On the Use of IAn6uisti¢ Quantifying 0pera~ors in the 
Logico-Semanttc Structure Representation of Utterances 
Irena Bellert 
Warsaw University 
I. Introduction 
By now it has become olee~ to most linsuists that surface 
structures of utterances in natural laD6uage are not a suf- 
ficient basis for the semantic interpretation, an~ that an 
abstTact ~eep structure representation has to be assumed in 
a lin6uistlc desc~Iption, whlch la supposed to correlate the 
surface strua~xre hierarchical representation of each utter- 
ance with its msaniDg (or meanings in case of homonimi~y)° 
Since the problem of what should be understood as the meanln6 
of an utterance is not clear, the question of how deep etTuc- 
tures should be represented remains open for linguists, even 
for those who have been known as adherents of the transforma- 
tional generative 5Tammar, where deep structures are deter- 
mined in terms of generalized phrase markers (or some other 
similar concepts which get modified in the course of work). 
The questions which arise in postulating deep structure 
representations are often due to the lack of a possible guide 
llne ¢oncernin6 the division between the knowledge of l~a~e 
and knowled6e of the world, and thus between the information 
which should be included in a full description of a lan6ua~e 
a~ that which shoul~ or need not. The classical distinction 
between syntax, which concerns relations between lan~ua6e 
-2- 
signs, and semantics, uhich columns relations bergen lan- 
~a6e signs and extraliD6uis%-lc "objects" (or extraliz~aist- 
ic relations), has also become blurred up by the fact of in- 
troducinK into the lin~uistic des~pttem abstract struc- 
tures which are only indirectly related to the surface signs 
representin~ the elements t2~at actua/ly occur in utterances. 
However, even if we reckon the abstract deep structure dee- 
crip~lons as pertainin6 to syntactical relations - in spite 
of cex~ain attempts tO the contreury 3- we will still be left 
with difficulties in trying to establish ~he scope of semant- 
ic relations, that is, the relations between linguistic signs 
which occur in deep structure rep~esent~a~ions and extralln- 
Kuistio "objects" or relations. 
The difficulties whi=h arise in establiahln~ the scope of 
semantics are before all due to the fact that the overhel~n 6 
majority Of utterances contain siKns mhich are used in refer- 
ence to the addresser, addressee, t~e time, place and situa- 
tion in which a given utterance is produced2. Therefore, if 
we wanted to take s~tously the requizement that semantic re- 
lations should consist in relat~ S~DS with extTa~stic 
"objects", such a task would s~ply be unfeasible for a lin- 
~/st or semanticist, for it is cleeur that a~y two identical 
utterances used at a different time, place, or produced by a 
different speaker, should be inte:preted differently if they 
contain "token-reflexive" signs, ~ obviously they are relat- 
ed to two different extr~stic situations. 
-3- 
It is certain~ much more reasonable to follow a view held 
by some philosophers, logicians and linguists, which can be 
briefly recalled by means of a quotation from Roman Jakobson: 
"the meanln~ of any linguistic sign is its translation into 
some further, alternative sign, especially a si@u "in mhich 
it is more fully developed" as Peirce, the deepest inquirer 
into the essence of signs, insistently stated "3. The gener- 
al idea is certainly right, but such an approach leaves much 
freedom with respect to various possible ways of presentin~ 
"the alternative signs". Ne will not discuss here the differ- 
ent proposals connected with such an approach to semantics, 
their assets and drawbacks, but - accepting in principle 
the thesis that a semantic model for natural language can on- 
ly be established by means of "alternative signs" - we will 
suggest one of the possible ways of describi~ the semantic 
interpretation of utterances. 
Following a concept which has already a certain tradition 
in philosophy, semantics an~ logic ~, but has never been taken 
seriously by linguists, I will accept the view that the sem- 
antic interpretation c~ an utterance is the set of consequen- 
ces which can be derived from that utterance (or more strict- 
ly, from its deep structure description) on the basis of 
certain implicatienal rules that can be established for the 
given language. Accordingly, I attempt to search for such 
a description of deep structures for which it ,/ill be pos- 
sible to formulate the rules ~hich i call quasi implica- 
tions 5. In order to avoid confusion in using the term "deep 
structures" (which by now is employed in different senses, but 
should be reserved for transformational deep structures, for 
which it has been clearly defined), I will refer to the logi- 
co-semantic structure (LS structure) of utterances 6. 
The identification of the semantic interpretation of an 
utterance with the set of consequences or conclusions which 
can be drawn on the grounds of that utterance is very close 
to our intuitive understanding of how we interpret utterances. 
To say that the addressee understands an utterancep only if he 
is able to draw all the conclusions implied by the given ut- 
terancep seems to be compatible with the ordinary thinki~ and 
the estimation of a fully adequate understanding of an utter- 
ance. The fact that certain conclusions are based on prem- 
isses corresponding to the addressee's beliefs which belong 
to his knowledge of the world precisely reflects what has 
been mentioned earlier about the lack of a clearcut division 
between the knowledge of language and knowledge of the world. 
