c o n d i t i o n a l s , q u a n t i f i c a t i o n
AND BIPARTITE M EANINGS
L
ászlóK
álmánR
esearchI
nstitute forL
inguistics, H
ungarianA
cademy ofS
ciences Wo r k in g Pa pe r s in t h e Theory of Gr a m m a r, Vo l. 1, N o . 3Re c e i v e d: Oc t o b e r 19!M
CO NDITIONALS, QUANTIFICATION AND BIPARTITE MEANINGS
L
ászlóK
álmánTheoretical Linguistics Programme, Budapest University (E L T E ) Research Institute for Linguistics, HAS, Room 119
Budapest I., P.O. Box 19. H-1250 Hungary E-MAIL: kalmanfinytud.hu
T
heoreticalL
inguisticsP
rogramme, B
udapestU
niversity (E L T E )R
esearchI
nstitute forL
inguistics, H
ungarianA
cademy ofS
ciencesBu d a p e s t
I., P.O. Box 19. H-1250
Hu n garyTe l e p h o n e:
(36-1) 175 8285;
Fa x:(36-1) 212 2050
In this p a p er I will p re sen t a non-conventional approach to conditional a n d quan- tificational sentences. T h e conventional dynam ic in te rp re ta tio n of c o n d itio n als can be p arap h rased as follows:
(1) a. If p, then if.
b. \/w £ W ( p ( w ) —> tf(w))
The form ula in ( lb ) is a so-called test: it does not have any d y n am ic effect in the sense th a t it does no t foreground any entity th a t can be referred b ack to by anaphoric expressions in subsequent discourse. This, how ever, is in co rrect:
(2) I f a client turns up, offer him a cup of coffee. Show him around the premises.
The second sentence in (2) is to be in terp reted in the sam e possible w orlds in which the consequent in th e first (conditional) sentence (nam ely, th e possible w orlds in which th e antecedent is tru e); th e anaphoric pronoun him in th e second sentence in (2) refers back to th e eventual client in the first sentence. (T his p h en o m en o n has been called m odal subordination since R oberts (1987).) U nder th e tra d itio n a l view form ulated in ( lb ) , th is should be excluded: n e ith e r th e possible w orlds in which th e antecedent is tru e n o r a client m ay be foregrounded by th e first sentence if it is indeed tra n s la te d as a test.
According to th e solution to be proposed in this p a p e r, cond itio n al sentences are in terp reted as th e dynam ic conjunction of a fo rm u la of assignm ent a n d the consequent. Inform ally:
(1') a. If ip, then if.
b. {W := {u; £ W : p( w) } ) A Vic £ W(i f (w)).
The form ula in ( l 'b ) is no t a test: it has the dynam ic (foregrounding) effects of b o th of its conjuncts. In p a rtic u la r, th e set W of possible worlds in w h ich p holds is foregrounded as a consequence of th e first conjunct (th e so-called assignm ent).
This can be taken u p by subsequent anaphoric expressions. (In fact, it is picked up by th e consequent itself, which m entions W; note th a t then in th e conseq u en t is itself a n anaphoric p ro n o u n .) This predicts th a t th e in te rp re ta tio n o f subsequent sentences may be relativized to the possible worlds in which p is tr u e , as is the case in (2). The first conjunct stores all th e <p-worlds to W , and th e seco n d asserts if a b o u t each of th o se worlds. Moreover, it seems th a t th e form ula em b ed d ed in th e assignm ent (i.e., ip) m ay also have dynam ic effects (nam ely, fo reg ro u n d in g the client in (2)).
N ote th a t th e dynam ic effects of a formulae em b ed d ed in a co n d itio n a l m ust be restricted to th e possible worlds singled out by th e antecedent. F o r exam ple,
2
0. Introduction in o rd e r for th e client in (2) to b e an available antecedent for a subsequent ana- p h o r, th e sen ten ce in which th e an ap h o r occurs has to take u p th e possible w orlds fo reg ro u n d ed by th e a n tec e d en t o f the co n d itio n al (as is th e case in (2)). T h e l a t t e r p h en o m en o n will not b e explained in th is p ap er, b ecau se th e logic th a t I w ill in tro d u ce is fa r too sim ple to deal w ith m odalities. W h a t w ould be required for its tre a tm e n t is a concept o f inform ation s ta te s which sto re in fo rm atio n a b o u t sev e ra l possible w orlds at th e sa m e tim e (see section 3 .1 ).In conventional dynam ic th eo ries, q u an tificatio n al sentences are effectively tr e a te d as conditionals:
(3) a. Every P Q.
b. Vx ( P( x ) —» <5(x))
So q u a n tific a tio n a l sentences a r e also tra n s la te d as tests. T h is p red icts th a t a q u a n tific a tio n al sentence c a n n o t foreground any en tity for f u r th e r reference. T his is in co rrect:
(4) Every client left. They didn't buy a single piece of furniture.
