T~YE 'TI~!.'~ CAT~.GO~Y ' I~, ~ ~A_bR~\]L I,!.~_~C.UAGES 
AI~D ITS SE\]'.TANTIC I_..~ :,- P...T.~_ION 
~. The api~roach out1~ed below is to be understood as a compo- 
nent of a more general method of semantic interpretation of natu- 
ral languages, 
Roughly spea~.ing th~s method (develor~.e6 in my forthcoming 
Elements of a Sem~.ntic Theor~r of }T~tur~J Lan6u~es) might be cha- 
racterized, as fol\].ows: 
I °. A semantic ~ystcm S in a very generP.\] form (like that 
of Carn~p's 'Language A' or 'L~n:~e~ b ,-o- ~' - c~._ Carn~p, Introduc- 
tion to S~.bolic Logic and Its A~,\]ic,~t~ons, 1958) is constr~cted: 
this system contains : 
-A \]ex~con (si, eeifying t~e ~ig~z u~.ed) 
- ~\]es of c~esi~nz, tion (el. C~-~ocp, ~ea~ing an~ Neces 
~, ~96o, ~. 4) 
- Truth conc\]itions 
~-T~ans f~rmation rules. 
2 o . Rules of trans\].ation from a n~.tur~.l \].~.n~age, I~, into ' 
such c. seme.ntic system ~.re established. 
3 ° . System S~is required to fulfil ~o~e cx-,-lic~t con~Stions 
in order to make each \]'ernel sentence from ~, transl~.tab~_e in S. 
4 ° . A new system, SL, is const~cted, ~-l~ch actu~,\]Jy fulfi\]_~ 
the impose d conditions on trans\]ability in S. St, in its gener~.l 
form, becomes an extension of S; when S~ ~s i'ut into corresyon- 
dence ~--ith a concrete \]o~n~-~age, the 'meanin,is' (i.e. des~n~t~) 
assigned by these rules to different descrSptive signs of S& be- 
.','hhichi c _ 
come more definite. Under such conditions, ever~j sign from S~ 
a translation of a sign from L. has the s~,e ~cnotstum as the 
corresponding sign from \]~-. & 
- 2 - 
.~°. Under condition 3 °, if ~ is a translation in S~ of a 
sentence ~ from ~, every characterization which holds for ~i 
bo\]c\]s for the corresponding P~. too. 
o l~et us assume that, in agreement with the translation rules L" 
each ~erneI sentence of the simplest form (that means sentences 
u'~th no adverbials determiners) 
(I) N Art V 
(2) N Art V N Art 
..°,..°°. o.o.°o...o ~., 
c~ be transJated in S by an individual description (of course, 
only uqlen the article has the function of individualization). 
In agreement with this assumption, if L~ would be English, a 
~entence like 
(3) the horse is runnin~ 
--:oul~ have as its appropriate translation in S~ the exT~rer~ien 
(4) (~y)~x)~HOx~ (x=y)).RU d 
(vhere~\]~O ~is a predicate consts~t which is a translation of 
c 1 ~'~'._~j. hors_~e, RU is a predicate constant which is a translation of 
~. It is obvious that a translation like (4) does not account 
~^~ of ~,r ~ .... tense the verb. 
~n order to be able to represent in our semantic ~ystem the tez 
.~c ~tinction from natural languages, we take the fol\]ov-ing way: 
~o. Ue shall transform our earlier system S: into a eoordi- 
~te ~,au'~a_~ (in t1~e sense of Carnap's, Introduction .... , i~p. 161- 
171; tee also Carnap, ~eanin~ and Necessity, 196o, pp. 7~,-75). 
The individual expressions in st.andard form are referr: 
o 
ir~ to '~fos~tions' in an ordered domain. An expression like 'a ~- ' 
J 
v'ou\]~ ~esignate the 'l~osition i' at the 'time j'. 
For our further discussion is enough to interpret each 
-3 
4 
location '~"4, ~" ..__a\[' as different "things' in the universe, and 
a ~...a ~' as different "locations" ezch expression of the form 'al, --& "~ 
in time of the same "thing". The expression 'a ~' has to be inter~ --@ 
preted as designsJting a thing with no respect to its "time loca- 
tion"; in other words such an expression is to be understood as 
referring to a thir~ "abstracted" from time, or - what iz the 
snme for us - being in any time. The expression i refers to the 
"empty" position or to the "nul\]-thing". The number of the "posi- 
tions" is, perhaps, unfinite. 