In fact such a division can only be arbitrarily established 
for a given description of language. For instance, in des- 
cribing a lexicon (or the rules of the lexicon in a theory 
of language), we have to make a decision as to Whether cer- 
tain information concerning a lexical item should be includ- 
ed in the lexicon~ or treated as encyclopaedic information, 
which pertains to such or other domain of science, speciali- 
zation, etc. The arbitrariness of this division ooncerns, 
l 
however, usually the boundary problems with respect to 
which such questions arise, but it does not effect the fact 
-5- 
that in the majority of problems there is a general agreem- 
ent of lin6uists as to what syntactical and lexical inform- 
ation should be included in the linguistic description in 
some or other way. Once such a decision is made, and the in- 
formation is included in a lin6uistic description, we should 
be able to define clearly what consequences can be drawn on 
the basis of a given utterance and linguistic quasi iMplica- 
tions, and what ones require additional premisses which be- 
lon~ to the knowledge of the world. 
To give an example, we may say that a speaker or author 
uses appropriately 7 the utterance : 
(1) ~ixon has left the United States 
8 
only if his purported belief is that : 
(la) there is one and only "object" which is bein~ referred 
to bj him as "Nixon" 
(Ib) there is one and only "object" which is being referred 
to by him as "the United States" 
(1¢) Nixon was in the United States before 
and if his purported claim is that : 
(1~) Nixon is not in the United States at that time. 
The propositions (la, lb, lc and ld) can be derived formal- 
ly from (I) on the basis of certain linguistic quasi i~pli- 
cations 9, and they below, among ethers, to the set of con- 
sequences which constitutes the interpretation of (I). On the 
other hand, the proposition 
(le) The President of the United States has left the United 
State s 
is a conclusion based on the premiss :"Nixon is the President 
Of the United States"~ which may belong to the speaker's and 
heater's knowledge of the wOrld, but if not included in the 
-6- 
description of the lexicon, it will not be derived formal- 
ly as a consequence. 
It is worth noting that the propositions (la, Ib, ic) 
concern the speaker's purported beliefs, whereas the pro- 
pOsition (ld) concerns the speaker's purported claim or 
assertion. The difference is significant, for if we con- 
vert (I) into a ~aestion, negation, wish, command, etc 
(Has Nixom left the United S~ates. E ~ixon has not left the 
United States, I want Nixon to leave the United States, etc) 
then the consequences pertaini~6 to the speaker's beliefs 
will remain the same, and it is only the consequence (Id) 
pertalnin6 to the speaker's assertion that will become 
oorrespomdln61y d/fferent. In general all the consequen- 
ces derived from an utterance can be accepted only as a 
set of propositions which correspond to the purported at- 
titude of the speaker, n.~ as a set of propositions which 
hold true. The question of w~ether such propositions are 
true or not is not a linguistic question, similarly as the 
problem of whether the "object" being referred to exists 
in reality or is to be assumed in the context of a novel 10 
In terms of the approach suggested here~ontological consld- 
erations have no beariD6 on the LS structure description 
of utterances, from which ~he same consequences can be 
d~awn~independently of whether the speaker is sayIn6 the 
l 
truth or lyin6, whether he is relati~ his dream, tellln6 
a story or repcrtiDg facts. 
In this paper we will discuss only those aspects of the 
LS structure representation which concern certain liz~ist- 
-?- 
ic quantifyiD~ operator2. As in general we assume that the 
LS s~ructure could be represented in a language somehow an- 
alogous to that of a modified predicate calculus, our aim 
in the present discussion is to suggest a certain w~y of def- 
ining the use of linguistic quantifyi~, operators which 
would be in agreement with the interpretation of utterances 
in natural language ~ the present paper is concerned with 
11 English utterances only. 
The problem of defining the use of linguistic quantifying 
operators in the LS structure description seems to be one 
of great significance for the semantic interpretation of 
the surface syntactic relations, for it appears that it is 
hardly possible to assign an adequate semantic interpreta- 
tion 12 to an utterance, if its LS structure is not conceived 
of in terms of at least one predlcate and its ars~ment (or 
arguments) prefixed by some linguistic quantlfyi~ operator. 
AD~thing we talk about~ that is~ any subject (or sub~ects) 
of predication, is either a particular "object", a particul- 
ar relation between "objects" of some sort, a particular si- 
tuatlon, event, stc~ or else it m~y be a certain number 13 of 
~'objects"p situations, etc which are such and such, or final- 
ly the subject of predication may be each "obJect"~ situation, 
ere, which is such and such. Generally speaki~, en utterance 
is analogous to a logical sentence or proposltion~ rather 
than to a propositional function with free variables~ and 
~hus the LS structure of an utterance may be best conceive~ 
as a fo~nula in which ~e make use of some sort of lin@~ulst~ 
Io quantlfyin~ operators. 
