HOW DOES NATURAL LANGUAGE QUANTIFY? 
Michael Hess 
University of Zurich, Seminar of General Linguistics, 
Plattenstrasse 54, CH-8032 Zurich, Switzerland 
ABSTRACT 
It has traditionally been assumed that Natural 
Language uses explicit quantifier expressions 
(such as "all" and "most", "the" and "a") for the 
purpose of quantification. We argue that expressi- 
ons of the first type are comparatively rare in 
real world Natural Language sentences, and that 
the latter (articles) cannot be considered stra- 
ightforward quantlfiers in the first place. How- 
ever, practically all applications of Natural 
Language Processfng require sentences to be 
quantified unambiguously. We llst a few possible 
( syntactical, semantical, and "pragmatical") sour- 
ces of "implicit" quantiflcatlonal information in 
Natural Language; they combine in sometimes 
intricate ways to give a sentence a (more or less) 
unambiguous quantification. 
i. THE LACK OF EXPLICIT QUANTIFICATION IN 
NATURAL LANGUAGE 
- " I. i INTRODUCTION 
The subject of the present paper is not strictly 
one of Computational LinEuistics. Neither does it 
outline a working computer program, nor investi- 
gate a linguistic problem with the help of compu- 
tational methods. A/though the subject may be 
purely linguistic in character it is particularly 
relevant to Computational Linguistics. Moreover it 
seems to have been ignored by most non-computa- 
tional linguists. 
Computational as well as non-computational 
linguists agree that we have to represent Natural 
Language sentences as quantified logical senten- 
ces, either in a graphical variant of logic such as 
semantic networks, or in some other form of 
logic. However, non-computational linguists do 
not very often use real-world examples in their 
investigations; they create their own example sen- 
tences to make a certain point. Everything which 
is not in the prhnary focus of their interest is 
made so explicit as to become largely self-expla- 
natory. They tend, for instance, to create only 
sentences where quantification is explicit. Com- 
putational linguists, on the other hand, have to 
use real world texts. They have to face certain 
nasty facts of life which they, too, would prefer 
to ignore. One of them concerns the way in which 
Natural Language quantifies. 
1.2 THE TRADITIONAL POINT OF VIEW: 
QUANTIFIERS ARE EXPLICIT 
Traditionally it has almost always been assumed 
that quantification is expressed in Natural Langu- 
age by explicit means. The most traditional view 
had it that simple surface words correspond one- 
to-one to the two classical quantifiers: "every" 
and "all" stand for the universal quantifier, 
"some" for the existential quantifier: 
every man is mortal 
some gods are mortal 
However, it has long been known that the over- 
whelmlng majority of real world sentences simply 
don't contain any of those explicit simple quanti- 
fier words.* For this reason (among others) Bar- 
wise and Cooper (1981) suggested that the con- 
cept of simple quantiflers should be extended to 
the concept of- gemern\]|~ed quant/fiers. They 
should take care of simple cases such as most men 
as well as of very complicated ones such as more 
than half of John's arrows. A generalised quanti- 
fer consists, in English, of a determiner (such as 
. 11 . n most or more than half of ) and a set expres- 
sion in the form of a noun phrase (such as "men" 
or "John's arrows"). Determiners are some, 
e'~e~, each, all, both, no, neither, many, fev;, 
most, a few, one, etc. However, even now a 
sizeable majority of sentences in any real world 
text would appear to lack quantification. That's 
why the most obvious determiners, viz. the and 
a (plus zero) have to be included in this list. 
But that's also where a new set of problems origi- 
nates. Articles have always caused problems 
when treated as quantifiers, and recently these 
problems have become increasingly' more difficult 
to ignore (Kamp 1981). 
1.3 PROBLEMS WITH THE INTERPKETATION OF 
ARTICLES AS QUANTIFIERS 
Again we start with the most traditional view of 
the question how articles could be interpreted as 
quantifiers. It saw both definite and indefinite 
articles as existential quantlfiers, with some addi- 
Uonal information in the case of the definite 
article. It was primarily this "additional informa- 
tion" which caused much discussion. 
* or verb phrases such as "there is" - quite pos- 
sibly the only "real" existential quantifier 
English has. 
