On Two Recent Attempts to Show that 
English Is Not a CFL 1 
Geoffrey K. Pullum 
University of California 
Santa Cruz, CA 95064 
Many of the purported demonstrations of the non-CF-ness 
of various languages that have appeared over the past 
twenty-five years (reviewed in Pullum and Gazdar 1982) 
have been replete with both mathematical errors and 
empirical shortcomings? In the wake of the renewed inter- 
est in the parsability of natural languages sparked by the 
work of Gerald Gazdar and others (see Gazdar 1981, 
1982), it has become somewhat more important to 
linguists to attempt to determine at least whether English 
- the most studied language in the era of generative gram- 
mar and the primary focus for natural language processing 
efforts - is context-free (CF) or not. The availability of a 
vast fund of information about efficient parsing of CF 
languages (CFLs) that could in principle be put to work on 
parsing English is enticing, and the idea that English and 
other natural languages might be a small proper subset of 
such a constrained and mathematicallY well-understood 
proper subset of the recursively enumerable sets is highly 
appealing. Chomsky (1981 : 233-234) has denied this, but 
the denial is something of a volte face, for in an earlier 
publication (1974: 48) he remarked: 
• . . the theory of phrase structure grammar (PSG) was 
methodologically preferable to transformation grammar 
(TG) .... PSG is both simpler, more homogeneous, and 
more restrictive, narrower in the range of permitted gram- 
mars, than TG. 
Among those who believe that English does not in fact 
lie within the CFLs, greater effort has recently been put 
into searching for subsets of English that appear to show 
crucially non-CF properties, and the mathematical work 
needed to support an argument for non-CF-ness has been 
conducted with much greater rigor than heretofore. Two 
entirely new arguments on the topic have recently 
appeared: one by Postal and Langendoen (in this issue) 
and one by Higginbotham (1984). In both, the mathemat- 
ical side of the argument seems sound, great care having 
been taken to present all the necessary steps in the proQf 
offered. In this paper, I shall briefly examine the claims 
they make. My conclusion with regard to each is that they 
fail to make their casd because closer attention reveals that 
their empirical claims about English are incorrect. More- 
over, both arguments concern anaphora, and both fail in 
ways related to that concern. 
1. Postal and kangendoen on Sluicing Clauses 
Postal and Langendoen (henceforth P&L) argue as 
follows? Consider the class of English sentences meeting 
the schema 
Joe discussed some X but WHICH Yis unknown. 
The capitalization indicates contrastive stress on which, 
and Y is anaphorically de-stressed by virtue of reference 
back to X. Such examples are called "Sluicing" sentences 
(the sense suggests that, in "transformational terms, an 
additional clause Joe discussed has been "sluiced" away 
from the position following which Y). P&L's claim is that, 
if this schema is filled out with English compound nouns 
from the regular set 
I I am grateful to Barbara Partee and Ray Perrault for useful discussions, 
and to Terry Langendoen and Paul Postal for providing me with a copy of 
their paper before its publication. 
2 They continue to be cited and elaborated upon nonetheless, and state- 
ments still standardly appear in the literature of linguistics to the effect 
that context-free parsing cannot be used for natural languages; see Rich 
(183: 314-315) for yet another recent example. Gazdar (1983) provides 
a literature review of the topic. 
3 A refinement of the context of discussion which l will ignore here is that 
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. 
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0362-613X/84/030182-05503.00 
182 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 
bourbon (hater + lover)* 
in the positions X and Y, a sentence will be obtained if and 
only if an exact string match obtains between X and Y. 
That is, strings like (la) are grammatical but those like 
(lb) are not, according to P&L. 
la. Joe discussed some bourbon-lover-hater but WHICH 
bourbon-lover-hater is unknown. 
b. *Joe discussed some bourbon-lover hater but WHICH 
bourbon-lover-lover is unknown. 
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 bour- 
bon lovers), and so forth, is infinite (which seems reason- 
able 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. 
The flaw in this argument is subtle, and has to do with 
the relation between sentence syntax and discourse struc- 
ture. Note first that the "Sluicing" construction illus- 
trated 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 encount- 
ered: 
2A: Joe has been blaming the fracas last night on a 
certain well-known bourbon-lover. 
B: Oh really? 1 can't imagine WHICH bourbon-lover. 
Notice that in such discourses, B can interpolate addi- 
tional 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. 
B: Oh really? You surprise me. I can't guess WHICH 
bourbon-lover. 
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. 
B: Oh really? I'm fairly well acquainted with the people 
involved, but 1 can't guess WHICH bourbon-lover. 
This possibility spells the downfall of the empirical side of 
P&L's argument. By careful context construction, we can 
get extremely close to a legitimate context of use for exact- 
ly the sort of sentences that they rule out. Consider this 
discourse: 
5A: It looks like they're going to appoint another bour- 
bon-hater as Chair of the Liquor Purchasing 
Committee. 
B: Yes-even though Joe nominated some bourbon-lov- 
ers; but WHICH bourbon-hater is still unknown. 
\ 
The approach is close enough for the failure of the argu- 
ment 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 preced- 
ing 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. 
Hence sentences on the pattern 
Joe discussed some X but WHICH Yis unknown. 
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&L have no argu- 
ment for the non-CF-ness of English. 
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. 
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 inter- 
section 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 > 0, 
and, reading from left to right, the number of occur- 
rences 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. 
Higginbotham approaches his task with much more 
rigor and detail than has been customary in the linguistic 
literature. But as with the P&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 more- 
over, 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 "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" and 
"N is any noun that agrees properly with the pronoun in 
number and gender". 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 assump- 
tion 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. 
