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<Paper uid="J84-3003">
  <Title>On Two Recent Attempts to Show that English Is Not a CFL 1</Title>
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3 A refinement of the context of discussion which l will ignore here is that
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    <Paragraph position="0"> these authors have argued that natural languages contain sentences of infinite length (e.g., infinite coordinations, see Langendocn and Postal (1984)), which means they are not recursively enumerable, and not even sets. From this perspective, the present discussion concerns those proper subparts of natural languages that contain just finite-length sentences.</Paragraph>
    <Paragraph position="1"> Copyright 1985 by the Association for Computational Linguistics. Permission to copy without fee'all or part of this material is granted provided that the copies are not made for direct commercial advantage and the CL refcrcnce and this copyright notice are included on the first page. To copy otherwise, or to republish, requires a fee and/or specific permission.</Paragraph>
    <Paragraph position="2">  in the positions X and Y, a sentence will be obtained if and only if an exact string match obtains between X and Y.</Paragraph>
    <Paragraph position="3"> That is, strings like (la) are grammatical but those like (lb) are not, according to P&amp;L.</Paragraph>
    <Paragraph position="4"> la. Joe discussed some bourbon-lover-hater but WHICH bourbon-lover-hater is unknown.</Paragraph>
    <Paragraph position="5"> b. *Joe discussed some bourbon-lover hater but WHICH bourbon-lover-lover is unknown.</Paragraph>
    <Paragraph position="6"> If this is true, and if the set of compound nouns such as bourbon-lover-hater (hater of those who love bourbon), bourbon-lover-hater-hater (hater of those who hate bourbon lovers), and so forth, is infinite (which seems reasonable to me), then, as they show, there is a simple argument from intersection with a regular set to obtain a string copying (xx) language, and the conclusion is that English is not CF.</Paragraph>
    <Paragraph position="7"> The flaw in this argument is subtle, and has to do with the relation between sentence syntax and discourse structure. Note first that the &amp;quot;Sluicing&amp;quot; construction illustrated by sentences like Joe discussed some bourbon-lover but I don't know which bourbon lover is not exclusively intrasentential. Dialogs like the following are encountered: null 2A: Joe has been blaming the fracas last night on a certain well-known bourbon-lover.</Paragraph>
    <Paragraph position="8"> B: Oh really? 1 can't imagine WHICH bourbon-lover.</Paragraph>
    <Paragraph position="9"> Notice that in such discourses, B can interpolate additional sentences before the one containing the which-phrase, provided the thread of the anaphoric connection is not thereby made opaque: 3A: Joe has been blaming the fracas last night on a certain well-known bourbon-lover.</Paragraph>
    <Paragraph position="10"> B: Oh really? You surprise me. I can't guess WHICH bourbon-lover.</Paragraph>
    <Paragraph position="11"> Now notice that the interpolated material may even be conjoined on the beginning of the clause containing the anaphoric which: 4A: Joe has been blaming the fracas last night on a certain well-known bourbon-lover.</Paragraph>
    <Paragraph position="12"> B: Oh really? I'm fairly well acquainted with the people involved, but 1 can't guess WHICH bourbon-lover.</Paragraph>
    <Paragraph position="13"> This possibility spells the downfall of the empirical side of P&amp;L's argument. By careful context construction, we can get extremely close to a legitimate context of use for exactly the sort of sentences that they rule out. Consider this discourse: 5A: It looks like they're going to appoint another bourbon-hater as Chair of the Liquor Purchasing Committee.</Paragraph>
    <Paragraph position="14"> B: Yes-even though Joe nominated some bourbon-lovers; but WHICH bourbon-hater is still unknown.</Paragraph>
    <Paragraph position="15"> \ The approach is close enough for the failure of the argument to be clearly seen; it is permissible for the antecedent of the anaphorically de-stressed constituent in a construction of this type to be in a previous sentence in the discourse, and for the anaphor relation to hold across an intervening conjunct with arbitrary content. There is no reason in principle why a clause like which bourbon-hater is unknown should not have a conjoined clause like Joe discussed some bourbon-lover intervening between it and the antecedent for its anaphoric reference, and the same holds for all other choices of compound noun. The syntax of English does not demand that the immediately preceding clause contain the antecedent for the anaphoric relationship that holds here, any more than it demands that the most recent noun phrase in the current sentence should be the antecedent for a pronoun - notice that she can mean Julia in a discourse like (6): 6. I've decided to appoint Julia. Mary wanted me to choose Kathy, but I'm sticking by my decision. She'll do a great job.</Paragraph>
    <Paragraph position="16"> Hence sentences on the pattern Joe discussed some X but WHICH Yis unknown.</Paragraph>
    <Paragraph position="17"> are grammatical whether X matches Y or not (though if not, then Y will not be taken as anaphorically related to X in this construction). This means that P&amp;L have no argument for the non-CF-ness of English.</Paragraph>
    <Paragraph position="18"> 2. Higginbotham on such that clauses Higginbotham (1984) argues that English can be shown to be non-CF on the basis of the such that relative clause construction. This type of clause, he claims, is constrained to contain a pronoun anaphorically bound to the head.</Paragraph>