I. 3. i Is the Definite Article an Existential 
Quantifier? 
Russell, in his classical analysis of the definite 
article (1905), maintained that a sentence such as 
1) The President of France is bald 
should be interpreted as follows 
EXISTS X: (president_of_frence(X) AND 
NOT(EXISTS Y: (presidant_of_frence(Y) 
AND NOT(X=Y))) AND bald(X) ) 
Here the "additional information" is given in the 
universal statement that X is the one and only 
President of France. Strawson (1950) pointed out 
that sentences such as 2 
2) The king of France is bald 
wou/d simply be false irrespective of whether a) 
there was exactly one king of France but he was 
not bald, b) there was no king of France to 
begin with, or c) there were several kings of 
France. Our intuition tells us that in case a) 
sentence 2 would certainly be "simply false" but 
in cases b) and c) it would be false "in a diffe- 
rent way". Strawson argued that Russell hadn't 
made the distinction between a sentence as such 
and the statement made by the use of a sentence. 
Sentences such as example 2, uttered at the pre- 
sent time, and under condition a), were non-eva- 
luable (not Strawson's term) rather than false. 
They may be evaluable, and even true, at other 
points in time (or space, we might add). A defi- 
nite noun phrase, then, does not assert the exi- 
stence of some object, it only refers to it, and in 
doing so it presupposes its existence. In the same 
sense it doesn't assert the uniqueness of the 
object referred to, either, it only presupposes it. 
Unfulfliled presuppositlons don't make sentences 
false, they make them" non-evaluable, i.e. the 
question of whether they are true or false doesn't 
arise. Whether the presuppositions of such a 
sentence are fulfilled depends on the concrete 
circumstances, given by the context. 
Subsequently it was noticed that Strawson's 
analysis gave no satisfactory explanantion for 
cases such as 3, 4 and 5: 
3) The unicorn is a mythical creature. 
4) The lion is a dangerous animal. 
5) The dog is barking. 
In 3 we certainly don't presuppose the existence of 
unicorns, but the sentence makes nevertheless 
perfect sense. 4 is actually the same case 
although the fact that lions do exist may obscure 
this fact at first. We obviously presuppose the 
existence of the concept of unicorns and lions in 
the listener's mind, but not the existence of these 
animals in the real world. 
Example 5 shows that definite noun phrases 
don't presuppose uniqueness of real objects, 
either. 5 makes perfect sense, in the appropriate 
context, but nobody would presuppose that there 
is only one dog in the world. The suggestion 
that we could temporarily restrict the universe of 
discourse to the point that it contains only one 
dog, precisely the one that is barking, is hardly 
very convincing on intuitive grounds alone, and 
furthermore McCawley (1981:265) pointed out that 
it would make sentences 6 and 6a equivalent, 
which they definitely are not. 
6) The clog likes all dogs. 
6a) The dog likes itself. 
It might be more appropriate to talk about uni- 
queness in a contextual domain (McCawley 
1981:265, expanding on Karttunen 1976; also Plat- 
teau 1980, Kamp 1981, Frey/l%eyla 1983) whose 
members are created by the context, and are not 
necessarily elementary real world objects (as in 
the universe of discourse) but can be sets of real 
objects, or possibly even purely notional objects 
such as concepts. As the problems of definite reference are 
treated in-depth elsewhere in this volume 
(Berry-Rogghe) we will restrict ourselves to this 
very sketchy outline of the problem. The main 
point in this context is that any notion of the 
definite article having an existential quantifier as 
one of its components has evaporated along the 
way from Russell's analysis to contemporary 
views. Without additional sources o£ quantification 
a considerable proportion o£ real world sentences 
would now appear to be merely un-quantified, 
meanlngless, expressions, which they certainly 
aren't. But it gets even worse. 
I. 3.9. Is the Indefinite Article an Existential 
Quantifier? 
The indefinite article seems, on the surface, to 
cause much less trouble than the definite article. 
Its interpretation as an existential quantifier 
always looked quite straightforward. However, it 
was noticed (Kamp 1981) that indefinite articles 
sometimes must be represented as universal quan- 
riflers. Prominent among these cases are the so- 
called donkey sentences, exemplified by sentences 
7 and 8. 