-8- 
The analogy with the language of predicate calculus is not 
very precise though, and - as we shall try to show - the lin- 
guistic quantifying operators must be defined differently than 
these defined in logic. In the first place, there is a great- 
er number of linguistic devices which function as quantifiers 
of some sort, and in the second place, even those devices which 
show an analogy with the operators used in logic have a slight- 
ly different semantic function and cannot be defined for our 
use in the same way as those defined in logic. In the pres- 
ent paper we shall discuss only two linguistic quantifying 
operators I@, one being analogous to the iota operator def- 
ined for the predicate calculus, the other one being analog- 
ous to the general quantifier. 
2- The linguistic iota operator 
The iota operator, as defined in logic 15 can he used in 
the expression (~x)~(x),only if the propositional function 
is a unit function, that is, if it satisfies two con- 
ditions, one concerning the existence, the other the unique- 
ness of the "object" which is ~ . Such conditions ms2 be 
expressed formally as 
The expression (~x)~(x) has the category of an argument 
(not of a statement), and may be interpreted as the English 
expression of the category of a nominal phrase, namely, :"that 
one and only object which is ~ ". 
Now when comparing the expressions in English which have 
-9- 
a similar semantic function as the unit function, namely, 
lingulstlc indices 16, it is immediately obvious that we 
are not in a position to prove that they satisfy the con- 
ditions of existence and uniqueness, on the contrary, it 
would be hard if not impossible to find a single lin6ulst~c 
index which, as such, would satisfy such conditions. 
~evertheless, it is an empirical fact quite evlden~ ~hat 
whenever an addresser uses an utterance containiDg an in- 
dex ~ in the normal ~ process of communicatlon, it 
is always in accordance with his purported belief that 
there is one and only "object" which is being referred to 
as ~ • 
In contradistinction to a formal system for which we 
have ~e define the rules and conditions of correct use, 
the linguist works in the opposite direction. For we al- 
rea~7 have a given system which we all use successfully 
for the purpose of intercommunAcation, and the linguist's 
or the semanticist's job is to detect the rules that make 
possible the achievement of mutual understandln 6 among 
~he competent users of the given language system• Thus 
in the first place we can analyse utterances only with 
the assumption that they are used appropriately - other- 
wise no consistent analysis would have been possible. 
The appropriate use of language, as defined for our pur- 
pOSeSD is nothing mere than a use which is consistent with 
~he rules of language and with the speaker's purported 
propositional attitudes. It would be thus unreasonable 
~o reject such an obvious assumption. 
-lO- 
We may trytthen)to establish quasi implications ~lich will 
held truelTand thus yield the correspondi~ consequences for 
all eases of lin6uistic use in the process of communication. 
Accordin61y, we will show that what is defined as a condition 
of correct use in a formal system, will be derivable in our 
oase as a consequence of a given utterance. 
In the second place, we take into account the fact that 
utterances of natural lan6uage are never, so to speak, hun6 
in the air, but are always interpretable in terms of what we 
18 call the propositional attitude p or modal frame 19 when refer- 
riD6 to its explicit representation. For no utterance used 
in the process of communication can be fully interpreted 
without our understandiD6 it as a proposition which expresses, 
amoD6 other things, the speaker's or author's propositional 
attitudes, which may be beliefs, assertions, doubts, requests 
(for oral or other responses) or any other attitudes. 
Accordin6 to such an argumentation, the propositions which 
correspond to the two conditions for the correct use of a 
unit function, (a) and (b), will be accepted in our case as 
consequences which beloD6 to the interpretation of any utter- 
ance ~ containin8 a linguistic index . Such propositions 
cannot,however, be represented as ocourrin~ in an assertorio 
modal frame, but in the modal frame :"The speaker believes 
that ... " (where the term "believe" is used in the sense of 
purported belief). The quasi implicational scheme on which 
such consequences are drawn is roughly speakin6 as follows: 
For any linguistic index ~ , the speaker uses appropriate- 
W ~ only if he believes that there is an "object" which ly 
-ll- 
is ~ , and that the "object" being referred to as ~ is 
uni que. 
Since the consequent of this statement can be assumed to 
express one of the necessary conditions for the antecedent 20, 
we ma~ consider the whole statement as a quasi iMplicatisn. 
Thus in the case of any utterance which contains a lin@uist- 
accept 
ic index, we may ~ a statement correspon~ing to 
the antecedent as hold~ true - by virtue of our general 
assumption of appropriate use - end therefore we can al- 
ways infer the corresponding consequent as a consequence. 
