa-ration.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 modern logic. 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.R. Jakobson, A. N. Chomsky, M. HalleA. ON THE LIMITATIONS OF CONTEXT-FREE PHRASE-STRUCTURE DESCRIPTION1. IntroductionAlthough the term "phrase-structure grammar" appears widely in linguistic litera-ture, it is, considered from the formal point of view, ambiguous. In fact, multiply so.*This work was supported in part by the National Science Foundation (Grant G-7364and Grant G-13903).231(XXV. LINGUISTICS)Chomskyl has considered two types of phrase-structure systems. One of these consistsof productions of the form 'a --- B', where a is a single symbol and B is a non-nullstring distinct from a. Since each of these is to be interpreted as the instruction"rewrite a as B," this type of system consists of rules that are free of context restric-tions. That is, the rewriting of a is not determined in any way by the surroundingsymbols of the string in which a is embedded. A finite set of rules of this form iscalled by Chomsky a "context-free phrase-structure grammar," and languages that canbe generated by such grammars are called "context-free languages."Mohawk is one of the five living Northern Iroquoian languages and is spoken by sev-eral thousand people in Canada and New York State. The chief purpose of this reportis to show that Mohawk is not a context-free language. That is, it is impossible toconstruct a finite set of context-free rules that will enumerate all, and only, Mohawksentences. It has been proved by Chomskyl that the language consisting of all and onlythe strings /anbmanbmccc/ is not a context-free language, and a similar, althoughmore complicated, proof yields the same result for the general case, that is, for thelanguage /XX/, where X is a variable over strings of arbitrary length. All of thesentences of such a language have a dependency structure like that shown in Diagram 1,in which xn+i must equal xi for all i.DIAGRAM 1x . . . . xn xn + . . xn + ral a2 a 3 ' \an a 1 a2 a3 anX XWe shall demonstrate that Mohawk lies outside the bounds of context-free description byillustrating that it contains, as a subpart, an infinite set of sentences with the formalproperties of the language /XX/.2. DemonstrationA simple Mohawk sentence may consist of a subject noun, a verb, and an object nounin that order. A noun consists of a noun prefix, a noun stem, and in some cases a noun232(XXV. LINGUISTICS)suffix. A verb consists minimally of a pronominal prefix, a base, and a suffix. Hencewe have sentences likeEl kaksa?a kanuhwe? s ne- kanuhsa? 'the girl likes the house'1 2 13  4 15116 7 8 1Here,1 = noun prefix 6 = article2 = noun stem 'child' 7 = noun prefix3 = pronominal prefix 8 = noun stem 'house'4 = base = verb stem 'to like' 9 = noun suffix5 = suffix = serial aspectIt should be noted that the base constituent of the verb in E 1 is simply a verb stem.However the base constituent may also consist of an incorporation marker plus a verbstem. That is, one of the rules of the grammar isBase - (linc) + Verb Stemin which the parentheses indicate an optional element. And there is an interestingtransformational rule that incorporates the noun stem of the object of a sentence likeE 1 into the verb by substituting the noun stem for the incorporation marker. In thesecases the base constituent then has the structure: Noun Stem + Verb Stem. Thusthere are sentences likeE2 kaksa?a kanuhs'nuhwe?s 'the girl likes the house'The crucial fact about incorporation from the point of view of this report is thatunder certain conditions, which need not concern us here, the incorporation rule alsoleaves the original noun behind so that we find sentences likeE3 kaksa?a kanuhsdnuhwe?s kikz kanuhsa? 'the girl likes this house'In such sentences there is a strict dependency of exactly the type shown in Diagram 1between the incorporated noun stem and the noun stem of the object noun. Thus,although there are sentences such asE4 kaksa?a kanuhwe?s ne- ka?sreht 'the girl likes the car'E5 kaksa?a ka?srehtanuhwe?s 'the girl likes the car'E6 kaksa?a ka?sreht/nuhwe?s kikz ka?sreht 'the girl likes this car'there are no sentences such asE7 * kaksa?a kanuhsXnuhwe?s kikz ka?srehtorE8 * kaksa?a ka?sreht'nuhwe?s kikz kanuhsa?There is then a subset of sentences in Mohawk which contain constituents whose233(XXV. LINGUISTICS)structure is representable by Diagram 1. Sentences can contain both incorporatednoun stems and external noun objects only if the noun stem of the object is the same asthe incorporated noun stem. Hence, in order to show that Mohawk is not a context-freelanguage, it is only necessary to show that the number of noun stems that can occur insuch sentences is unlimited. But this is in fact the case.There is a nominalization transformation that applies to the base constituent of averb and that adds a nominalizing morpheme (tsra/hsra) to produce a noun stem. Thusfrom the verb base nuhwe? one can produce the noun stem nuhwe?tsra that occurs inthe noun kanuhwe?tsra? 