T h e a n a p h o ric p ro n o u n they in th e second sentence o f (4) refers back to th e clients m e n tio n e d in th e first sentence, w hich should b e im possible if we were to tra n s la te th e first sentence as a test. O n th e oth er h an d , th e tra n sla tio n th a t I will propose in th is p a p er can b e inform ally ch aracterized as follows:
(3 ') a. Every P Q
b. (X := { x e U : P{ x ) } ) A Vx 6 X{ Q( x ) ) .
T h is sch em atic tra n sla tio n is an alo g o u s to th e tra n sla tio n sch em a for conditional sen te n c es in (1 '), so the p a ra lle lism is preserved u n d er this ap p ro ach . However, th e in te n d e d d y n am ic in te rp re ta tio n of the fo rm u la in (3'b) h a s th e effect of fore
g ro u n d in g the set X of P -e n titie s , w hich yields th e prediction th a t th a t set will be fo reg ro u n d ed , a n d subsequent a n a p h o rs m ay refer back to it, as is th e case in (4).
A s can be seen in the tra n s la tio n s proposed in ( l'b ) an d (3 'b ), we will need a d ev ice th a t allow s us to m o d e l set-type e n titie s ’ (discourse re fe re n ts’) ab ility to b e fo reg ro u n d ed in discourse. To th a t effect, in section 1, I will develop a p lu ra lized version o f D ynam ic P re d ic a te Logic (D P L , G ro en en d ijk an d S to k h o f (1991)), different fro m (and sim p le r th an ) van den B erg ’s (1990). P lu ralized D P L allow s variables to b e assigned s e ts o f individuals as values, w hich m akes it possible to fo rm u la te tra n sla tio n s sim ilar to those in ( l 'b ) an d (3 'b ) w ith th e ir in ten d ed in te rp re ta tio n .
A fte r in tro d u cin g the n ecessary form al to o ls a n d fo rm u latin g th e proposed tra n s la tio n s , I w ill fu rth er develop th e tre a tm e n t to deal w ith presuppositions in sectio n 2. This m e an s th a t I h av e to develop a partialized version o f th e logic p ro p o sed so th a t th e tran slatio n s o f sentences m ay b e assigned un d efin ed sem antic
values if th eir presu p p o sitio n s fail to hold. The reason for th is is th a t th e m ost problem atic properties of conditional an d quantificational sentences are th e ir j^re- suppositiona-l properties. Accordingly, I have to exam ine th e ‘p ro je c tio n ’ (inheri
tance) p roperties of sem antic value gaps and see how th ey correspond to existing views on th e ‘pro jectio n p ro b lem ’ for presupposition in g en eral, and th e p ro je c tio n of presuppositions in conditional and quantificational sentences, in p a rtic u la r. I will show th a t the p red icted in h eritan ce phenom ena are essentially co rrect: they harm onize w ith K a rttu n e n and P e te rs’ (1979) and H eim ’s (19S3) o b serv atio n s, b u t they fare b e tte r th a n H eim ’s (1983) tre a tm e n t for q u an tificatio n al sentences.
In section 3 I will briefly sum m arize the residual p roblem s to u ch ed u p o n in earlier sections which I believe are independent of th e m a in topic of th is p a p er.
Finally, section 4 is only tan g en tially related to th e to p ic of c o n d itio n a l and quantificational sentences. It is ab o u t th e m ethodological assu m p tio n s t h a t un- derly th e proposed tre a tm e n t. K álm án and Szabó (1990) arg u ed on in d e p en d e n t grounds th a t u tte ra n ce s have a bipartite semantic stru c tu re , sep aratin g th e pieces of m eaning which d eterm in e how certain referents are to b e grounded in th e p re
vious context from w h a t th e sentence claims. I will look a t som e consequences of th a t view, including th e tre a tm e n t of quantificational s tru c tu re s.
I will conclude th a t th e sem antic stru ctu re of u tte ra n c e s is p a rtly in d e p en d e n t of b o th th e underlying logic and th e syntactic stru ctu re, w hich m eans t h a t n o t all sem antic properties of n atu ral-lan g u ag e sentences need to be p re d ic ta b le from th e logical or sy n tactic p ro p erties of th e building blocks from which th e ir sem antic rep resen tatio n s are co n stru cted . This implies a sort of autonom y of sem an tics. For exam ple, using the form ulae of a pluralized and partialized dynam ic p re d ic a te logic as the basic elem ents o f ou r b ip a rtite m eaning rep resen tatio n s does n o t m e a n th a t th a t logic m ust account for every relevant sem antic phenom enon. T his challenges some syntactically o rien ted definitions of the principle of com positionality.