7) If Pedro owns a donkey he is rich. 
8) If Pedro owns a donkey he beats it. 
The trsditlonal, and most natural, representation 
of 7 is 7a 
7a) EXISTS X: (donkey(X) AND owns(pedro,X)) 
IMPLIES rich(pedro). 
where the top-most syntactic connector of the 
English sentence, i.e. the conjunction "if", cor- 
responds to the top-most connector of the logical 
form, i.e. the implication. However, if we apply 
the same schema mechanically to example 8 it will 
produce the non-sentence 8a: 
8a) EXISTS X: (donkey(X) AND owns(pedro,X)) 
IMPLIES beats(pedro, X). 
This is not a logical sentence because the variable 
"X" in the consequent is outside the scope of the 
existential quantifier and remains unbound. 8 
must therefore be represented as 8b 
8b) ALL X: ((donkey(X) AND owns(pedro,X)) 
IMPLIES beats(pedro, X)) 
where the indefinite article is now represented as 
a universal quantifier. Now we are in the most 
unsatisfactory situation that we have to represent 
two s~rntactically very similar surface sentences 
by two radically different logical sentences, and 
that the same noun phrase has to be mapped into 
9 
an existential quantifier one time, into a universal 
quantifier another time. 
If we try to consistently represent indefinite 
articles as universal quantfflers we get 7b as 
representation for 7 
7b) ALL X: ((donkey(X) AND owns(pedro,X)) 
IMPLIES rich(pedro)). 
which is indeed logically equivalent to 7a, but on 
purely formal grounds. The scope has been artifl- 
cially extended to span over terms without any 
variables, which certain/y runs very much against 
our intuition about the meaning of the original 
sentence. The conclusion cannot be avoided that 
even the seemingly innocuous indefinite article 
cannot be represented as a straightforward exi- 
stential quantifier. 
i. 4 COUNTEREXAMPLES: MOST QUANTIFI~.RS 
ARE IMPLICIT 
However, if articles are no longer available as 
explicit quantiflers we are in real trouble: Either 
all those Natural Language declarative sentences 
that do not contain any of the explicit quantifier 
expressions ("most", "some", "there is" etc.) 
cannot be represented as logical sentences at all 
for their lack of quantification, or else we have 
to find sources of ciuantiflcatlonal information 
other than explicit quantifier expressions. Now, if 
we look at sentences 9 to 14 we have to admit a) 
that they are reasonably normal sentences, b) 
that they contain no explicit quantifier expressi- 
ons, and c) that our intuition tells us neverthe- 
less that they are unambiguously quantified. 
9) A dog is eating meat. 
10) A dog eats meat. 
10a) Dogs eat meat. 
Ii) A man who loves a woman is happy. 
12) A man who loves a woman respects her. 
13) A man who loves a woman will Elve her a ring. 
14) A man who loves a woman will defend her 
ag-ln~t an attacker. 
We think, therefore, and try to show in this 
paper, that there must be many more sources of 
quantificatlonal information in NL than \]ust the 
traditional, explicit, cases. But the information is 
scattered over whole sentences, or even para- 
graphs, and must be combined to get a (more or 
less) reliable quantification for a sentence. 
This is a rather unattractive state of affairs: 
Traditionally, it was assumed that at least the 
form of quantifiers in hrL sentences was unproble- 
matical, and that we could concentrate right away 
on the questions of their scope, monotonlcity 
etc., difficult enough in their own right. If our 
diagnosis is correct, this is not so. In the rest of 
the paper we will try to list some of the other 
possible sources of quantiflcational information in 
NL. None of them will be of the "on/off"-variety; 
they are all more llke interacting forces resulting 
in a net force tipping the balance one way mr the 
other. We will go through all the examples listed 
above, considering slightly more complex cases as 
we go along, and try to show how different these 
seemingly similar examples ~really are as far as 
their quantif~cati0n is concerned. 
• ..i 
2. 