We thus preserve the uniqueness of the purported "object" 
by means of inserting into the common (and thus intersubJee- 
tire) semantic interpretation of indices a parameter which 
isrttoken-reflexiverPand which serves its purpose(a~ time an 
utterance is actually used~ in relating signs to extralin- 
~stic "objects" or relations,throug~h the identification 
of the speaker, the time, place and situation in which ~he 
given utterance is used. Accordingly;the value of the argum- 
ent - which in the case under discussion is a linguistic in- 
dex~ is understood in any particular case, without being 
possibly indicated in a general linguistic description. In 
refers other words~ the fact that 
the speaker ~ to one 
am~ only "object"! each time he is using an imde~ belongs to 
the semantic Interpretatlonpan~ is reflected in the propose~ 
LS structure representation and the corresponding consequen- 
ces "which ere derivable from It, but the question of what 
"object" me~ actually be identified by means of such an ex- 
pression does not belong to the domain of lingaistics° 
- 12 - 
A~ such "object" m~y only be described in terms of linguist- 
ic expressions - it may either be pointed to by means of 
a name used as an index, or described in terms of the lex- 
ical items contained in the definite description used as an 
21 
index. A linguist solves thus the problem of how an "ob- 
ject" is described or pointed to in order to be identified, 
and he ~ not be concerned with Iha___~t it is. 
It thus appears that the lin6uistic iota operator is a 
close analog to the iota operator as defined in logic, the 
dif~erences lying in our treating the conditions of correct 
use defined in logic as the consequences of the ever-assumed 
appropriate use of utterances, and in our introducing the 
propositional attitudes into the LS structure description. 
As it will be argued below, the next linguistic quantifyin~ 
operator to be discussed in this paper, namely, the all-op- 
erator, will also be defined partly by analogy to the iota 
operator, for the reasons based on linguistic evidence. 
The all-operator 
In the preceding section we have discussed a certain type 
of ars~Ament prefixed by the iota operator. Such an argum- 
ent will be referred to as an argument of type I. Its ex- 
plicit exponent on the surface can only be a linguistic 
index, and its role is to indicate one and only "object" 
to which a given predicate applies. At present we will 
discuss another type of argument - which will be referred 
to as an argument of type 2 - whose role is to indicate all 
the "objects" to which a given predicate applies. The ex- 
plicit exponents on the surface of English utterances are 
usually nominal phrases preceded by "all", "every", "each". 
-13- 
However, it is not always the case that such nominal phrases 
are to be interpreted as arguments of type 2 (consider 
phrases such as, for instance, "all the country", every sec- 
ond French man", "each time", etc). Let us now discuss the 
followln6 examples by means of which we will show the anal- 
ogy between arguments of type 1 and those of type 2. 
(2) John has awaken 
(3) JY father has awaken 
(4) Ky parents have awaEen 
(5) All the members of my family have awaken 
(6) All the inhabitants of this house have awaken 
(7) All the inhabitants of the moon have awaken 
Independently of other problems connected with the proper 
LS structure representation of utterances in which a predi~ 
applies to each individual of a set determined by a given ~es- 
22 
cription, we have to admit that all the nominal phrases in 
our examples have a similar function ; they serve to identify 
either a single individual (utterances 2 and 2), or a certain 
number of individuals (utterances 4,5, 6 and 7), and thus 
serve to indicate the values of the argument used with the 
predicate "has awaken". Thus if we compare : 
(8) The boy standing in the doorway is tall 
with 
(9) All the boys standing in the ~oorw~7 are tall 
it seems clear that the difference between the t~ lies in 
that the nominal phrase in (8) serves to indicate or identify 
one indlvldual~ whereas the nominal phrase in (9) serves to in- 
dicate or identify a certain number of individuals, both n@~- 
inal phrases beinK used as "instructions" for identification, 
and as such correspond to the argument of the predicate "tall". 
Such "instructions " are used approprlatelyponly if the speak- 
er believes that there is a boy standing in the doorway (for 
8 ) and that there is more than one boy standin 6 in the door- 
way (for 9). Consequently by virtue of our Keneral assmap- 
tion of appropriate use, it is possible to infer such pseudo- 
existential propositions in the model frame "The speaker be- 
lieves that • •.." 
One might object to this interpretation of all-statements 
and try, by analogy to logical statements with a general quan- 
tifier, to interpret them as implicational statements :For a~ 
if x is ~ , then x is ~ . Under such an interpreta- xp 
tion the utterance (9) would be a paraphrase of -- 
(i0) If anythlng is a boy standing in the doorway it is tall 
If anybody is a boy stsnding in the doorway he is tall 
Anybody who is a boy standin6 in the doorway is tall 
Even if we ignore ~he awkwardness of utterances such as (i0), 
we cannot accept such utterances as paraphrases of (9) for 
reasons. First, (i0) could, then, equally well be taken as a 
paraphrase of (9) as that of (87, as there is no uention with 
respect to the plurality of the individuals being referred to. 