2 ° . 'fie introSuce now the :fo\]\]owing tv,o-ar~ents predicates 
nrith the corresponding designn, tion ~\]es: 
(5) SI~xY = 'x is ninu\]t~neous to y' 
(6) I~0$xy = 'x is posterior v;ith res~pect to y' 
(7) A!TT~,.~y = 'x Jr r~nterior v~'ith r spect to y' 
Relation' referred to by (5) ja reflexive, s v~.~etri¢ and 
rg_ t-~ansitJve. Rel~,tious rc~ fred to by (6) ~n~ (7) ~re irreflexive, 
~ntis~.-~;~etric, but transitive. 
Pinal\]y ~"e Jntro~uce *be D~eSJe',lie 'I" by ~eans of the 
fo\] ?_cv:i~ definit~ t 
(S) Ixy = (x = y) o~ 
!ierefrom we can state: 
(8') ~Z=y = (x ~ y). 
3 °. 'Fie establish now the fol.\]ov'ing '~leaning 7o~tuls.tes' 
(inr~the sense of Carnap's, ~(eanir~ sod Necessity, $ur, plement: _P. 
.... anlng ~ostu\]ates, ~p. 222-229). 
~:~eaning Dostulates : 
(9) (x)(~xa~ ~Sn~xa$) 
-(Is) (x) (Zxa~im ~osxa~) 
-4 - 
The exprem~ion~'a~ ' in (9)-(13) above refers !;o in ~.r~cJtr~.- 
-~ ' 7f,"c .~oe: rich" oil" ~9\]~ ~ 'i}~J~' 
". It is \]~u~own that, as far as~ the natural languages are con- 
ccrned, the category of tense could be roughly defined as the 
relation between the time of the action (,expressed by the verb) 
:~nd the time when the message is uttered; that• is to say the pre- 
rent "expresses" the simultaneity with the time the message is 
uttered, the ~osst expresses the anteriority with respect to the 
time of the message an8 the future expresses the ~osteriority 
:-Jth respect to the time of the message. 
T~.J.s use of defining tenses suggests the fol\]owing treatment 
of tense estegory in terms of our semantic system: 
\].o. The time of the message is to be represented by any 
v,~.._!ue of ~ from the expression 's~'. 
2 ° . If x is the 'thing' referred to by an individual desc- 
~5pt~'on, then an expression like 'SIT~a~ .' expresses exactly the 
rel~=.t~on of the 'thing' referred to by t~e varmable x and the 
• time of the message" expressed by 'a~'. That is, 'SI~.Z~a. ~' means 
"~_'. i~ simultaneous ~:,ith the time of the rues:nags", u%ich correspo 
t " nd.~ o tD~. _ definition of the ioresent. Analogously we. may inter- 
7ret the expressions 'POSxa°. ' , 'ANTxa B.' as corresponding to the 
rcfJnitions ~Tiven to the future and the past, respectively. 
-\scorching ~m with 1 ° an~ 2 ° , we may establish the fo\]lowing 
tr~'~nc~ ~tJ on ~le : 
" (14) Translation rule: Replace• the symbols Prez, ~ast, 
~uture from the sequences Prez Verb, Past Ver___~b, 
Future Verb generated by~ a grcmmar G~ by the 
expressions: 'Sl~\[xa;', 'ANTxa;', 'POSxa~', respec~ 
ively. 
- 5 - 
Let us assui~e ~ow sentence (3) i~' .Tfiven together with its 
underlying P-marRer inthe three tense versions above discussed. 
We shall get the following three trans2ations: 
(4a) (~y)(x)L(HOxaI~).RUy.SlMxa~\] 
(4c) (~y)(x). \[(H0x ~Ixy) @ RUy ~0~xa~ 3 
Obviously (4a) is the translation for the ~-resent version, (4b) 
- for thep~ast vers'ion, (4c) - for the future version. 
Letus suppose that, in the'state of ~ffs, irs t referred to by 
our expressions, the only thing having the ~roperty 'horse' is the 
thing being in the point 'a6~;o let us consider further 'a~'Irepre - 
senting the 'time of the message'. In this case, if we put 'a#' 
instead of ~, we may say that 
is true; moreover, (4a) is factua~l~ true. 