2.1 
SOURCES OF IMPLICIT QUANTIFICATION IN 
NATURAL LANGUAGE 
SYNTACTIC MEANS TO EXPRESS 
QUANTIFICATION 
2.1. I Verbal Form 
The most important way to determine the quantifi- 
cation of a sentence by syntactic • means is 
through the choice of the verb form. This beco- 
mes particularly clear when we look at examples 9 
to 10a. They are striking cases in that 9 is a 
prototypical case of an assertion about an indivi- 
dual event and 10 and 10a are equally prototypi- 
cal universal ~ules. However, it could be argued 
that the mass noun used ("meat") unnecessarily 
complicates the situation. So let's replace them 
with the perfectly regular examples 15 to 18.2 
15) A text editor makes modifications to a text 
file. 
16) A text editor is making modifications to a 
text file. 
17) A text editor made modifications to a text file. 
18) A text editor has made modifications to 
a text file. 
In example 15 we say that a text editor makes 
modifications to a text file in general, almost by 
deflnltion. We might read this sentence in a 
system manual. In 16 to 18 we say, on the other 
hand, that there is, or was, a case of a text 
editor making modifications to a text file. These 
remarks might be made by a system operator, 
watching his screen. In 16 to 18 we express, of 
course, additional information about the temporal 
relationships involved, but we will ignore them in 
the present context, a Sweeping under the carpet 
the question of how we would have to represent 
the sentence predicate we could, as a very first 
approximation, represent the example with the 
verb in the present tense, 15, as 15a and the 
examples with verbs in either the past tense or in 
the perfective or progressive aspect, 16 through 
18, as 16a: 
15a) ALL T: (text_edltor(T) 
IMPLIES makes_modlfications .... (T)) 
16a) EXISTS T:(text_editor(T) 
AND makes_modifications .... (T)). 
We must qualify these statements at once. 
I. In many cases the future tense is prefer- 
red over the present tense for the kind of 
general statements given in example 15. 19 
is definitely more acceptable than 20: 
19) A man who loves a woman will stroke 
her. 
20) A man who loves a woman strokes her. 
2 Here, and in all the other examples used, the 
indefinite singular could be replaced by the 
plural without any change in quantification. We 
will ,for reasons of simplicity, use only singu/ar examples. 
10 
Dynamic verbs, such as "to stroke", seem 
to call for the future tense, whereas static 
verbs, such as "to respect", seem to go 
better with the present tense. The reason 
for this seems to be that static verbs do 
not require the future tense to express 
their permanent validity, as their very 
meaning as verbs of disposition etc. 
already conveys this connotation. Many 
other verbs go either with the present or 
with the future tense: "Oil floats on 
water" is as acceptable as "Oil will float on 
water". 
2. The past tense can express a universally 
quantified assertion, as in "A student read 
books when I was young", contrary to 
what we said above. However, for this 
universal quantification to be possible the 
sentence requires a spatial or temporal 
postmodifier, as the one printed in italics. 
The universal quantification is then not 
contributed by the verbal form but rather 
by the postmodifier; the present tense of 
the verb merely admits it. 
3. The progressive aspect can express unl- 
versa/ quantification, as in "John is always 
coming late". Again, thls is only possible 
it the quantification proper is contributed 
,~alulte explicitly by phrases such as 
ways", "in general", "regularly" etc. 
The sentence is more emotional than the 
version in the present tense. 
Ignoring all these exceptions we can formulate the 
tentative rules i%1 and 1%2 to sum up what the 
examples considered so far seem to suggest. 
1%1) The subject of a sentence is 
existentially quantified if the VP is 
I. in the past tense, 
2. in the progressive aspect, or 
3. in the reflective aspect. 
1%2) Otherwise the subject Is universally 
quantified, in particular ff it is 
1. in the present tense or 
2. in the future tense. 
3 See des Tombe et al., this volume, for a tho- 
rough treatment of the problems connected with 
the representation of temporal information. 
2.1.2 Restrictive Constructions 
Once we have determined the quantification of the 
sentence subiect we have to do the same thing for 
all other sententlal components. Examples Ii and 
12 for instance, repeated here for convenience, 
11) A man who loves a woman is happy. 