Thus (i0) could be accepted as one of the consequences from 
(9), (and this will be shown below to be the case), but not as 
an equivalent proposition. Second,, the speaker implies by (9) 
his purportecl belief that there are individuals who are boys 
standing in the doorw~7, whereas no such izplication bholds 
for (10). To give a clearer example, if someone says 
(11) All the inhabitants of the moon must feel cold 
the heater's reaction might be expressed by ~'"~at are ~ou 
- 15- 
talklng about. ~- There are no inhabitants on the moon." On the 
other hand, no such reaction would follow if someone says : 
(12) If anything is an inhabitant of the moon it must feel cold 
The response might then be : "Right you are, but fortunately 
there are no inhabitants on the moon". 
£nother argument supportin6 this interpretation may be provid- 
ed by the followin6 test. If we consider the utterance: 
(13) I doubt whether there are inhabitants on the moon, but 
all inhabitants of the moon must feel cold 
it leaves the impression of a certain awkwardness, ~hich is a 
result of the inconsistency between the expressed doubt and 
the i~lied belief concerning the same proposition. On the 
other hand, the utterance : 
(1~) I doubt whether there are inhabitants on the moon, but if 
anything is an inhabitant oZ the moon it must feel cold 
does not seem awkward, since according to our argumentation 
implicational statements do not imply ext7 belief or assumption 
concernlng existence. Evidently there are different i~lioa- 
tional rules concerning the if.oothen-statements, and they 
depend on the tense used in the If-clauseo If we denote the 
if-clause by S~ the hea~er may infer, for instance~ that the 
speaker believes that S~ or believes that it is not the case 
that S~ or believes that it is probable that S~ etco 
In any case~ it seems clear for the reasons ~iven above 
that (I0) is not a paraphrase of (9), nor (12) is a paraphrase 
of (11). In spite of the fact that implicational statements 
can be considered as truthfunctionally equivalent to the cor- 
responding all~statements (and this is the basis of the log~Ic- 
al equivalence)~ yet they cannot be represented by the same 
- 16- 
LS structure, for obviously the latter convey additional sem- 
antic information, that is, additional consequences can be in- 
ferred from them. 
A¢cordin61y, instead of making use of a general quantifier, 
we will introduce a quantifying operator which we mall all-op- 
erator. The all-operator is assumed to be an argument-forming 
eperator, not a statement-forming speratorp as in the case of 
a general quantifier in legic. In other words, it is not an 
operator which makes a statement when prefixed to a proposi- 
tional form, but one which makes an argument when prefixed 
to a function representing a nominal phrase in the plural 
role 
form. It ~hus has the same ~ as the iota operator, which 
is used to make an expression of ~he category of an argument 23. 
We assume here that the all-operator belongs to a speclf- 
ic class of modifiers which we call ~ linguistic quantl- 
lying operators. Such operators will occur in the LS structure 
representation;always being prefixed to a variable x. 
A logical statement which is prefixed by a general quantifier 
with limited range • 
is an abbreviation for the i~lieational statement 
We will, however, use a different expression, provisionally 
denoted by (All x) ~ (x), which will not be interpreted as 
a statement equivalent to an impli'cati@nal statement, but 
- by analogy to the expression bound by the iota operator - 
it will be interpreted as an expression of the argument 
type : all the "objects" which are ~ . According to our 
interpretation, the corresponding implicational statement 
- 17 - 
will be accepted as one of the consequences which follow 
from all-statements. 
By analogy to the case of the iota operator, we can 
here also establish a quasi implication concerning the 
use of the all-operatorpon the basis of ~he empirically 
given conditions of appropriate use of all-statements 
Consider the following propositional schemes: 
(a) There is more than one "object" which is 
,or any "objeot-. if it i, . it is 
The two propositional schemes correspond to propositions 
which may be considered only in terms of certain proposi- 
~ionsu% attitu£es of the speaker who is ut-beriag an all- 
statement. We ma~ define a general quasi implicationsul 
scaeme whiCh, roughly, will be as follows: 
A speaker uses appropriately an al ! statementponly if his 
purpoz~ed belief is that there is more than one "object" 
w~ich is ~ , and his pu~orted claim is that any "ob- 
ject" which is ~ is ~ • 
Now by our general assumption that we are concerned only 
with those utterances which are appropriately used, we can 
always derive a proposition corresponding to (a) as repre- 
senting the speaker's belief, and a proposition correspond- 
tng to (b) as the speaker's claim or assertion, and both 
belong to the set of consequences of an all-statement. 