1. Form al Tools: P lu ralizin g DPL
As I have said in th e I n t r o d u c t i o n , we need to extend th e language o f D ynam ic P red ic a te Logic (D PL , G roenendijk and Stokhof (1991)) to cope w ith p lu ra l ana- phors. My p lu ralizatio n of D PL is sim ilar to van den B erg ’s (1990), w ith technical differences th a t I will n o t go into. In stead of collecting assignm ent fu n c tio n s, I will rely on assignm ent fu n ctio n s th a t assign sets of individuals ra th e r th a n ind iv id uals to variables. In section 1.1, I introduce DPL, th e n in section 1 .2 I develop th e pluralized version. Section 3 sum m arizes the m ost basic consequences of the tra n slatio n s proposed.
4 1. Formal Tools: Pluralizing DPL
1 .1 . D P L
T h e sy n tax o f D P L is th a t o f first-o rd er p re d ic a te logic w ith identity. (H ere a n d in th e follow ing, the sy n tactic clauses are im plicit in the defin itio n of th e sem an tics.) I define th e sem antic-value function [ - ] ^ . T he m odel M = (U, T) consists o f th e n o n -e m p ty universe o f in d iv id u als U a n d th e in te rp re ta tio n function J . T h e in te rp re ta tio n function assigns each n-ary p re d ic ate co n stan t P a set of n -tu p le s over th e u n iv erse U\ J ( P ) £ V(jU n). The value o f J ( P ) is also called P ’s extension in th e m odel A4, and will b e w ritte n as P + . T h e sem antic-value function will be w ritte n as [•] (w ith o u t th e s u p e rsc rip t) for th e sake of sim plicity. In this logic, a co n text or inform ation state is ch aracterized w ith a set o f assig n m en t fu n ctio n s, i.e., it expresses potential v a lu es of variables. T his m eans th a t contexts are re p re sen te d as p a r tia l knowledge a b o u t certain individuals (identified by variables or discourse m arkers) th a t have b e e n foregrounded (‘in tro d u ce d ’) in earlier discourse.
T h e sem an tic value of a fo rm u la is a fu n ctio n from contexts to contexts: it ex
presses how th e in te rp re ta tio n o f a sentence m ay update an in fo rm atio n state. T h e orig in al fo rm u latio n of D PL u ses a slightly different term inology, b u t is effectively equivalent to w h a t follows h ere.
([»]) [P (a:1, . . . , x n )](G ) = {g € G : ( g{ xx) , . . . ,$r(xn )) £ P + }.
A p p ly in g th e n -ary predicate P to n argum ents ( a q ,. .. , x n are variables) is a so- called test. T h is m eans th a t its value is a su b se t of its arg u m en t: it sim ply selects som e assig n m en ts from it. T h e assignm ents th a t it selects fro m G are th e ones w hich assign a p p ro p ria te values to those variables (the n -tu p le th a t th ey c o n stitu te m u st be in P ’s extension).
([“ ]) ix = y](G ) = {g £ G : g( x) = g{y)}.
A n o th e r test. It selects those assignm ents in G th a t yield id en tical values for x a n d y.
( [iü]) [“VKGO = {g £ G : M({<7>) = 0}.
N eg atio n c re ate s tests as well.
( M ) [ f A V>](G) = (>/>)([v’](G )).
D yn a m ic co n ju n ctio n , defined as fun ctio n com position. The d y n am ic effects of th e fo rm u lae g> a n d xj, if any, are p reserv ed , b ecause we use th e value o f [cp] a t G as th e a rg u m e n t o f {xf\.
(M ) [e«](G) = {h v*rW : V iW M -e
Here g[x]h m eans th a t h differs from g a t m ost in the value th a t it assigns to x.
T his type of form ulae, called random assignment, is the only source of d y n am ism , i.e., the only one whose sem antic value is no t a subset of th e arg u m en t set (it is n o t eliminative). It assigns (‘sto res’) an a rb itra ry value to th e variable x. O rd in a ry (dynam ic) existential quantification can be expressed w ith ex :
3x( p) = def e* A <p,
w hereas universal quantification can be espressed in term s o f ex isten tial q u a n tifi
cation, as usual:
Vx(<p) —def ->
3
x(-'v?) = ~‘(ex A So universal quantification is by definition a test.The usual connectives ‘V’ and P can be expressed in term s of co n ju n ctio n a n d negation as usual:
P V
0
=def - ,( _V A —*t/»);P -> V* “ def -■(P A ~‘\p).
Accordingly, every disjunction is a test, and b o th of its m em bers act as te s ts as well (they m ay have no dynam ic effect on each other), so disju n ctio n is said to be internally static. M aterial im plication is a test as well, b u t it is internally dynamic in the sense th a t th e eventual dynam ic effects o f th e an teced en t affect th e in te rp re ta tio n of th e consequent (because of th e d y n am ic con ju n ctio n in its definition). So it is im p o rta n t th a t we do no t use th e a lte rn a tiv e d efin itio n of m a terial im plication, in term s of disjunction:
p —t xp ^ —'p V xp = —'(—I— A ~‘ip).
