19 
1965 International Conference on Computational 
Linguistics 
PUSHDOWN STORES AND SUBSCRIPTS 
Jacob Mey 
Lingvistisk Institutt 
Universitetet i 0slo 
PoBo 1012, Blindern, 
Oslo 3, Norway. 
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Mey 2 
PUSHDOWN STORES AND SUBSCRIPTS 
Abstract 
Va~rious devices for the imp rovement of phrase 
structure grammars (PSG) have been suggested 
recently. In particular, the PSG model with 
a pushdown store (PSG/PDS) a s described by 
VoYngve, and the PSG with subscripts (PSG/S) 
as described by G oHarman are considered. 
It is contended that such devices, even if 
they may do away with some of the difficul_ 
ties of PSG, do not contain sufficient gene_ 
rative power to produce the structurally corn_ 
plicated sentences that are generated by other 
gramma rs (e.g., of transformational type). 
The handling of multiple disco,Ltinuous con_ 
stituents (DC) in PSG/PDS, as well as the use 
of :leletion rules in PSC./S is examined and 
criticized. It is shown that the improvements 
on PSG will not allow the grammar to generate 
a ii the sentences of the language that a trans_ 
formational grammar (TG) does; moreovdr, the 
improvements on PSG a re obtained only at the 
cost of introducing too much power at the PS 
level, so that the improved gr;~mmars in some 
cases will exceed the requirem@nts of the de_ 
scription, i.e. generate non_grammatical sent_ 
ences. 
Mey 3 
O. Introduction 
NoChomsky has argued that a PSG is not suff_ 
icient to generate all the grammatical sent_ 
ences of a language (Chomsky 1957:3~ ff.). 
Recently, this conceotion of PSG has been 
criticized as being too primitive (Yngve 
1960:445a, Harman 1963:604 fro), and several 
ways of improving such a grammar have been 
suggested: a PDS has been connected with a 
PSG (Yngve 1960, 1961, 1962); the use of 
subscript notation has been recommended to 
give PSG a fair chance in competition with 
TG (Harman 1963). 
i. PSG/PDS 
l.lo PSG and DC 
The problem of the so_called discontinuous 
sonstituents (for a detailed treatment, see 
Wells 1947:96 ff.) has always been a crux in 
IC analysis. One of the drawbacks of PSG as 
described by Chomsky, is that it is not able 
to handle these constituents in a way that 
satisfies both the formal criteria of the 
grammar and the intuitive feeling that call 
and up in, e.g., I called him u~, belong to_ 
gether and should be treated accordingly in 
the analysis. Chomsky, in his discussion of 
PSG limitations, admits the possibility of 
"extending the notions of phrase structure 
to account for discontinuities" (Chomsky 
Mey 4 
1957:41), but, he adds, "...fairly serious 
difficulties arise in any systematic attempt 
to pursue this course." 
An attempt in this direction is described by 
V.Yngve in several articles (see especially 
Yngve 1960); a lthough the presence of DC 
is the most annoying of the complications 
under the PSG model (Yngve 1960:448a), the 
solution ~ffered to this particular problem 
implies a wider claim, namely, that "any 
shortcomings /of PSG, JM/ can be overcome" 
(Ib.:445a). Accordingly, I will discuss be_ 
low not only the problem of DC, but also the 
more general one of structure in a PSG/PDS. 
1o2o DC and PDS 
The crucial step in the derivation of DC by 
the automaton (for a full description, see 
Yngve 1960:448_9) is the question asked: 
Does the right half of the grammar rule in 
question (GRi) contain the symbol "..." ? 
(where ".. o" stands for "discontinuity in 
rewriting the symbol on the left hand side 
of the rule") If the answer is Yes, we have 
to roll out the temporary memory (TM) ta~e 
one space (in a flow chart, one woul~ sym_ 
bolize this by the index notation 1 --I --> i, 
where 1 stands for "leftmost": "rolling in" 
tape would then be indicated by 1 + • --> i, 
see Fig. ~). During this operation, the 
original content of TM 1 (the leftmost loca_ 
Mey 5 
tion of TM) has to be kept in place, that is, 
the blank has to occur after the original TM 1 
(on the right side, if the tape is thought of 
as moving from the left, see Fig° ~). If, how_ 
ever, the answer is No, we have to make sure 
that we have space for all the symbols on the 
right hand side of the rule and roll out tape 
accordingly. Let ~ be the number of symbols 
on the right hand side of GRi: then we can 
symbolize the rolling out by the index formula 
i -- (n -- ~ the first symbol always goes 
to the computing register. 