The difference between the speaker's propositional atti- 
%-ude with z~spect to (a) and (b) is analogous ~hen ~e con- 
vert an all-sta~ement into a corresponding negation, question, 
\ 
~ ~8 m 
request, doubt, etc, for it will appear that the proposition 
~orrespoD~ling to (a) in the~ frame "The speaker believes 
that ..." can be derived as a consequence, whereas the propo- 
sition oorrespondi~ to (b)lalthoug~a also derivable as a con- 
sequence, will occur in each ease in a dlf£erent modal frame, 
~hich will express correspondingly the various propositional 
attitudes of the speaker (The speaker denies that °.., q~ae 
speaker wants to know if .°., etc) 
For instance, for the utterance which is a ~uestion : 
(17) ~e all the inhabitants of this house sick. ~ 
we have a set of consequences to which belong, among other 
propositions, the following two : 
(18) The speaker believes that there is more than one "object" 
whlch is an inhabitant of this house 
(19) The speaker wants to know if eu~ "object" which is an 
inllabitant of this house is sick. 
These aonsequsnces are obtained on the basis of a very ~ener- 
al quasi impllcational scheme conoerniD~ all-stateRents con- 
verted into this type of questions. 
In conclusion it may be ~rth emphasizin~ that by intro- 
• uciDg propositional attitudes into the lin~Aistic desc~il>- 
tion,a~i by defining quasi i~plications in terms of proposi- 
tional attitudes, we are able to derive the correspondlng 
consequences not only from declarative sentences, but from 
all ~y~es of utterances. Thus the scope of our rules of in- 
l 
ference ~ is much wider than the scope of such rules 
in logic. Accordln~ly the identification of the semantic in~ 
terpretation of an utterance with the set of its consequen- 
ces is possible for all types of utterances. 2~ 
- 19 - 
Footnotes 
1. See U. Wein~eich, Exploration in Semantic Theory, in 
Current Trends in Linguistics, Vol. 3, e4. T.A. Sebeok, 
Mouton, The Ha6ue, 1966, where the author argues in 
favor of an approach which makes no attempt "to fence 
off mutually exclusive domains for syntax and semantics" 
and thus he is against the assumption that semantics 
begins where syntax ends. Deep structures are con- 
ceived of by him in terms of both the syntactical and 
the semantic relations. 
2. Such signs have been widely discussed by logicians and 
llnguiets. They are referred to as token reflexive 
signs (by Hans Reichenbach), as egocentric particulars 
(by Bertrand Russell), and as shifters (by Roman Jakob- 
son~. 
3- Roman Jakobson, On Linguistic Aspects of Translation, in 
On Translation, ed. R.A. Brower, Oxford University Press, 
New York, 1966, p. 232. 
@. See C.J. Lewis, The Models of HeaDing, Philosophy and 
Phenomenological Research, Vol. IV, No 2, 19~, for his 
conoept of connotation or intention, which bears an in- 
~an~l G. Frege'~ fluence of J.S. Uill~s • ee a so R. Carnap, Em- 
piricimm, semantics and ontology, in Revue Internationale 
de Philosophie~ No @, 1950, where the author accepts the 
view that the set of consequences following from a sen- 
fence may be identified with the meaning of that sen- 
tence. Such an idea was also professed by H. Hi~ during 
his lectures on semantics (University of Pennsylvania, 
- 20 - 
• 1965). 
5- The conoept of quasi implications was Introduced in my 
papers : On a Condition of %he Coherence of Texts, 
paper delivered at the International ~mposiue on 
Semiotics, Warsaw, Aueust, 1968 j On the Semantic In- 
terpretation of Subject-Predicate Relations in Sentences 
of Particular Reference, to appea~ in Progress in Lln- 
~tistics, eds. Bie~rlsch and HeidolI~h, Mouton et Go., 
~he Hague ~ Ar~mente and Predicates in the Logico- 
8emanti@ Structure of Utterances, to appear in Studies 
in Syntax and Semantics, ed. F. Kiefer, Foundations of 
Language Supplementamy Series, D. Reidel et Go., Dor- 
drecht-H elland. 
6. The term logico-semantic structure was used in my foa- 
mer papers (see footnote 5)- 
7- In 5eneral I say that a speaker uses appropriately an 
expression or an utterance, if he uses it consistently 
with the rules of languaKe an~ with hie purported be- 
liefs (see footnote 8, for the term "purported belief"). 
For a consistent semantic interpretation of utterances, 
we have to consi4er only those utterances which are 
used appropriately, as the appropriate use in this 
sense of the term is nothin~ more than the assumption 
~hat the speaker knows the lan6uage he is using and 
says only what he intends to gay ( he makes a correct 
use of an utterance accor~i~ 8 with what he wants to say). 
8. From the point of view of the semantic interpretation, 
it is irrelevant whether the speaker in fact believes 
- 21 - 
or only pretends to believe that such and such is the 
case. I therefore use the term "purported belief", 
and ~nenever I use here the expression "The speaker 
believes that ..." it is only in this sense of the 
term. The same holds true of any other propositional 
attitudes. 