12) A man who loves a woman respects her. 
are variants of the donkey-sentences quoted 
above (7 and 8). There we had the problem that 
the object of the restrictive relative clause ("a 
donkey") had to be quantified existentially in the 
first case, and universally in the second, syntac- 
tically very similar, case. Analogously, we must 
now determine how "a woman" is to be quantified. 
Again, intuition tells us that it is to be quantified 
existentially in example ii but universally in 
example 12. However, how could we derive this 
fundamentally different quantification from the 
syntactically similar surface sentences? 
It's an intriguing observation that a simple 
change in notation will make the problem go away. 
Instead of the Predicate Calculus representation 
lla and 12a with their different explicit quanti- 
fiers 
lla) ALL M: (man(M) AND EXISTS W: (woman(W) 
AND loves(M, W)) 
IMPLIES happy(M) ) 
12a) ALL M:(man(M) IMPLIES (ALL W:(woman(W) 
AND loves(M,W)) IMPLIES respects(M,W)) 
we represent 11 and 12 in Horn-Clause logic as 
llb and 12b: 
Ub) happy(M) :-man(M), woman(W), loves(M,W). 
12b) respects(M,W) :- man(M), woman(W), 
loves(M, W). 
Under the standard interpretation of Horn-clauses 
(as in Prolog) a variable is implicitly universally 
quantified if it appears on the left hand side of a 
clause, but existentially quantified if it appears 
exclusively on the right hand side. The intere- 
sting fact is that the Horn-clause representations 
of the surface sentences are structurally as simi- 
lar to each other as the surface sentences are, 
and they differ exactly in the same way the sen- 
tences do. The seemingly minor change from a 
intransitive verb phrase ("he is happy") to a 
transitive verb phrase referring to an element of 
the antecedent ("he respects her") turns an exi- 
.stential quantification ("any man is happy if there 
ls a woman he loves") into a universal quantifica- 
tion ("any man respects any woman he happens to 
love"). And this is the quantification which virtu- 
ally "falls out" of the Horn-clause representation 
of theses sentences. 
It will be obvious that other restrictive 
constructions have to be treated the same way. 
Whether we say "a man loving a woman repects 
her" or "a woman loved by a man adores him" or 
"a man respects a woman provided he loves her" - 
in each case we will have to represent these 
restrictive expressions as right hand terms, as 
additional conditions on the values of the corres- 
ponding variables. We could therefore sketch the 
following informal translation correspondences: 
11 
1. the main verb (or the predicatively used 
• ~! ), noun or adjective, if the verb Is to be" 
i.e. the grammatical predicate of the sen- 
tence becomes the logical predicate consti- 
tuting the clause head; 
2. an indefinite NP becomes a predicate on 
the right hand side of the the clause; 
3. pronominal reference is represented by the 
use of the same variable name within one 
clause : 
4. restrictive phrases ( restrictive relative 
clauses, restrictive adiectlves, conditional 
clauses) become additional terms on the 
right hand side of the clause. 
Using these straightforward translation rules, we 
get a representation of surface sentences where 
the correct quantification, in many cases, "falls 
out" of the Horn-clause representation. In these 
cases we can then say that an indefinite noun 
phrase corresponds neither to a universal nor to 
an existential quantifier but that its quantification 
is a function of its position in the sentence. We 
will soon see that this kind of nice one-to-one 
mapping is possible only in a few, simple, cases. 4 
If we try to sum up what we gleaned from 
examples Ii and 12 we could sketch a rule i%3: 
1%3) In a restrictive noun phrase those of 
its arguments are universally quanti- 
fied that are referred to by the main verb; 
otherwise they are existenti-l\]y quantified. 
If we combine restrictive constructions with "exi- 
stentially quantiflying" verb forms, as in example 
21 
21) A text editor which made modifications 
to a text file erased it, 
we notice that the quantification imposed by the 
main verb overrides the quantification suggested 
by the restricitve construction. Example 21 would 
have to be represented somehow along the lines of 21a: s 
21a) text_editor (editorl). 
text_file(filel). 
modifies(editorl, fflel, timel). 
erases ( editorl, filel, timel). 
before(timel, now). 