Let further ~ be the subscript for right hand 
side symbols of GR i. The rest of the operation 
is then performed as routine counting on GRi. , 
3 i being set at 2 (the first symbol has already 
been taken care of). There should, of course, 
be a proviso for the symbol "..." itself, so 
that it will not be copied onto the TM taoe. 
The method as described here will work neatly 
even in those cases where DC are "nested~ that 
is, if the expansion of some DC turns out to 
be another DC (and so on, at least theoretical_ 
ly). As an example, one may try out the doubly 
discontinuous as far as the corner, where all 
the necessary rules are sDeclfied by Yngve 
himself (1960:449a). 
An implicit assumption throughout the descrip_ 
tion of the mechanism is that DC can be repres_ 
ented by the simple formula A --> B + 9,o + C. 
It follows that there are two cases that cannot 
Mey 6 
be handled directly by the machine: the first 
one can be symbolized by A --> B + ... + C + 
... + D ("mul~ple discontinuous constituents"); 
this reduces easily to double discontinuity by 
a suitable manipulation of the inout rules. 
The other case could be labeled "discontinu_ 
ous multiple constituents": formula A --> B + 
C + ..o + D (or some variation on this theme), 
which would imply that the blank has to occur 
two spaces from leftmost ins~ad of one. Foll_ 
owing the instructions given by Yngve we would 
not obtain the right string of symbols in this 
case (as examples, one may try: He's not that 
bin a fool, or: As nice a little parlor as ever 
you did see, or the Soanish sentence: Habla mas 
de lo que sabe 'He talks more than what he knows' 
(Bolinger 1957:63), where common sense would 
prefer the analyses that bi~ ... fool, as nice 
( • .. ~arlor, mas de ... que see diagrams in 
Fig. 2), thus pre3erving analogy with construc_ 
tions like such a fool etc. The program could 
be accommodmted to perform this by combining 
a counting operation with the check on " " o.o , 
whereafter the continuous part of GRi's right 
hand side could be thrown in with the non_DC 
rules. Derivation being different, there would 
be no interference from constructions like 
that big fool, that are treated in the normal 
way by the machine. 
A device like the one described here will, 
within its obvious limitations, be able to 
randomly generate sentences that are for the 
most part quite grammatical (Yngve 1962:70). 
Mey 7 
The question is: will it generate all, and 
only, the grammatical sentences of a fang_ 
uage? I will try to answer this question in 
the next paragraph. 
1.3. Limitations of PSG/PD ~ 
Although the model as proposed by Yngve in its 
original form only uses the PDS technique to 
solve a minor problem in syntactic analysis 
by the machine, the scope and use of PDS are 
by no means limited to this particular pro_ 
blem of DC (For a detailed discussion, see 
Oettinger 1961:126_7). The elegancy and sim_ 
plicity of PDS algorithms make them well_ 
suited for procedures of automatic syntactic 
analysis of languages. 
There are, however, some inherent limitations. 
Common to all PDS techniques is the fact that 
information stored in this way only is access_ 
ible in accordance with the formula "last in, 
first out". Being essentially a linear array 
of information (Oettinger 1961:i04), the user 
(the machine) will not be able to draw on other 
information than is given by the leftmost sym_ 
bol in a left_to_right production (the temDo_ 
rary memory tape in Yngve's machine, see Fig.l). 
Since, on the one hand, the machine output is 
past control (what is Drinted, is no longer 
available to the machine for inspection) and, 
on the other hand, the internal state of the 
machine is entirely determined by the current 
input symbol, one has to keep careful account 
Mey 8 
not only of the current derivatlonal steps, 
but also of the "left_overs" from earlier 
steps. This is exactly what a PDS can do, 
and the ~roblems in connection with this 
technique are, as shown above in the case 
of the so_called discontinuous multiple 
constituents, are mainly technical (provid_ 
ing indexes etc.) 
The linear character of the memory, however, 
together with the finite state oroperties of 
the model itself give rise to a~other problem 
that seems unsolvable under the following ass_ 
umptions for our machine: a finite number of 
states, a linear temporary memory, and a 
transition from one state into anether by one_ 
symbol inout. The problem is the following: 
given any internal state of th~achine that is 
determined by more than one symbol simultane_ 
ousiy, will the supplementary device of a PDS 
be able to suDply the necessary instructions 
to the machine that are not contained in the 
current symbol? 