9- Linguistic quasi implications can be defined for the 
use of lexical items and for the use of certain struc- 
tures. In our example, the consequences (la) and (Ib) 
ere based on a quasi implication concerning the use 
jof linguistic indices (see Section 2, below), where- 
as the consequences (Ic) and (Id) are based on a quasi 
implication defined for the lexical item "to leave" 
(For more details, see the section on implicative 
terms in my paper On a Condition of the Coherence of 
Texts, op. cir.) 
10. The term "object" is used here also in the sense of 
"purported object", that is, for anything namable. 
Evidently the knowledge of the type of discourse 
(everyday, scientific~ literary, etc) may tell us 
whether the speaker or author believes that a given 
"object" exists in reality, or it is to be assumed 
as in a hypothetieal theory, or imagined as in a nov- 
el. But such n considerations have no bearing on 
our present discussion. 
11. In general, it seems that the concepts we are discus- 
sing concern other languages as well. If in a given 
language there are no explicit exponents on the sur- 
face which would correspond to the interpretation 
we are assuming, for instance, for linguistic in- 
- 22 - 
dices used in English, the~e are probably some way to 
distinguish the utterances in terms of similar con- 
aepts, for it is hard to imagine how people could 
manage to communicate without maklr~ use of this rath- 
er general concept and others discussed here. 
12. By an adequate semantic interpretation I mean such 
an interpretation which is compatible with the lin- 
~alstic intuitions of coherent speakers, and testable 
a~ainst the practice of linguistic communication. Ex- 
amples of • such semantic tests are given below (p.14,15), 
13. The number may be exactly specified by a numeral, or 
expressed in an indefinite way, for instance, by words 
such as "man~", "few", "the majority of", etc. 
14. See my paper, Arguments and Predicates...", op. clt. 
for a rough discussion of Other quantifying operators. 
15. The iota operator was first defined and used by Peano, 
then by Russell, Reichenbach, Mostowski and several 
other logicians. 
16. A lin~ulstio index was defined in my paper, On the Sem- 
antic Interpretation .. :, op. cir. Rou6hly, a liD6uist-- 
ic index is a personal pronoun, a proper name or a def- 
inite description (that is, a nominal phrase preceded 
by a definite determiner, used in an identifying role) 
17. In general the quasi implications which we define hold 
true by virtue of the empirically ~iven conditions. 
The truth of the consequent in our quasi ilpllcations 
always constitutes the necessary condition for the truth 
-2~- 
of the antecedent, and thus we may consider the mhole as 
a valid conditional (material implication). 
It may be interesting to compare the various approaches 
to the concept of"presupposltions" (as referred to in the 
literatu~re),which we describe here as consequences. (See 
G. Fre~e, Sinn und Bedeutung, Zeitschrift fur Philosophie 
und philosophische Kritik, 1892 ~ P.F. Strawson, On Refer- 
ring, ~ind, 1950; O. Ducrot, Los pr~supposSs, conditions 
d'emplo~ ou @l@ments de contenu, paper delivered at the In- 
ternational Symposium on Semiotics, Warsaw, 1968 ~ A. Wierz- 
bicka, 0 sp6jno~ci semantycznej tekst-u wielozdaniowego, 
paper delivered at the Conference on Semiotics, IBL, War- 
saw, 1968 ~ C.J. Fillmore, Types of Lexical Information, 
Working Papers in Linguistics, i~o 2, The Ohio State Univer- 
sity, november 1968~ • In the present approach, presuppo- 
sitions are identified with those propositions which belong 
to the set of consequences following from a given utterance 
and are provided with the modal frame :"The speaker be- 
lieves that...': Such propositions belong accordingly to the 
semantic interpretation of a given utterance. This approach 
is close to that of O. Ducrot (Les presupposes..., op.cit.), 
who also treats such propositions as constituting part of 
the meaning of a given utterance, rather than as the requ- 
ired conditions of use9 or as propositions which are pre- 
supposed to be known by the hearer, etc. The difference 
beSween the two approaches (which have been developed in- 
dependently of each other) consists thus in my attempt to 
-24- 
account for this element of the mani~ of a Given ut- 
terance by scans of derivin~ such propositions as con- 
sequences baaed on the corresponding quasi i~lications 
defined for partlcule~ lexical items and particular 
structures. Such a treatment is consistent with the 
general proposal to identify ~he meani~ ~ an utter~ 
ance with the set of its consequences. 
Fillmore, on the other hand, distinguishes between 
"the presupposltional aspect of the semantic structure 
of a predicate and the "meenln~" proper of the pred- 
icate". He identifies the presuppositions of a sen- 
tence as those conditions which must be satisfied be- 
fore the sentence can be used in an~ of its functions. 
Thus the sentence "Please open the door" according to 
Fillmore (Types of Lexlcal luformation, op. cit)"cen 
be used as a command only if the TL " (that is, the 
addressee) "is in a position to know what door has 
been mentioned a~l onl~ if that door is not at TLA" 
(that is, the time of producing the utterance) "open". 