This contains a noun phrase of the form "Det... N such 
that z" where z contains no pronoun bound to the head 
noun (couples); yet it seems fully grammatical. 
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 gram- 
matical categories like 'verb', 'noun', 'subject', and 
'object', such that theories of universal grammar refer 
to languages as being SVO, VSO, SOV, etc. 
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. 
There is no pronoun referring back to the head noun atti- 
tude here, so it does not conform to the constraint that is 
crucial to Higginbotham's argument. 
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 "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". 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; rath- 
er, 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. 
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 pronomi- 
nal 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 vari- 
able pronouns that Higginbotham's generalization 
demands. 
Moreover, even if it were possible to embellish these 
examples with prepositional phrases to carry bound vari- 
able 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 
"taken as elliptical" 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 "taken" to be there. 
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 exam- 
ples, is a fact of grammar, for which the alternative 
suggestion provides no explanation. 
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 deno- 
tation 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 trian- 
gle is isosceles; the triangle is equilateral; the triangle is 
scalene but two sides of a previously mentioned quadrila- 
teral are equal; the two sides in a recently discussed hock- 
ey 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-condi- 
tion interpretations are consistent with the more likely 
ones. 
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 prag- 
matic 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. 
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). 
12a. The man such that the man such that she gave this 
to him gave him to this left. 
b. The man such that the man such that she gave this 
to him gave this to this left. 
Both of these, being double center-embedded, are prohib- 
itively 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. Rath- 
er, given a clear picture of what generalizations are opera- 
tive in more natural cases, we apply the familiar 
methodology of generative grammar and extend those 
generalizations to the cases where unaided intuition would 
fail. 
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. 
3. Conclusion 
I think there are lessons to be learned from this admittedly 
negative review. It is clear that linguists have not 
succeeded in developing strong and predictive theories of 
what belongs to the domain of syntax and what belongs to 
semantics. Rather than attempting to discern the status of 
each new fact as it becomes crucial to some dispute, we 
ought to be developing general theories of language from 
which the correct conclusions follow in a principled way. 
Notice, in the present context, that both the arguments I 
have reviewed relate to the topic of anaphora. In both 
cases, I have presented evidence against the assumption 
that certain anaphoric elements are syntactically 
constrained to be identical and clausally adjacent to their 
antecedents (section 1) or to be present in the string 
(section 2). I suspect that it is generally true that 
anaphoric devices that can be controlled across sentence 
boundaries in discourse are never subject to any intrasen- 
tential constraint on identity or overt presence. As things 
stand, however, this is nothing more than a hunch. One 
conclusion we can draw from the present discussion is that 
we are in need of a general and widely accepted theory of 
the syntax and semantics of anaphoric devices. 4 
A second conclusion I would draw is that it is time to 
start applying to semantically interpreted linguistic 
systems the kind of mathematical analysis that so far is 
mostly conducted with regard to stringsets. We know 
little about what mathematical or computation power is 
inherent in particular systems that do not merely generate 
sets of strings but pair strings with representations of 
meanings that are appropriate to particular situations. 5 It 
would be useful to have more clear results about combined 
syntactic and semantic systems, since no one doubts that it 
is the entire mapping between structure and meaning that 
linguists are ultimately interested in. Moreover, it has 
been argued fairly convincingly that some natural 
4See Sag and Hankamer (in press) and work cited there for some impor- 
tant progress in this direction. 
5See Pullum (1984:117-118) for one minor and nor very surprising 
result, observed by Len Schubert: the set of sentences assigned deno- 
tations by a semantics associated with a CF-PSG can be non-CF. Partee 
and Marsh (1984), stimulated by Higginbotham's paper, discuss a prob- 
lem that has potential relevance here. They note that the set of predicate 
calculus formulae with no vacuous quantification is not a CFL, and 
conjecture (but are not able to prove) that it is not even an indexed 
language. 
Computational Linguistics, Volume 10, Numbers 3-4, July-December 1984 185 
Geoffrey K. Pullum On Two Recent Attempts to Show that English Is Not a CFL 
languages cannot be described by a CF grammar in a 
manner that allows a suitable syntax-to-semantics 
mapping to be defined (see Bresnan, Kaplan, Peters, and 
Zaenen (1982) on Dutch)/' 
~'Shieber (in press), which I saw in a preliminary version after complet- 
ing this paper but have not seen in its final form at the time of going to 
press, extends the result about Dutch to make a much stronger claim 
about a related language, Swiss German, namely that it has a syntactic 
analog of the Dutch pattern and overall is not even CF. Moreover, 
Culy (in press) also has evidence of a natural language (Bambara, 
spoken in West Africa) that appears to be other than CF. This changes 
the background to the current dispute a lot, of course. If Shieber and 
Culy are right, there are some aspects of the syntax of some natural 
languages that call for parsing by a device with greater than CF power. 
What I have said above about English remains true, of course, but 
although there may be general facts about how anaphora works that 
could have enabled us to predict this, we cannot predict it simply from 
the proposition that universal grammar does not allow supra-CF gram- 
mars. This makes me much less confident about being able to answer 
the rejoinder to this article that Langendoen and Postal publish in this 
issue. Although their facts, which 1 saw just as this article went to 
press, are not totally convincing (because the repeated-head-noun 
appositive relative construction they discuss is so awkward and unna- 
tural even at the best of times), 1 now do not see why in principle they 
might not be right. Perhaps I have been speaking and writing a non-CF 
language all these years, and simply hadn't realized it, like Moli6re's M. 
Jourdain, who didn't realize he had native competence in prose. 

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