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<Paper uid="J87-1006">
  <Title>TECHNICAL CORRESPONDENCE SUBJECT-VERB AGREEMENT IN RESPECTIVE COORDINATIONS AND CONTEXT-FREENESS</Title>
  <Section position="1" start_page="0" end_page="0" type="metho">
    <SectionTitle>
TECHNICAL CORRESPONDENCE
SUBJECT-VERB AGREEMENT IN RESPECTIVE
COORDINATIONS AND CONTEXT-FREENESS
</SectionTitle>
    <Paragraph position="0"> Langendoen (1977) advanced an argument against English being a context-free language involving cross-serial subject-verb agreement in respectively constructions such as (1).</Paragraph>
    <Paragraph position="1"> (1) The man and the women dances and sing, respectively.</Paragraph>
    <Paragraph position="2"> As noted by Pullum and Gazdar (1982), however, and acknowledged subsequently by Langendoen (personal communication), such examples are unacceptable, and the argument collapses on empirical grounds.</Paragraph>
    <Paragraph position="3"> However, at least some speakers reject examples like (2) as well.</Paragraph>
    <Paragraph position="4"> (2) The man and the women dance and sing, respectively.</Paragraph>
    <Paragraph position="5"> This fact leads directly to a demonstration that there is, after all, a cross-serial dependency involving the grammatical number of subject NPs and verbs in respectively constructions. However, it is not clear at present how representative such speakers are, and so instead of making claims about English in general, we will confine them to just those varieties of the language that stigmatize examples like (2), which will be denoted as English1, leaving to one side any varieties of which this may not be true (English2). I In English1, a verb that formally distinguishes singular from plural, i.e., a non-auxiliary present tense verb, cannot occur in a respectively construction if the corresponding subject NP is singular. This cannot be accounted for merely by barring marked singular verbs from occurring in coordinate predicates of respectively constructions. Such a move would correctly exclude examples like (1), but it would allow sentences like (2), with plural verbs corresponding to singular subjects. Nor is it possible to simply bar singular subjects from occurring in respectively constructions, since they are perfectly possible provided the corresponding verb is either a past tense, as in (3a), or an auxiliary, as in (3b). (3) a.The man and the women danced and sing, respectively.</Paragraph>
    <Paragraph position="6"> b.The women and the man sing and can dance, respectively.</Paragraph>
    <Paragraph position="7"> This means that a singular subject can only co-occur with a past tense or an auxiliary verb, whereas a plural subject can take a non-auxiliary present tense verb as well. The difference in the co-occurrence possibilities of singular as opposed to plural subject NPs amounts to a peculiar kind of number agreement. 2 This fact leads quite directly to a demonstration that English 1 is not context free. 3 Consider the regular set (4).</Paragraph>
    <Paragraph position="9"> This is the set of all strings 4 (only some of them grammatical in English) consisting of .any number of occurrences in any order of the phrases the man and the women, with an and between the last two, followed by  any number of occurrences in any order of the words danced and sing, with an and between the last two, followed by the word respectively.</Paragraph>
    <Paragraph position="10"> According to what has been said, the intersection of (4) with English 1 must be (5).</Paragraph>
    <Paragraph position="11"> (5) {the man x and the women danced y and sing</Paragraph>
    <Paragraph position="13"> This is the set of all those strings of (4) that meet the additional condition that every occurrence of the man must be matched by an occurrence of danced and every occurrence of the women by an occurrence of either danced or sing. This matching is achieved by defining the substitution s o~ of the man to be the set {danced} and that of the women to be the set {danced, sing} and requiring y to be equal to o 1 of x.</Paragraph>
    <Paragraph position="14"> We now define a substitution o 2 such that</Paragraph>
    <Paragraph position="16"> We now intersect (6) with the regular set {a + b + a + c + d + c +} to obtain (7).</Paragraph>
    <Paragraph position="17"> (7) {a nb ma Ic kdjc i I n &lt; k;m &lt; j; l_&lt;i;n+m+l=k+j+i} The set in (7) can be shown trans-context-free by pumping. Take the string z = akbkakckdkc k (where k is the constant of the pumping lemma). On the one hand, if we pump only in the first or only in the second half of the string, the resulting string will violate the condition  is the constant of the pumping lemma, the pumped substring cannot be longer than k, and therefore the only other place we might be able to pump would be in the middle as and the middle cs, But this would result in violating the condition that l may not be greater than i. Thus, z cannot be pumped without violating the pumping lemma, and hence (7) is not context free. Since context-free languages are closed under intersection with regular sets, it follows that (6) is not context-free either. Since context-free languages are also closed under substitution, this means that (5) is also not context-free. Finally, since (5) is the intersection of English, with the regular set (4), it follows that Englishj is not contextfree. Q.E.D.</Paragraph>
    <Paragraph position="18">  1. Pullum and Gazdar (1982) state that they &amp;quot;'can tolerate&amp;quot; examples like (2), and Langcndoen (personal communication) agrees. 2. In other terms, we must be able to tell which verb would agree with  which subject given the chance, and disallow just those combinations where the result would be a marked singular verb. 3. Ignoring, for the sake of simplicity, the arguments advanced in Manaster-Ramer (1983; in press) about the need to state formal results about natural language in other than weak generative capacity terms.</Paragraph>
    <Paragraph position="19"> 4. Ignoring, for the sake of readability, the punctuation that would normally be required in written English and the suprasegmental features that would occur in the spoken language.</Paragraph>
    <Paragraph position="20"> 5. In the discussions of formal properties of natural languages, substitutions have not figured at all prominently, whereas homomorphisms, which are just a special case of substitutions, have. it may be helpful, therefore, to point out that a substitution is a mapping like a homomorphism except that it is usually denoted by o rather than h and that it may associate each element in the vocabulary of a language with a whole set (possibly infinite) of strings rather than with just one string, as in the case of a homomorphism. In the present case, we needed to employ a (slightly more general kind of) substitution in order to be able to associate the women with sing as well as danced. It should also be noted that, while the man and the women are linguistically analyzable, we have for technical convenience treated them as single elements of the terminal vocabulary in dcl'ining Ihc substitutions.</Paragraph>
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