    <Paragraph position="19"> Thus he regards phrases as the woman such that she left as grammatical but the man such that I saw Mary as ungrammatical. Because of this, he reasons, the intersection of the regular language L = the woman such that (the man such that)* she (gave (this + him) to (this + him))* left is here with English is the following language, to be referred to as A: {the woman such that (the man such that) n she ((gave llim to him) + (gave him to this) + (gave this to him) + (gave this to this)) n left is here \[ n &gt; 0, and, reading from left to right, the number of occurrences of this never exceeds by more than 1 the number of occurrences of him} This is shown to be non-CF by a direct application of Ogden's Lemma, hence showing that English is non-CF.</Paragraph>
    <Paragraph position="20"> Higginbotham approaches his task with much more rigor and detail than has been customary in the linguistic literature. But as with the P&amp;L argument, the flaws lie in Computational Linguistics, Volume 10, Numbers 3-4, July-December 1984 183 Geoffrey K. Pullum On Two Recent Attempts to Show that English Is Not a CFL the attention to detailed description of English, and moreover, relate to the treatment of anaphora. In Higginbotham's argument, it is crucial that English allows as a noun phrase any string of the form the N such that z where &amp;quot;z is an ordinary English declarative sentence that contains an occurrence of a third-person pronoun that does not have to be taken as having its antecedent within z&amp;quot; and &amp;quot;N is any noun that agrees properly with the pronoun in number and gender&amp;quot;. But it also crucial that only if there is such an unbound and properly agreeing pronoun in z is the string a grammatical noun phrase. The latter assumption is plainly false. Consider this example: 7. Over many years, it has become clear that Lee and Sandy were just one of those couples such that people always reported loving her but hating him.</Paragraph>
    <Paragraph position="21"> This contains a noun phrase of the form &amp;quot;Det... N such that z&amp;quot; where z contains no pronoun bound to the head noun (couples); yet it seems fully grammatical.</Paragraph>
    <Paragraph position="22"> In Pullum (forthcoming) I give many more examples, varying the head nouns through a considerable range. I will not repeat all of them here, but lest anyone should think that I am using solely my own judgments here as the crucial evidence in a case of disputed data, let me point out that examples of the relevant sort can be adduced from the written English of other speakers through the written history of English. For example, a colleague found the following sentence in a manuscript under anonymous review for publication: 8. Modern linguistic theory makes crucial use of grammatical categories like 'verb', 'noun', 'subject', and 'object', such that theories of universal grammar refer to languages as being SVO, VSO, SOV, etc.</Paragraph>
    <Paragraph position="23"> And in the prose of G. O. Trevelyan (1876: 137) one may find the following very stylish example: 9. On the 20th of February the House of Commons was called upon to express its gratitude to the Governor-General; and a debate ensued, in which the speeches from the front Opposition bench were as good as could be made by statesmen, who had assumed an attitude such that they could not very well avoid being either insincere or ungracious.</Paragraph>
    <Paragraph position="24"> There is no pronoun referring back to the head noun attitude here, so it does not conform to the constraint that is crucial to Higginbotham's argument.</Paragraph>
    <Paragraph position="25"> Surprisingly, Higginbotham knows that sentences of this general sort exist, for he sites the following two noun phrases in his first footnote: 10a. every triangle such that two sides are equal b. the number system such that 2 and 3 make 5 and addresses the issue of how they are to be distinguished from examples he counts as ill-formed, such as 1 la. every book such that it rains b. the man such that I saw Mary He considers but dismisses the possibility that &amp;quot;all of these examples are grammatical NPs, although \[those in (11)\] are not interpretable in any natural way, perhaps owing to the irrelevance of the sentence following 'such that' to the content of the head noun&amp;quot;. His argument is as follows. First, the sentence following 'such that', even in cases like \[those in (10)\], is in fact never interpreted as closed; rather, it is interpreted, where possible, as elliptical for a sentence that is not merely relevant to the content of the head noun, but further supplies a place into which binding is possible* Thus, \[(10a) and (10b)\] are intuitively taken as elliptical for (iii) and (iv), respectively: (iii) every triangle such that two sides of it are equal (iv) the number system such that 2 and 3 make 5 therein Their mode of interpretation, then, not only is consistent with, but further supports, the premise employed in this article.</Paragraph>
    <Paragraph position="26"> Higginbotham is apparently committed to the view that any sentence violating his alleged constraint will be purely an elliptical version of a longer one that observes it by virtue of containing a prepositional phrase with a pronominal NP that acts as a bound variable. But with examples l have cited, it does not even seem possible to insert extra prepositional phrases to force them to have the bound variable pronouns that Higginbotham's generalization demands.</Paragraph>