The answer is in the negative, precisely be_ 
cause the memory is linear, and there is no 
"look_up" for items in the memory° What is stor_ 
ed in the memory can only be brought up to the 
surface by something outside the memory itself, 
that is, I have to create an "expectancy" that 
is specific for each item in the PDS. Only 
under these conditions the state of the machine 
can be defined as determined by the current 
symbol plus the oontents of the temporary mem_ 
ory (Yngve 1960:~49). This is essentially the 
Mey 9 
procedure described by Harris for keeping 
track of nested constructions ("incurrence 
and discharge of requirements", Harris 1962: 
53). The reason why the machine is able to 
handle DC is that this "nesting" occurs in 
one level, so that the symbols involved can 
be uniquely determined as belonging to the 
same dimension of analysis. 
Where "surface structure" is explained only 
by underlying "deed structure" (Hockett 1959: 
246 ff.), the machine will not be able to carry 
out the analysis correctly. The structure that 
underlies a symbol X 1 may be bound up with a 
special PS derivation, so that rules concern_ 
ing structures like, say, X 1 + X 2 + X~ will 
be ambiguous in their a~plication. One could 
place restrictions (in Harris' sense) on (one 
of) the symbols, thus creating a multiple path 
through the derivation, possibly combined with 
a cycling device: this is what the subscriot 
technique does, see 2.4 for a detailed discuss_ 
ion. Some of the difficulties are removed in 
this way, but others persist, like those cases 
where pairs of symbol formulae are involved 
(the so_called "~eneralized transformations" of 
early TG, Chomsky 1957:113); this point is also 
discussed below. While placing too many restr_ 
ictions on the symbols has serious disadvant_ 
ages (some of which will be discussed in sect_ 
ion 2 of this paper), it certainly exceeds the 
capacity of the model as described by Yngve: 
his rules are all of the context_ free form. 
Mey I0 
Thus, structure in a sufficiently powerful 
PSG is not only a matter of specifying the 
right rules, but also of choosing the right 
rules and combining them at the right places. 
There is still another factor that we have 
left out of consideration so far: the order_ 
ing of the rules. Yngve states that any order 
will do: an alphabetical order may be conven_ 
lent (1960:445)o NOW this has two consequen_ 
ces: first, all of the rules have to be run 
through every time a symbol is expanded (per_ 
haps only a minor drawback in a computer_ 
oriented analysis), second, the advantages of 
ordered rules (economy, elegancy, accuracy) 
are lost ("forcing all kinds of low_level 
detail into the rules" , Bach 1964:53) . Besides, 
ordering of the rules is indispensable in 
cases where complicated high_level structural 
descriptions are involved: thus an immediate 
derivation of each non_terminal symbol all the 
way down to word level would not be permitted 
in any kind of PSG, not even the most context_ 
sensitive ones. Being es~entially context_free, 
Yngve's grammar will 6~enerate what is usually 
called "kernel sentences" (Chomsky 1963:152): 
unambiguous derivation of more complex struct_ 
urea (derived sentences) will only be feasible 
under a careful specification of the order in 
which the rules have to apply (as an example, 
cf. the discussion of w__hh_transformations as 
depending on the interrogative transformation 
in Chomsky 1963:140). 
Mey ii 
There is another way out of the difficulties 
that have been sketched in this section: phrase_ 
structurizing at different levels, these being 
kept together by the representation relation 
(see Sgall 1964b). This solution is based on 
a somewhat different interprd~tion of PSG 
functions (not only syntactic, but also semant_ 
ic rules az'e included); a PDS is coupled with 
the PSG of the lowest level. A detailed dis_ 
cusslon of this system will have to wait for 
more details, but it seems that grammars based 
on dependency relations have received too 
little attention so far (for a compalison of 
IC and dependency theories, see Hays 1964: 
519_22)o 
1.4. Grammar and psycholqgy 
Referring to experiments performed by G.Ao 
Mill~r, Yngve establishes an analogy between 
the "depth" of memory ~n the human brain and 
the depth of sentence construction in the model 
(1960:452). The human brain is not capable of 
stvrlng more than, say, seven plus minus two 
items a t a time (for references, see Yngve 
ibid.). In other words, the human brain has a 
limited capacity, just like the temporary mem_ 
ory of Yngve's machine. One of the conditions 
to be put on a flawless handling of "deep" 
constructions is that the storage capacity is 
not exceeded by the number of symbols to be 
developed later on. In this connection Yngve 
makes the in~ere~ting observation that senten_ 
ces and constructions in general actually do 
Mey 12 
have a sort of limited depth, i.e. the number 
of regressive nodes is bound by more or less 
the same uoper limit as that for human memory's 
simultaneous storage caoacity. 