If the position referred to by a ~ does not have actually thr --0 
properties predicated by (4a5 or if there are seve___ral positions 
having the properties predicated by (as!). , then (4a) is .~s,~. e, snd 
moreover, factually false. 
In contradistinction with the truth conditions of (4a), ~" " ~ 7~1e~2 
are factua2, th~ 
logical; 
(4a'l) 
( 4 a '~) 
(4b I) 
(4b") 
(4e') 
(40,) 
It is obvious 
sequence of 
truth conditions of the folio:ring expressions are 
\[ 
_~ ~ n o 
(x) \[(TIOz 6 , ~ Ixa¢ ), RUa~, AETxa ~J 
$ GR^ ~ o 
(x)" \[(HOx R Ixa~).RUa~ POSxa:_ 3 
that a23 these expressions 'are faIse onlyas con 
the ing 1-ostulates (9)-(13) and hence are 2ogica\]_ly 
-6- 
fn\] me. " "~ 
The intuitive interpretation of the L-falsehood of these exPres 
sions ~ns c~s follows: for instance (4a") says that a past event 
~n ni~=~O_taneous with the time of the message; ,sentence (4a") says 
~.ture 
that a - event, " 
tlt:,t is an event which is not yet oceuring in the time of the mes 
sa-ce is simultaneous with the time of the message. These interpre- 
t~.tions seem to me s.s giving a purely semantic expression of prag- 
r_~tic~\] f~cts ~'~here the 'atitude' ~of the speaker towards the uni- 
verse iz involved. 
r. The above Troposed interpretation may account also for some 
",~.bl~T~o_es of the natural langu~ges. We shall ta\]re an example 
fl-o~, other lan~uage t~an English, which makes a distinction ,bet- 
"::een the 'pure present' and the "irogressive present". For ~nstan- 
ee, in French the sentence: 
(\]5) Le ehien cui dor~, mange beaucoup. 
nig~ht be int~:rpreted as saying that: 
(15a) the dog ~ and eats at the time ~vhen the mes-, 
sage is uttered 
(15b) the dog sleeps at the time when the message is 
uttered and in c~eneral eats (much). 
Obviously interpretation (15a) chars~cterizes (15) as L-felse, 
(15h) ~-s possibly F-true. 
Thir: situation can be accounted for by supplementing the tran~ 
\]~t~n ~.1\]e (14) with the following statement: 
(14a) RepZace the symbol Prez by : 
(~) S I~xa~ 
or by 
(N sn~a" 
~es 
-7- 
The underlying structure of (15) is represented by the senten- 
(15~) Le chien dors. 
(15~ Le chien man~e (beaucoup). 
(We sb~ll disregard the word beaucou~, because it is ~rrelevant 
for our disc~ssicn.) 
Let 'CH'~, 'DO, ~r.d '1~t~' be the predicates by which chien, __d°r- 
N:~ir nnd ~ ~rc to be translated in S~ ~nd 'a I' the time of the 
message. The tr~.~slation of (15~,l~o~ wfil\] be, resi.ectively: 
YAye Sl~¢\[xa~\] 
Let u~' consider S~, accounting for French, has a mea_~ing postu- 
late saying predicates 'DO' n~ 'ITA' are incompatible simultaneous 
\]y. 
Obviously, in t\]'.is c~se the c_lass comprising sentences (15~L', 
~,I) it: inconsistent, or: the conjsnct~on of (15g') and (15~') is 
L-false. 
If we choose the other ~o~ib\]e tr~.nslation, i.e. 
(i5~) 
Then the class coml-.rising (15~#, ~") can be ~o~sibly F-true and. 
so can be their corresponSing conjunction. 
Translations (15~', ~'~ account for tl~e 'meaning' (15a); tr~tns- 
Sations (15~ ~, ~") account for the r~eaning (15b). 
It is easy to see that the fccts nccounted for in ~ are of pu- 
rely semantic nature, in contradistinction with the merely pragma- 
tic nature of the facts accounted for in 4. In the former case on- 
ly the 'meaning' of the expressions 'CHx', 'DOx', '~Ax' an~ 
'SIK'xa~' is involved, whereas in the cases under 4 we h~ve had to 
do with various possibilities of "referrfing,, beJ~ at the ~isposal" 
of the speaker. 