'the liking'. But this nominalization rule applies as well to baseconstituents that contain incorporated noun stems. Hence from the verb ka?sreht(nuhwe?sin E5 we can produce the noun stem ?sreht/nuhwe?tsra that occurs in the nounka?srehtnuhwe?tsra? 'the liking of the car'. But now complex noun stems producedby this nominalization rule are themselves capable of being incorporated in verbs, hencecapable of renominalization, of reincorporation, and so on. Thus the process of noun-stem formation is recursive and there is no bound on the length of noun stems, and nolimit to the number of noun stems.We can illustrate this process of noun-stem formation by building up a rather longnoun stem. We omit here the subject noun.1. katsories ne- kanuhsa? - kanuhsxtsoriesincorporation'she finds the house'kanuhs tsarihsra? 'the finding of the house'nominalization2. kanuhwe?s ne- kanuhsxtszrihsra? . kanuhs/tsarihsranuhwe?sincorporation'she likes the finding of the house'0- kanuhsxtszarihsranuhwe?tsra?nominalization'the liking of the finding of the house'3. yao?taksz? ne- kanuhsxtszrihsranuhwe?tsra? -incorporationyaonuhs/tszrihsranuhwe?tsraks? incorporation'the liking of the finding of the house is evil'P kanuhs/ts rihsranuhwe?tsraks hsra?nominalization'the evil of the liking of the finding of the house'4. kaharatats ne- kanuhsxtszrihsranuhwe?tsrakshsra? skanuhs ts rihsranuhwe?tsraksDhsrakaratatsa incorporation'she praises the evil of the liking of the finding of the house'nominalizationkanuhsxts rihs ranuhwe? tsraks chsrakaratts ra?'the praising of the evil of the liking of the finding of the house'234(XXV. LINGUISTICS)This last noun can occur perfectly well in a sentence with an incorporated noun stemidentical to its own. ThusE9 tkanuhs/tsorihsranuhwe?tsraks hsrakarattsrayeri kikzkanuhs/ts rihsranuhwe? tsraks ohsrakarattsra?'this praising of the evil of the liking of the finding of the house is right'We therefore see that the subset of sentences in Mohawk which requires an identityof constituents is in fact infinite and that the set of constituents that must be identical(noun stems) is infinite. But, since these are the crucial formal properties of thelanguage /XX/, it follows thatTHEOREM: Mohawk is not a context-free languagebIncidentally, the process of noun-stem formation which we have considered hasanother interesting consequence. It has been suggested by Yngve, 3 ' 4 on the basis ofthe assumption of finiteness of memory plus a certain model of speech production, thata general feature of human language will be the assignment of phrase structure tosentences in such a way as to guarantee that the branching of phrase-structure treesto the left does not exceed some small finite number of successive embeddings, proba-bly seven. But if we now look at Diagram 2, which presents the structure of the verbin E9, we see that the processes of noun-stem formation and base formation are leftbranching and these processes are recursive. Therefore there is no bound whateveron the branching of trees to the left in Mohawk. Since the assumption of finiteness ofmemory is unassailable, it follows that the model of speech production which yieldsthe prediction of a general restriction on left branching cannot be correct.DIAGRAM 2VERB STEM = VNOUN STEM = NNOMINALIZER = nCVERBSUFFIXBASEN V>RE PRO BASE PERFECTIVEBASE nN VBASEBASE VN V+ - ka - nuhs - - tsori - hsra -nuhwe? - tsra - akso - hsra - karatat - tsra - yeri -235(XXV. LINGUISTICS)3. SignificanceWe can now ask: What is the importance of the fact that Mohawk is not a context-free language? First, as pointed out by Chomsky,5 context-free grammars appearto be the natural formalization of the type of grammar which would result from themethods of immediate constituent analysis c as these have been understood in contempo-rary American descriptive linguistics.d Insofar as this is true, we have a proof thatthese methods, which depend chiefly on substitutability operations, cannot yieldcorrect grammars for natural languages. Second, we have increased to a significantdegree the strength that is provably necessary for any general theory of linguisticstructure. That is, by considering only the weakest of all of the possible formalerequirements on grammars - that they enumerate the correct set of terminal strings -we have shown some phrase-structure systems to be inadequate for the generation ofnatural languages. Results of this type will be of quite limited interest, however, untilthey can be extended to more flexible systems. Context-free grammars are of littlelinguistic interest, since, on the basis of the contingencies of actual linguistic descrip-tion, it is known that