4 We do not propose that all natural language 
sentences can be represented as (the 
Horn-clause version of) First Order Predicate 
Calculus sentences. But it seems a sensible idea 
to start our search for sources of implicit quan- 
tificational information with those simple cases 
where it is possible. 
s Existentially quantified variables not in the 
scope of a universal quantifier are represented 
in Horn-clause logic as a system-generated con- 
stant, a so- called Skolem-constant, such as 
"filet". 
We thus have to modify i%1 to the effect that the 
main verb form enforces its quantification for all 
dependent values. 
2.1.3 Non-restrictive Constructions 
Nearly all restrictive constructions of the type 
mentioned in the last section have their non-re- 
strictive counterparts. The restrictive relative 
clause in example 22 has its counterpart in 
example 23, where an additional pair of commas is 
the only syntactic difference, although the mean- 
ing of the two relative clauses differs fundamen- 
tally. 
22) Swap space which is used for storing editor 
programs is kept small. 
23) Swap space: which is used for storing editor 
programs, is kept small. 
In 22, the restrictive relative clause adds, of 
course, one mope restriction. In 23, the non-re- 
strictive relative clause asserts additional informa- 
tion. The author wants to make sure that the 
reader is aware of these facts, and that he 
absorbs the information if it's new to him before 
he goes on reading. Accordingly we would have 
to represent these examples as 22a and 23a 
22a) kept_small(S) :- swap_space(S), 
used_for_storing_editers (S). 23a) 
kept_small(S) • - swap_space(S). 
used_for_storing_editors (S) : - swap_space(S). 
We used the verb in the present tense to keep 
the situation as simple as possible. If we now 
consider the other possible case, with the verb in 
the past tense or in one of the marked aspects, 
we will note that 24 is odd to the point of being 
ungranunatical, while 25 is perfectly normal. 
24) A text editor, used for making modifications to 
a text file, brought the system to a standstill 
25) A text editor used for making modifications to 
a text file brought the system to a standstill 
We can consequently outline rule i%4 
1%4) Non-restrictive constructions translate 
into additional, universally quantified, 
assertions. 
Apart from the relative clauses and the redu- 
ced relative clauses in the preceding examples we 
can find non-restrictive constructions in the fol- 
lowing cases : 
I. Present participle : 
26) A text editor corrupting text fries is 
utterly useless. 
2V) A text editor, making it easy to modify 
text files, is eminently useful. 
2. Appositive constructions: 
28) A message that deleted files will be ex- 
unged by the system will be displayed 
ve minutes before expunging takes place. 
12 
L 
3. 
29) Another kind of m:%~ that the 
system is about , will be displayed 
about one millisecond 
before it actually happens. 
30) My friend Peter was here last night. 
31) My friend, Peter, was here last night. 
32) A command to delete a file will be 
executed with priority. 
33) Another type of command, to save a file, will be postponed 
for a few minutes. 
34) The decision whether to save or delete 
a file is normally made by the user. 
35) Another decision, whether to crash or 
not to crash, normally isn't. 
Prepositional phrases: 
36) A backup file on disk is immune from 
the effects of system crashes. 
37) A backup file, on disk, is immune 
from the effects of system crashes. 
In this case the non-restrlctlve variant, 
37, has a strong connotation of causality: 
" As the file is now on disk, it is immune 
from the effects of crashes". 
In all these cases the non-restrlctive 
construction asserted additional universally 
quantified information, although the appo- 
sitive constructions seem to cause more 
problems than the other cases. 
39a) prints(P, C) 
bold_faced(C) 
:- centronics_printer ( P), character(C), 
escape_sequence(E), receives(P, E). 
: - eantronics_printer(P), 
character (C), 
escape_sequence(E), 
receives ( P, E). 