Now, I think that the analogy between the two 
kinds of "storage" should not be overstressed. 
It rests primarily on the tacit assumption 
that the model should, or could, be considered 
as a more or less true_to_life representation 
of human linguistic activity. As I have remark_ 
ed before, this supposition is altogether 
groundless, and will at best hamper an exola_ 
nation of such activity in truly linguistic 
terms. A remark made by Yn{~ve in this connect_ 
ion may clarify the issue. Yngve says (1960: 
452b; see also 1961:135_6 for an even more ex_ 
plicit commitment): 
"The depth limitation does not apply to algebra, 
for example, because it is not a spoken langua_ 
ge. The user has paper available for tempmrary 
storage . " 
But so has the user of any other language, e.g, 
human everyday sooken language. The fact that 
we do not use paper actually when speaking has 
nothing to do with greater or lesser depth of 
sentences (or, if it does, the depth differences 
occur only to one side, namely that of decreas_ 
ing depth). One could pursue this analogy ad ab_ 
surdum by assuming two kinds of depth, one un_ 
limited, for written languages, and one limited, 
for spoken languages. The results would be dis_ 
astrous for any description of any language: 
sentences of the type: "That that that they are 
Mey 13 
both isosceles is true is obvious isn't clear" 
(Yngve 1960:458b) are as ungrammatical in 
written as they are in spoken English. Of 
course Yngve is perfectly right in attribut_ 
ing the difference between the above non_ 
grammatical (deep regressiv~ that_clause and 
its grammatical (progressive) counterpart: 
"It isn't clear that it is obvious that it 
is true that they are both isosceles" to ex_ 
cess depth. So, there is a depth limitation 
and this limitation is gramatically relevant. 
But this linguistically fruitful concept should 
not be confounded with hypotheses from des_ 
criptive psychology. 
That the claim for descriptive similarity be_ 
tween psychology and linguistics is latent in 
Yngve's model can be seen from another instan_ 
ce. \]Iis second assumption for the model (1960: 
445) is that "the model should share with the 
human speaker o.. the prooerty that words are 
{~roduced one at a time in the proper time se_ 
quence, that is, in left_to,right order ..." 
(the first assumption, vim. that any shortcom_ 
ings of the PS model can be overcome, has Dart_ 
1y been dealt with above, and will be treated 
at length in the second half of this paper). 
This restriction, I think, on a model (or a 
grammar, insofar as the grammar is based on 
the model) is unnecessary and self_contradict_ 
ory. It is unnecessary, since the model should 
only copy relevant traits in the speech pro_ 
duction of the individual; and even though it 
may be true that words are produced in a linear 
Hey 14 
sequence (as already Saussure has remarked), it 
has not yet been shown how this linearity is to 
be interpreted in human speech production: I 
think it is only weakly relevant, that is to 
ssy, linearity alone will never suffice to 
give a complete picture of the speech event. 
For a full_fledged description of speech I 
suppose the assumption that we speak in senten_ 
cesra ther than in words will have many advant_ 
ages. 
Moreover, the claim that the model should du_ 
plicate the property of left_to_right product_ 
ion in the human speaker cannot be brought to 
harmon2ze with the model. In fact, the model can 
only examine one symbol at a time: the machine 
may erase or delete or read only that section 
of the memory tape that is closest to the roll, 
i.e. the leftmost symbol only (Yngve 196o:446). 
Now, the limitation of human memory is on re_ 
I)roducing more than a certain number of items 
at the same time. The analogy clearly does not 
hold between human memory and machine storage: 
the explanation is that the machine produces 
symbols, whereas the speech of humans is struct_ 
ured. In other words, a left_to_right product_ 
ion may in many cases be explained by a linear 
structure in the oroducer; the pushdown store 
is a linear memory device. But there are other 
left_to_right productions that are structured 
in such a way that a PDS or other left_to_right 
arrangements will not suffice. It is of course 
true that a structural description is not alto_ 
gether absent from a PSG/PDS: Yngve's machine 
produces as its output a string of symbols 
Mey 15 
containing both syntactical markers ("flattened_ 
out trees") and terminal symbols. This will 
suffice to "infer the derivational history of 
each string from that string in a single way" 
(S~all 1963:41), but only insofar as the struct_ 
ure can be described in one_level terms, cf. 
discussion above (see also Sgall 1963; 1964a). 