According to my approach, such an utterance will be 
interpreted in any case as a command, for its inter- 
pretation cannot be dependent on whether the above 
mentioned conditions are,or are notpsatiefied. Sup- 
pose I hear somebody ringing the bell add I ask my 
sister Please open the door". I~ may happen that the 
~oor is open at that t~me, but the state of the door 
(its bei~ open or closed) has no bea~i~ on the in- 
terpretation of this utterance - which in any case 
10. 
19. 
20. 
- 25 - 
is intende& by the addresser, and interpreted by the 
addressee, as a command. Thus, as it appears from the 
evidence of fan.age use, it is only the addresser's 
purported belief :"The door is not open" which may 
be safely assumed with respect to the given utterance. 
The term "propositional attitude" is adopted from Ber- 
trand Russell, Inquiry into Meaning and Truth (Pen- 
guin Books, Baltimore-Maryland, 1962). 
The term "modal frame" has been coined by A. Wierzbicka 
(0 sp6jno~ci semantycznej..., op. cir, and her o~her 
papers). I use the term "propositional attitud~'when 
referring to the content oi" an utterance, and the term 
"modal frame", when referring to its explicit repres- 
entation (which in the present paper is only rendered 
in words ). 
This thesis is based on empirical evidence. If we 
seem to find apparent counterexamples, it always ap- 
pears that they are cases of linguistic misuse, and 
thus they do not falsify lu~ the quasi implication, 
in such oases the antecedent is false. We are con- 
cerned, of course, only with the normal use of utter- 
anoes in the process of communication, not with cases 
in which utterances are used as examples, when in- 
dices are not supposed to identify anything. 
There remains one more remark to be made in connection 
~ith our quasi implicational scheme. The copula "is" 
~aich is used in the consequent should be interpreted 
as, so to speak, tenseless, for its tense is dependent 
- 26 - 
the tense of the verb in the predicate which applies 
to the "object" referred to by ~ in a given utter ~ 
a~lce. 
21. The definite description used as an index is best 
conceived of as an "instruction" for identlfieaticn. 
The linguist is thus concerned with what the "instruc- 
tion says, rather than with the problem of what a 
given "object" is. The "object" in our sense of the 
term mej be conceived of as just the value of the 
argument • 
22. Notice incidentally that there is a differenae bet- 
ween utterances such as (4) and, for instance, "XY 
parents bought a house", where the desorlp~on "my 
parents" should be represented as a linguistic in- 
dex (argument of type I~ which has a unique value) 
by means of which we identify one and only neglect" 
(a couple of individuals as a ~hole ) to which the 
~iven predicate applies. The predicate is not used 
here distributively as in the case of (~), inhere it 
applies to each individual referred to by the des- 
cription "my parents". 
23. The expression (~ x)~(X) is interprete~ as "that 
one and only object which is ~ ", add not as "there 
is one and only object which is V ". 
1 24. Finally, I wish to excuse myse f for a ratheE loose 
way I am using certain terms which are well defined 
in lo~ic (for instance, arE~,ment, value). I hope , 
\ 
- 27 - 
however, ~at the reader will get from my rough 
presentation the underlying linguistic concepts 
which I a~temp~ed to submit for discussion. 
7 

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U. Wein~eich, Exploration in Semantic Theory, in 
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Roman Jakobson, On Linguistic Aspects of Translation, in 
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C.J. Lewis, The Models of HeaDing, Philosophy and 
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Irena Bellert 
On a Condition of %he Coherence of Texts, 
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Irena Bellert 
On the Semantic In- 
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of Particular Reference, to appea~ in Progress in Lln- 
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~he Hague ~ 

Irena Bellert 
Ar~mente and Predicates in the Logico- 
8emanti@ Structure of Utterances, to appear in Studies 
in Syntax and Semantics, ed. F. Kiefer, Foundations of 
Language Supplementamy Series, D. Reidel et Go., Dor- 
drecht-H elland. 

G. Fre~e, Sinn und Bedeutung, Zeitschrift fur Philosophie 
und philosophische Kritik, 1892 ~ 

P.F. Strawson, On Refer- 
ring, ~ind, 1950; 

O. Ducrot, Los pr~supposSs, conditions 
d'emplo~ ou @l@ments de contenu, paper delivered at the In- 
ternational Symposium on Semiotics, Warsaw, 1968 ~ 

A. Wierz- 
bicka, 0 sp6jno~ci semantycznej tekst-u wielozdaniowego, 
paper delivered at the Conference on Semiotics, IBL, War- 
saw, 1968 ~ 

C.J. Fillmore, Types of Lexical Information, 
Working Papers in Linguistics, i~o 2, The Ohio State Univer- 
sity, november 1968~ • 
