EXPLICIT SE~ENCES ARD SYNTACTIC COMPLEXITY 
Re Zuber 
C~, Pazd.s, Prance 
Preneh sentence (1) can be translated into English 
either by (2) or (3): 
( I ) Leslie est 6tudlante 
(2) Leslie Is a student 
(3) Leslie Is a woman and Leslle Is a student 
It is clear however that nelther (2) nor (3) can be consider- 
ed as an "exact" translation of (1). Sentence (2) does not 
carry the information that Leslie Is a woman and sentence (3) 
does not carry thls-information in the same way as (1)i the 
fact ~hat Leslie is a woman Is presupposed by (1) whereas it 
is asserted by (3). In other words sentence (3) is more explg- 
clt than sentence (1). Following Keenan (1973) we will say 
that a sentence S is more explicit than a sentence TIff S 
and T have the same consequences but some, presupposition ofT 
Is an assertion of S. 
Not only translations can be more explicit. Per instan- 
ce (5) is more explicit that (4) since (4) presupposes (6) 
wherens (5) esserts (6): 
(4) Blll knows that Sue has phoned 
(5) Sue has phoned and Bill knows whether Sue has phoned or 
not 
(6) Sue has phoned 
RouKhly, defining sentences are, more explicit than "defined" 
sentenoese The questlon ld~ch we will try to answer in 
this paper is the follow~ one: are more explicit sentences 
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this paper is the following one: are more explicit sentences 
syntactically more complex ones (notice that (3) is syntact- 
ically more eo~aplex than (I) as well as (53 is more complex 
than (4)). 
We will show that at least for some simple languages 
this ie indeed the case: more explicit sentences are syntact- 
ically more complex. We will consider essentially proposit- 
ional categorial leaguage8, i.e. languages in which we have 
only the category of sentences end the category of sentential 
operators. Since we will distinguish two types of consequen- 
ces,. presuppositon8 and assertions, our language must con- 
tain strongly intensional operators. A sentential operator 0 
is 8aid to be strongly intensional iff for every possible 
world w and for every sentence P, if O(P) i8 true et X then 
there exist a sentence P" with the same truth value as P at w 
end such that O(P') is false at X (P end P" must be contigent 
sentences). Classic modal operators ere not strongly inten8- 
i One 1 ° 
Now a presupposition can be defined e8 s consequence 
which has an argument under the scope of a strongly opaque 
operator in the presupposing sentence. More precisely a sen- 
tence S presuppose8 a sentence Tiff S semantically implies 
T and S i8 of the foist O(R) where 0 i8 8 strongly intension- 
el operator and R and T have e co-~on argument. It can be 
shown that Presupposition defined in this way i8 equivalent 
to the classical definition if one accepts a negation which 
preserves inteneionality (cf. Zuber 1980~. Now given • simple 
measure of syntactic complexity and the above definition of 
presupposition the following property for our propositional 
lsngunge holds: 
If S i8 more explicit than T, then S is syntactically 
more complex then T. 
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References

Koenan, E.L. (1973) "Presupposition in natural logic", 
~, 57, No 3 

Zuber~ R. ~1980) "Note on wh~ faottves oannot assort whst 
their eentential complements express", ~e:antikos, 
• vol,, 4, NO 2 