The question will be treated at length in part 
two of this paper. 
2 p so/s 
2.1. The subscript notation 
The subscript method referred to here is not 
in the first place thought of a s a machine 
v 
program (even though its close affinity ~ith 
the computer language COMIT is asserted, see 
Harman 1963:608fn.). Accordingly, it has a 
more general scope: namely, to offer a full_ 
fledged alternative, in PS form, to other 
grammars (e.g. of transformstlonal obedience), 
thereby proving that "transformational gramm_ 
ar has no adva ntage over the phrase struct_ 
ure grammar" (Harman 1963:598). 
• ubscripts are added to the PSG rules in two 
ways: first, to introduce restrictions on such 
rules, second, to s:~ecify where those restr_ 
ictions apply. An example of the first kind 
is the rule S --> S1/NUMBER_SG (Harman 1963:609), 
and, in general, any rule of the type A --> B/J 
+ o,o . The second case obtains e.g. in the 
following rule: NP/NOT_WI{ --> DETERMINER + NOUN, 
and, of course, in all rules where subscripts 
Mey 16 
a re "lost" during expansion. I think there will 
be a third type as well, even t|iough this is not 
expressly mentioned in the articLe, namely, sub_ 
scripts that do both: introduce new subscripts 
at places indicated by old ones; but this is on_ 
ly a minor point. More important is the obser_ 
vation that subscripts can take care of all 
sorts of const itueJlts, both continuous and dis_ 
continuous. For the latter, the generation ru_ 
les are adapted Prom rules suggested by Victor 
Yngve (IIarman 1963:606; the reference quoted is 
Yngve 1960). Like in Yngve's model, the rules 
of PSG/S are unordered: all necessary informa_ 
tion about when and where to a'iply a rule is 
contained in the subscripts (which, by the way 
and perhaps afortiori, are said to occur in an 
unordered sequence). But, as will be seen from 
the following paFsgraphs, this "when"and "where" 
is not only a notational problem: in fact, it 
is one of the big underlying differences be_ 
tween PSG and TG. (0n the difficulty of ordering 
rules in a PSG, see Chomsky 1957:35). A further 
important difference from other PSG interpreta_ 
tions is the admission of deletion rules, that 
is rules of the form A --> @ (Harman 1963:60~); 
also this point will be discussed at length below. 
2.2. Subscripts And Transformations 
In general, One cannot deny the possibility of 
incorporating (by means of subscripts or other 
devices) some of the information that is con_ 
tained in a transformational grammar into a 
Mey 17 
~ne_level grammar of PS type. 
But the grammar thus constructed will never 
generate all and only the grammatical sent_ 
enc~s of the language. Either it will generate 
too little (the normal case for PSG without 
subscripts or similar devices) or, if it gen_ 
erates more, it will also generate some non_ 
grammatical sentences (Harman 1963:611:"... 
not all sentences constructed in accordance 
with this grammar 'are well_formed.") 
A very simole example will show this. Supoose 
we ~ant to transform optionally a sentence in_ 
to its question counterpart. To do this in the 
PSG/S according to Harman, we have to choose 
an appropriate expansion of the symbol $2 
(the same paths hold for number_ and mode_ 
restricted S : S1, resp. S2, Harman:600), na_ 
mely either the second or the fourth rule in 
3., the set of expansion rules for $2. We 
choose the second rule (normal question, the 
fourth rule concerns wh_questions): 
S2 --> VP/TYPE_QUES,NOT_WH + NP/CASE_NOM,NOT_WH. 
Now, note two things: in order to conform to 
the rules for this grammar, we have already 
added some of the subscripts from Rules 1 and 
2 to the symbol $2 (e.g., NUMBER_SG and MODE_ACT). 
These subscripts, together with the new ones, 
are to appear on every symbol that is contained 
in every rule from now on (unless a delete sub_ 
script is introduced, cf. below). This is nec_ 
essary, since we cannot let any information that 
is conveyed by the subscripts be lost, even if 
Mey 18 
it be irrelevant to the symbol in question (such 
as, say, a MODE restriction on a NP). One can 
easily imagine that rewrite rules of this type 
soon become very unwieldy ( even if we do not 
allow ,urselves to be frightened by the prospects 
of "millions of rules", Harman:605). Thus, in 
rule 7 of this comparatively simple grammar we 
already have 6 subscripts to each symbol. This 
number is substantially increased in the more 
elaborate version of the grammar (see Appendix 
to Harman's article). This is certainly not 
what one would call simplicity of description. 