In spoken language we could distinguish bet- 
ween the two readings of sentence 38 by means of 
stress: The second reading (38b) could be enfor- 
ced by stress on the verb ("A Centronics printer 
will PRINT a bold_faced character") while an even 
stress distribution on the whole verb phrase 
(",.. will PRINT A BOLD_FACED CHARACTER") 
would make the first reading (38a) far more pro- 
bable. In written language we could resort to 
topicalizers such as "even'r: "A Centronics printer 
will even print a bold-faced character ...". It is 
interesting to note that even in examples 39 and 
40 which are quantiflcatlonally unambiguous for 
syntactic reasons alone (39a) the stress is evenly 
distributed on the verb "print" and the adjective 
"bold-faced" (or on the adverbial "in boldface", 
respectively). As a matter of fact we could say 
that stress in English virtually marks certain 
words of a sentence as "to be represented as 
clause heads" in the Horn-clause translation of 
the sentence, with the consecmences for their 
quantification we just outlined, v 
2.1.4 Adjectives as Object Complememts 
If the verb of a sentence is a causative verb we 
can express the quantification of its argument 
values by the choice of the appropriate object 
complement.. Example 38 is ambiguous as far as 
the quantification of "a bold-faced character" is 
concerned (the two readings are "will print some 
bold-faced character", 38a, and "will print any 
bold-faced character" it gets, 38b), whereas in 39 
and 40 the same expression is unambiguously 
quantified; both 39 and 40 are mapped into 39a, 
meaning "will print in boldface any character" it 
gets. s 
38) A Centronics printer will print a bold-faced cha- 
racter whenever it receives an escape sequence. 
39) A Centronics printer will print a character 
bold-faced whenever it receives an escape 
sequence. 
40) A Centronics printer will print a character 
in boldface whenever it receives an escape 
sequence. 
38a) prints(P,skl(P,E)) :- oentrenics_printer(P), 
escape_sequence(E), 
receives(P, E). 
bold_faced(sk1(P,E)) : - centronics_printer(P), 
escape_sequence(E), 
receives (P, E). 
character(ski(P, E)) :- centronics_printer ( P ), 
escape_sequence (E), 
receives(P, E). 
38b) prints(P,C) :- centronics_printer(P), character(C), 
bold_faced(C), 
escape_sequence(E), receives(P, E). 
2.1.5 Conjunctions 
In the examples 38 to 40 we used the conjunction 
"whenever" instead of the neutral "if". This isn't 
quite unproblematical, as the choice of a conjunc- 
tlon may well have its own influence on the quan- 
tlflcatlon of some of the values in the sentence(s) 
involved. However, the precise character of this 
influence is unclear to us at the present time. In 
example 41 the noun phrase "a student" somehow 
seems to have a "higher content" of universal 
quantification than 42. 
41) If a student knows the words of a text he 
can translate it. 
42) When a student knows the words of a text he can translate it. 
But the two subtly different interpretations seem 
to be possible only because both "he knows" and 
he can are ambiguous: In 41 they can be read 
as "he already knows" and "he is capable of, 
knows how to", whereas in 42 they can be read . H . . 
as has looked up/has found out and he may . 
s Existentially quantified variables in the scope of 
a universal quantifier are represented as 
system-generated functions, so-called Skolem- 
functions, whose arguments are the variables 
over which these universal quantiflers range. 
v Phenomena such as the topic/focus-distinction 
and stress/intonation are often considered as 
purely styllstic in character. The examples used 
will show that this view is often unjustified. 
The Prague school has, of course, always 
emphaziaed that these linguistic means are often 
much more than "style". See the most recent 
contribution by the Prague school, Sgall 1984. 
13 
2.2 SEMANTIC MEANS TO EXPRESS 
QUANTIFICATION 
2.2.1 Meaning and Type of the Verb 
Although the syntactic means to express quantifi- 
cation can explain quite a few cases of "implicit" 
quantification there are cases where they are not 
sufficient. Two such cases are examples 43 and 
44. 
43) A man who loves a woman will defend her 
against an attacker. 
44) A millionaire who is concerned about his after- life will donate part of his money to a charity 
It is intuitively quite certain that we have to 
represent these sentences in a fundamentally dif- 
ferent way, namely as 43a and 44a. 
43a) defends_against(M,W,A) :-man(M), woman(W), 
loves(M, W), 
attacker (A, W ). 
44a) donates_to(M, skl(M),sk2(M)) :- 
millionaire(M), 
concerned_about_one' s_afterlife (M). part_of_money(skl(M)) :- 
millionaire(M), 
concerned_about_one's_afterllfe(M). charity (sk2 (M) :- 
miUionaire(M), 
concerned_about_one's_afterlife (M). 