    <Paragraph position="27"> Moreover, even if it were possible to embellish these examples with prepositional phrases to carry bound variable pronouns, this would be irrelevant to the matter at hand, since the claim at issue is about sets of strings, not their interpretations. The claim that the sentences are &amp;quot;taken as elliptical&amp;quot; is completely irrelevant. They are no more elliptical than Kennedy was assassinated, which lacks an agentive phrase by someone which semantically we might argue to be &amp;quot;taken&amp;quot; to be there.</Paragraph>
    <Paragraph position="28"> Higginbotham goes on to remark that *.. there is nothing semantically odd about sentences that use NPs of the sort shown in \[(11)\]; for instance, (v), whose subject is \[(lla)\], would, if grammatical, be  logically equivalent to (vi): (v) every book such that it rains is on the table (vi) either every book is on the table, or it does not rain  Hence the elliptical character of \[(10)\], and similar examples, is a fact of grammar, for which the alternative suggestion provides no explanation.</Paragraph>
    <Paragraph position="29"> Here Higginbotham recognized that there is no principle of logic that dictates uninterpretability, even for the bizarre cases in (11). We can assume that a noun like book denotes a set and a such that clause attached to it to make an N t denotes a condition that has to be satisfied by elements of the denoted set if they are to qualify as members of the denotation of the N r. In a bizarre case like 184 Computational Linguistics, Volume 10, Numbers 3-4, July-December 1984 Geoffrey K. Pullum On Two Recent Attempts to Show that English Is Not a CFL (1 la), the condition, if true, does not restrict the denotation of the head noun at all. In a less bizarre case like the woman such that she left, if the pronoun she is bound to the head noun woman, only a woman who left can belong to the denotation of the phrase woman such that she left. In interesting cases such as (10a), the condition is vague: two sides are equal could be true in many ways (the triangle is isosceles; the triangle is equilateral; the triangle is scalene but two sides of a previously mentioned quadrilateral are equal; the two sides in a recently discussed hockey game are equal in their scores; and so on). Naturally, some of these are much more likely and plausible than others in typical contexts, but clearly the vacuous-condition interpretations are consistent with the more likely ones.</Paragraph>
    <Paragraph position="30"> In the most interesting cases, those like (7), the such that clause suggests a constraint on the denotation set of the head noun without explicitly giving it in the syntax. In couple such that people always report loving her but hating him, the such that clause refers to a lovable female and a detestable male but does not specify grammatical roles for these individuals exterior to the clause. The pair are referred to, however, in a such that clause attached to the noun couple, which, pragmatically, provides us with an inferred him and her to allow for the interpretation of the such that clause people always report loving her but hating him as a restriction on the reference of the noun couple. There is no plausibility to an account that forces this pragmatic fact into the syntax by postulating an abstract prepositional phrase to contain a suitable bound variable (*couple such that people always report loving her but hating him \[of it~them\]). And even if there were, this would not bear on establishing the non-CF-ness of English given that the phrase in question is not required to appear in the string. Higginbotham is exactly right about the semantically unexceptional character of the cases in which the such that clause fails to restrict the denotation set of the head noun other than trivially, but that is precisely what shows he is wrong about the grammatical basis of the restriction condition.</Paragraph>
    <Paragraph position="31"> Higginbotham's argument fails, then, because, given the evidence above that such that clauses do not have to contain pronouns bound to their heads, we can see that the condition regarding the relative numbers of occurrences of the words him and this in set .4 does not have to be met by members of the regular set L in order for them to qualify for inclusion within English. English contains not only strings like (12a) but also strings like (12b).</Paragraph>
    <Paragraph position="32"> 12a. The man such that the man such that she gave this to him gave him to this left.</Paragraph>
    <Paragraph position="33"> b. The man such that the man such that she gave this to him gave this to this left.</Paragraph>
    <Paragraph position="34"> Both of these, being double center-embedded, are prohibitively hard to process or to contextualize, of course, but we do not operate in such matters by attempting to render naive judgments of acceptability on extreme cases. Rather, given a clear picture of what generalizations are operative in more natural cases, we apply the familiar methodology of generative grammar and extend those generalizations to the cases where unaided intuition would fail.</Paragraph>
    <Paragraph position="35"> If the count of him instances relative to this instances does not have to be maintained, then plainly there is no proof of non-CF-ness, since a context-free grammar is readily able to keep track of the number of the man such that sequences relative to the number of gave NP to NP sequences. It is only the additional burden of keeping the him~this count that allows for a proof that A is non-CF and thus that English is.</Paragraph>
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