\[Jut objections of this kind can be met by the 
following consideratiun: even if the multiDli_ 
cation of entia, i.c. symbols and subscripts, 
seems without rationale for humans, one can 
conceive of it as 8 necessity for computer data 
handling, and the computer certainly does not 
mind going through all the subscripts, adding 
some, deleting others, etc., every time a sym_ 
bol is mentioned or expanded. So, if one has a 
working program in which these restrictions can 
he written out as subroutines, and if the com_ 
i)uter space needed does not exceed that avail_ 
able, the objection just made does not hold 
(cf. Harman:61Ofn.: "Many of these grammars are 
in the form of computer programs for generating 
actual sentences.") 
The other question is far more important. It can 
be split up into ~¢o parts: 
i. Can all the data of the grammar be put into 
the subscript_restriction schema? 
2. Will the subscript_restriction schema not 
Mey 19 
put more data into my grammar than wnnted? 
The first question concerns the adequate re_ 
presentation of the structure, the other ex_ 
presses the fear that I may add structure to 
my grammar, thus oroducin~ sentences that are 
not grammatical (see Chomsky 1962:514ff.) 
Adoptin~ a distinction made by Chomsky, I 
make the following assertion: A PSG/S will serve 
as a more or less adequate observational and 
descriptive representation of the facts covered 
by a normal PSG; as far as TG is concerndd, the 
structure of the transformational model (how 
trees mad into trees) will not be represented 
adequately on the descriptive (and perhaps not 
even on the observational) level by a PSG/S. 
In no case the PSG/S will attain the level of 
explanatory adequacy. 
The first Dart of my assertion can easily be 
proved from the observation that a normal PSG 
and a PSG/S are strongly equivalent grammars, 
the only difference being the notation. (On the 
notion of equivalence, of. also Hays 1965:519). 
In fact, it makes no difference whether one ex_ 
pands a symbol on the basis of a rule to be af_ 
fixed to the constituent by means of a sub_ 
script, or on the basis of a rule contained so_ 
mewhere else in the grammar. The essential is 
that ~eration proceeds from left to right, and 
one symbol is F)roduced at a time. (See discuss_ 
ion above, 1.2). 
To Drove the other half of the assertion male 
above, I will try to give an answer to the two_ 
MeT 20 
fold question about representation of struct_ 
ure. Let's go back to the elementary example 
of the optional T , and try to imagine how this q 
is handled in a PSG/S. The main difference be_ 
tween PSG and TG is that the rules in PSG oper_ 
ate on symbols, in TG on strings of symbols. 
When I put a subscript on a symbol that is part 
of a string, and I want to mark off a struct_ 
ure that is based on several symbols occurring 
in a certain order, I will have to mark a Ii 
the symbols of my string in the same way, and 
this way of :~larking must be unique, i.e. de_ 
fine a unique path through the rules. This path 
may, in due course, require additions, deletions, 
permutations and the like. Now, in TG these op_ 
erations are carried out after the PS deriv&tion 
has been completed. In PSG/S, ho~Tever, the 
cleavage between affirmative and interrogative 
sentences occurs already in the third rule, 
where $2 is expanded into NP + VP, VP + NP, 
respectively (omitting the subscripts). The 
two derivations follow separate paths through 
the rules: in terms of tree diagrams, what is 
left in the one is right in the other of the 
two trees, In this way, many PSG rules are un_ 
necessarily duplicated (see above); moreover, 
the relationship between interrogative and de_ 
clara~ive sentences, as defined in TG, is reduced 
to a remote common source of derivation, namely 
$2. It is not true that "Sentences are ~rans_ 
formationally related' to the extent that the 
Mey 21 
same choice of restrictions is made in their 
derivations and if the same lexical c',oices 
are made where i~ossible" (Harman:608{ sincle 
quotes are his), unless one takes "'transfor_ 
mationally related'" in a sense rather differ_ 
ent from Chomsky's, namely: sentences that have 
a (partial) oath through the rules in common. 