The very meaning of "to defend" seems to enforce 
an universal quantification for both of thetwo 
object values, whereas the meaning of "to donate" 
seems to create an existential quantification for 
its two object values. We could, as a matter of 
fact, paraphrase 44 as "If you want to find a 
charity, or if you want to see some money, all 
you have to do is to find a millionaire with pangs 
of religion, and eventually you will see him give 
money to a charity". The meaning of "to donate" 
implies that the person donating something 
already has, or can easily get, whatever he dona- 
tes; he does not have to wait for it to come his 
way. Equally, the meaning of the verb implies 
that it will be a trivial task to find a taker for 
the donation. The meaning of "to defend", on the 
other hand, implies that the integrity of someone 
or something is defended against any conceivable 
threat, but only if and when a threat becomes 
visible. The same thing applies to the person etc. 
defended, hence both object values are univer- 
sally quantified (provided, of course, the form of 
the main verb permits it). 
2.2.2 Type of Direct Object 
There are relatively few cases where the meaning 
of a verb will unambiguously determine the quan- 
tifiaction of its argument values. One verb where 
this is certainly not the case is "to give". It has 
(among others) the meaning of "to pass on some- 
thing if and when one gets it" and "to hand over 
something one already has" (in this sense it is 
almost equivalent to "to donate"). It's these two 
readings which are unambiguously chosen in 
examples 45 and 46, respectively, as is made 
clear in their clausal representations 45a and 46a. 
45) Decent people will give lost and found property to the 
police. 
46) Decent people will give presents to their poor 
relatives 
45a) give(D,P,poUce) :- people(D), decent(D), 
lost_property (P), 
found(P). 
46a) give(D,skl(D,R),R) :- people(D), decent(D), 
relatives ( R, D), 
poor(R). 
presents(skl(D,R)) :- people(D), decent(D), 
relatives(R, D), 
poor(R). 
Again, we can say that the very meaning of the 
noun phrase "lost and found property" excludes 
an existential quantification. You simply cannot 
find something intentionally. On the other hand, 
a present is, by definition, something you make 
or buy, i.e. you virtually bring it into local (to 
the recipient) existence, unless, of course, you 
pass on a present you got, which is considered in 
poor taste in our societies. This last point 
brings us to yet another source of implicit quan- 
tificatlonal information: Pragmatic information, 
including world knowledge, situation and dis- 
course context. 
2.3 PRAGMATIC MEANS TO EXPRESS 
QUANTIFICATION 
Here we will look at the last remaining example of 
the original collection, viz. 
13) A man who loves a woman will give her a ring. 
Here, the meaning of the direct object "a ring" is 
not sufficient to determine its quantification. A 
ring could be found and passed on to someone 
one loves, as well as been bought and given 
away. However, our world knowledge (rather than 
our language knowledge) tells us that a man 
doesn't normally have to wait until he finds a 
ring if he really wants to give one to a cherished 
person. He can go and buy one; there are rings 
affordable to just about anyone. That's why 13a 
would be heavily favoured over 13b. 
13a) gives(M, skl(M,W),W) :- man(M), woman(W), 
loves(M, W). 
ring(skl(M,W)) -- man(M), woman(W), 
loves(M, W). 
13b) gives(M,R,W) :- man(M), woman(W), 
loves(M, W), ring(R). 
Similarly, discourse and situation context can 
determine the quantification in otherwise ambigu- 
ous sentences, such as 47. 
47) This printer will print a bold-faced 
character if you hit this key here. 
Here the situation context, as referred to by the 
three demonstratives, seems to impose an existen- 
w ,! . tlal quantification on a character . The sentence 
clearly means that pressing the key referred to 
will immediately result in the creation of a 
character, which will also be in boldface. 
14 
3. CONCLUSION 
There are quite a few sources of "implicit" quan- 
tification in English, most of them syntactic, some 
semantic, and a few pragmatic in character. Some 
of them fall into the category of linguistic means 
often considered purely stylistic, such as the 
toplc/comment-distlnctlon and stress/intonation. 
ACKNOWLEDGEMENT 
This work was supported under Grant Nr. 
81. 703.0.79 of the Swiss National Science Founda- 
tion. 

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