context restrictions are required in rules.Chomsky has also considered another type of phrase-structure system, Type 1grammars. These permit context restrictions and are undoubtedly strong enough toenumerate the sentences of natural languages. However, this is of no real linguisticinterest, either, since Chomsky 5 has shown that such grammars cannot ensure thecorrect assignment of constituent structure as can context-free grammars. It ispossible to produce permutations of elements within Type 1 grammars and no clearlinguistic meaning can be given to the structures that result from permutations withinphrase-structure systems. That is, the relation "is a" that we wish to hold between,say, "man" and "Noun" is not correctly reconstructed by Type 1 grammars. There-fore neither context-free grammars that are provably too weak for natural languagesnor Type 1 grammars that provably assign incorrect structure is an adequate formal-ization for natural language grammars. Parikh, however, has shown that there existsa phrase-structure system intermediate in strength 9 between context-free grammarsand Type 1 grammars. Let us call these "Type lB grammars." These permit the useof contexts but do not permit permutations of elements. Type lB grammars thus seemto provide an effective and natural formalization of the notions of constituent structure,thereby permitting the needed flexibility of context restrictions but prohibiting permu-tations that are incompatible with the desired linguistic interpretation of structure.The really interesting question at this point is to find out whether or not Type IBgrammars are provably too weak for natural languages. Chomsky was able to showthat Type 1 grammars can generate the language /XX/, which is beyond context-freedescription, by using the fact that Type 1 grammars can incorporate permutations. But236(XXV. LINGUISTICS)Type IB grammars do not have this feature, and therefore it seems very likely, on thebasis of exactly the sort of construction considered in section 2, that natural languageslie outside the range of Type lB description. If this is so, we shall have moved very fartoward demonstrating, in terms of formal considerations of generative power, thatwhich has already been shown in terms of considerations of simplicity and explanatorypower, namely, that natural languages require transformational devices that make useof variables and powerful formal operations (deletion, permutation) that are impossiblein phrase-structure systems.P. M. PostalFootnotesa The stem "to praise" has the shape haratat with no incorporated noun stem, butit has the shape karatat when a noun stem is incorporated.b A similar claim has been made in effect by Bar-Hillel and Shamir 2 for English. Buttheir remarks are based on constructions with "respectively," a rather peripheralaspect of English. The Mohawk construction that we have considered, on the otherhand, is not peripheral at all. The rules of incorporation and nominalization are centralfeatures of Mohawk syntax.c This claim is supported by the fact that context-free grammars and the other formal-ization of the notions of constituent structure, namely, the so-called categorical gram-mars of Bar-Hillel and others, 6 ' 7 have been proved to be equivalent in generative powerby Bar-Hillel, Gaifman, and Shamir.7d As developed, for example, by Wells.8e A more reasonable and more stringent requirement is that the right set of structuresbe generated. If we insist on this, then phrase-structure grammars in general appearinadequate, because of so-called co-ordinate constructions.References1. N. Chomsky, On certain formal properties of grammars, Information andControl 2, 137-167 (1959).2. Y. Bar-Hillel and E. Shamir, Finite-state languages: Formal represen-tations and adequacy problems, Bull. Research Council of Israel 8f, 155-166(1960).3. V. H. Yngve, A Model and an Hypothesis for Language Structure, TechnicalReport 369, Research Laboratory of Electronics, M.I.T., August 15, 1960.4. V. H. Yngve, The depth hypothesis, Structure of Language and Its MathematicalAspects, edited by R. Jakobson (American Mathematical Society, Providence, R. I.,1961), pp. 130-139.5. N. Chomsky, On the notion 'rule of grammar', Structure of Language and ItsMathematical Aspects, edited by R. Jakobson, op. cit., pp. 6-24.6. Y. Bar-Hillel, A quasi-arithmetical notation for syntactic description,Language 29, 47-58 (1953).237(XXV. LINGUISTICS)7. Y. Bar-Hillel, C. Gaifman, and E. Shamir, On categorical and phrase-structuregrammars, Bull. Research Council of Israel 9f, 1-16 (1960).8. R. Wells, Immediate constituents, Language 23, 81-117 (1947).9. R. J. Parikh, Language-generating devices, Quarterly Progress Report No. 60,Research Laboratory of Electronics, M.I.T., January 15, 1961, pp. 199-212.238

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