This is, in fact, the only 'transformational 
relation' that it is possible to define in a 
PSG/S, but unfortunately, it is not transfor_ 
mational. Even in the case that two paths coin_ 
cide, and coincide altogether, we do not have 
'transformational relatedness', but "grammatical 
similarity" (Harman:6OS). Lexieal choices have 
nothing to do with this relation: both in PSG 
and in rG the choice on the lexical level is 
made after the aoDlication of expansion, reso_ 
ectively transformational rules. (This is not 
altogether cor~.ect: lexical choices may be made 
earlier and thus affect the derivation, but 
this is beside the point; complex symbols (see 
Klima 1964) are not taken into consideration 
here, but they could be built into a PSG as 
well as into any other generative grammar. I 
think, e.g., that some com,~lex symbol could be 
devised to prevent sentences like The man 
walks the men, that could easily be generated 
in accordance with the rules described on TIp. 
609_10 of Harmsn's article.) 
In my opinion, a PSG/S will never be able to 
show transformational relationships as formally 
defined and described by Chomsky and oZhers; 
hence such a grammar, even though it may attain 
Mey 22 
a certain descriptive adequacy, will never give 
an explanation of the fact that precisely this, 
and not some other sentence, is t~ansformed 
into another structure. 
2o3. Deletion in a PSG 
Another difficulty in PSG/S concerns the problem 
of deletion rules. In normal PSG, no deletes 
are permitted (Chomsky 1961:9)o Harman gives as 
reason for this restriction that trees must be 
uniquely recoverable in a I~SG (p.603). This is, 
however, only part of the motivation. Deletes 
are not symbols: they cannot be expanded (un_ 
less one chooses to ex~)and them into deletes, 
which is obviously useless in a description)° 
Whenever a deletion rule occurs, the structure 
of the derivate is altered in such a way that 
rules may a~ply which originally should not. 
One could say that deletes are extremely con_ 
text_sensitive: in !{at;nan's PSG/S, which in 
reality is a highly restricted PSG, the number 
of rules having the form A--> Z is very limited 
indeed, even though the author advocates their 
use (9.605). In passing, I would like to remark 
that nearly all of the deletion rules have to 
do with the ex,oansion of NP/I~H (this subscript 
occurs only once in the smaller ~rammar, p.609, 
and should therefore be rejected by the machine, 
since there are no constituents on which the 
rule could a~ply.) 
The real reason why a delete cannot be admitted 
in a PSG (especially a highly context_sensitive 
Hey 23 
one) is that the rules following the deletion 
rules should be modified or alte~'ed completely 
, otherwise it would not be possible to keep 
the distinction between not_rewritten and re_ 
written symbols clear: the rules following de_ 
letion might thus operate on symbols orif~inally 
belonging to the context. (Note, by the x¢ay, 
that in the case of wh_words the context l~ro_ 
blem is somewhat simplified by the fact that 
these words normally stand at the beginning 
of a sentence, so that the left context can 
be thought of as zero.) In our example, the 
transformational rule for interrogative sent_ 
ences to be generated from declarative ones 
operates on a string of symbols that may be 
symbolized X 1 _ X 2 _ X 3 (Chomsky 1957:i12), 
carrying it into the shade X 2 _ X I - X 3. 
Now, suppose that in the course of the deriv_ 
Rtion to non_terminsl symbols (the kernel 
string) we have a deletlon rule operating, say, 
on "( Suppose moreover that the non_terminal i ° 
symbol following X 3 qualifies for the condi_ 
tions originally put on X 5. The transformatio_ 
nal rule will then operate on a string X 2 _ 
X~ _ X4, and carry it into X 3 _X 2 _ X~, thus 
generating a non_grammatical sentence. I do 
not pretend that the actual PSG/S as Drooosed 
and described by Harman in his article ~,,ill 
generate these sentences: as already sai~l, the 
grammar makes a very cautious use of deletions, 
so that sentences like the ones mentioned will 
not occur. This does not, ho~,yever, invalidate 
the criticism. 
Mey 24 
Subscripts may not only be added in A PSG/S, 
but also deleted. In this manner a restriction 
that has been put on a certain rule can be re_ 
moved (this deletion of subscripts is of course 
quite another matter than the deletion of sym_ 
bols discussed above). Subscripts may be su)er_ 
fluous, such as in Rule 8.1 (p.609), where 
the subscript AUX_MODAL is removed from the 
constituent INFINITIVE by the subscript 
--AUX_MODAL, even though the lexicon would offer 
no ambiguous rewrites in the case of a non_ 
removal of the superfluous subscript. One could 
perhaps wonder why this precaution is taken, 
since in many other instances superfluous sub_ 
scripts persist all the way through the deriva_ 
tion (see discussion above). In other cases, 
the removal of subscripts can be motivated 
by the desire to orevent ungrammatical "loops", 
i.e. endless recursive expansions that have no 
justification in the grammar. Thus in Rule 8ol 
the symbol VP3/AUX_MODAL is expanded into 
INFINITIVE/°.. + VP3/AUX_HAVE,--AUY_MODAL, thus 
preventing another expansion by the same rule 
of VP 3. If, on the other hand, we wish the 
symbol in question to be expanded recursively 
(and according to the latest develo,)ment in TG 
there should be no difficulty in admitting 
recurslvity for all symbols, S not excluded: 
see Klima 1964), we can restart the cycle by 
wiping our slate, i.e. deleting all the sub_ 
scripts by means of the instruction ERASE.0TIIERS, 
to be incorporated as a subscript on the right 
Mey 25 
hand side of the ruleo Naturally, we would ex_ 
pect a subscript of this kind to occur in those 
cases where a whole sentence is to be embedded 
into another hy means of what in early TG was 
called "generalized transformations" (Chomsky 
1957: 113) o Th~ominalizing transformation is 
an instance i~ind" under ~g in the extended 
PSG/S (p.613), we find, among others, the entry: 
NP8 --> Sl/CLAUSE. TYPE:NOMINALIZATION, SUBJ. INo 
GENITIVE, B, C ,D,E, Z,Y, ERASEoOTHERS 
This means that all the subscripts originally 
found on NP8 are to be deleted; the new sub_ 
scripts deal exclusively with the derivation 
of the embedded clause (as can easily be veri_ 
fled from the rules of the PSG/S as given in 
the Appendix of the article). 1~'hereas TG keeps 
track of the chan~es to be made by means of a 
structural description of the pair of kernel 
sentences involved, together with a formula for 
sh~/ctural change, in PSG/S we have only a con_ 
stituent NP to be expanded by means of DS rules° 
How this NP fits into the stmucture of the ori_ 
ginal kernel sentence (being essentially its 
path through the PS derivation) can be fo\] low_ 
ed in .nSG by tracing back the nodes of the tree 
representation. In PSG/S, this path is marked 
by the subscriots added to the NP in question. 
Now, all this information is struck from the 
record by the removal of the subscripts in 
ac,:ordance with the instruction ERASE OTHERS° 
~struCtural descri!)tion of the sentence as a 
whole is not available: the expansion of NP8 
destroyed our bridge back to the original So 
It is as if we ha~een expanding a constituent 
while forgetting what it was we were expanding. 
Mey 26 
2o Conclusion 
Of the two models discussed here, the first one 
(PSG/PDS) has not actually been proposed as a 
full_scale grammatical mo:Iel, but I have tried 
to show that the implications of the claim 
that any shorgcomings of PSG can be ow:rcome 
lead to difficulties of about the same nature 
as those encountered in the second molel (PSG/S). 
Descriptive adequacy is not attained in those 
cases where structural descriptions are rele_ 
vant for the operation of the rules: neither 
PSG/PDS nor PSG/S permits one structural descr_ 
iption to be carried over into another. As one 
will have noticed, the argument in both cases 
runs a lon~ the same lines. Moreover, of the 
several devices proposed by Har:~an to boost the 
.)ower of PSG, the deletion rule was explicitly 
rejected on the ground that it would add too 
much power to the ~rammaro On the other hand, 
the use of subscripts, no matter how carefully 
chosen, will not help enlarge the descriptive 
Dower oi" the gramm,~r (Harman 1963:605) enough 
to account for all the grammatical sentences of 
the language. Thus, one_level grammars like the 
ones discussed above will not attain explanatory 
adequacy in any case, and in some cases not even 
descriptive adequacy. "Dieser Versuch /namely, 
the defense of phrase structure, JM/ verfehlt 
den entscheidenden Punkt abet in zweifacher 
}{insicht: Erstens uberschreiten die Regeln 
Harmans die Kapazitat einer PSGo Und zweitens 
losen such sie nicht das Problem einer geigneten 
Zuordnung yon Stammbaumen." (I~ierwisch 1964: 
49fn. ii ) 
Mey 27 
Lg 2~ (1947), 81_117 
Mey 29 
I \] 
l+i I+2 
"~OLL.IN" 
i--~ I 
"ROLL.(N/T" 
FIG.I. THE T~I~MPORA~y MEMORY 
th@~ big 
as nlce 
-\] 
a fool 
j ! ~ j 
little parlor 
m~s de Io que sabe 
FIG. 2. DISCONTINUOUS ~IULTIPLE CONSTITUENPS 

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