Defining m aterial im plication in term s of disjunction w ould give rise to a n in te r
p re ta tio n th a t is effectively internally static: although it w ould contain a d y n am ic conjunction, the double negation of th e antecedent would m ake it static. In gen
eral,
-'-'P £ P
in D PL, because ->-np (som etim es also w ritten \tp) is a te st, even if <p h a p p e n s not to be.
6 1. Formal Tools: Pluralizing DPL
1 .2 . P l u r a l i z i n g D P L
As I have a n tic ip ate d , th e p lu ra liz e d version of D PL to b e used here allows us to assign sets o f individuals a s values to discourse m arkers (variables). T h e set V ar o f variables w ill contain o n ly on e sort, b u t th e ir values will all be sets. In d iv id u al variables w ill b e assigned sin g le to n sets as values. T h e em p ty set as a value of a variable w ill be treated a s a degenerate value, so th e assignm ent fu n ctio n s are effectively p a r tia l. This ra ise s some ad d itio n a l com plication in th e definitions. I in tro d u c e tw o m ore im plicit sy n ta c tic clauses: A x (for all variables x) assigns x n o n -em p ty s e ts of any c a rd in a lity (‘ab so lu tely ran d o m assig n m en t’). We will also n eed fo rm u lae o f the form M I , i ( y i ) , w hich select assignm ents th a t assign th e larg est p o ssib le sets to X sa tisfy in g ip, th e y assign som e elem ent of X to i , a n d u p d a te th e re su ltin g assig n m en ts w ith <p (‘m ax im izatio n ’). A form ula of th e form
X -x A t x A MAT, x{<p)
w ill sto re th e se largest sets to th e value o f X , assign an a rb itra ry elem ent of X to x, a n d do th e u p d a tes th a t ip requires.
T h e d o m a in and the r a n g e of the sem antic-value fu n c tio n are th e sam e as before, b u t I w ill use the n o ta tio n f-]A/( (or, ra th e r, [•], for th e sake of sim plicity) to d istin g u ish it from the p re v io u s one.
( P l) [í>(i , , . . . ,x„ )1 (G ) = {í € G : / \ S ( x , ) ^ 0 &
1 < l < n
& A ••• A (Ul > - - - ’Un) € -P+ }-
u i S s C x i ) u n e g ( x „ )
T h a t is, we select those a ssig n m e n ts in G th a t are defined for each arg u m en t.
E v ery n -tu p le w ith com ponents th a t are chosen from th e values of th e respective a rg u m e n ts m u s t b e in the e x te n s io n of P.
( liij) [* = y]{G) = {g e G : g{x) ± 0 & g(y) / 0 & g( x) = g(y)}.
T h e sam e as th e singular d e fin itio n , except th a t we have to check w h eth er th e v alu es of x a n d y are defined a t all.
([Hi])
S am e as for [•].
[ -v ] (G ) = {g G G : [^J({<7}) = 0}-
( M ) W A ipj{G) = Sam e as for [•].
( H ) Ie i](G ) = {h £ VarW : \ J g[x]h & |/i(x)| = 1}.
g £ G
As for [•], b u t we w ant th e new value of x to b e a singleton set.
([v ij) [A X](G ) = {h 6 VarW : \ J g[x]h & h(x) ± 0}.
S€G
T h e sam e as ex , b u t we only w ant th e new value of x to b e non-em pty.
([viil) | M l , I ( r t ] ( e ) = { l £ V" « :
V ( s P O ^ 0 & IsM I = 1 s p ) £
g &G
& A : i u }][x : M ] ) ) / 9{X) ) &
[y>]({$}))}.
T h e n o ta tio n g[x : {ii}] refers to a function th a t assigns th e sam e values to th e sam e variables as g, except for x, to which it assigns {u}. In te rp re tin g a fo rm u la of th e form MAT, x(<p) m eans to select those assignm ents from th e in fo rm atio n s ta te w hich assign to X th e largest set of individuals satisfying ip (so th a t x is e v a lu a te d to a m em b er of th a t set), and u p d a te them w ith <p. For exam ple, if we c a lc u la te
[ A x A ex A MAT, x (farm er(x ) A eyA donkey(y) A ow ns(x, y ))](G ) = G'
th en , if g' € G \ th e n g ' ( X) is th e set of all farm ers who ow n a donkey, g' ( x) is a singleton set of one of those farm ers, an d g'{y) a singleton set of a donkey th a t th a t farm er owns.
8 1. Formal Tools: Pluralizing DPL
1 .3 . C o n d i t i o n a l s a n d Q u a n t i f i c a t i o n
As I said in th e I n t r o d u c t i o n , conditionals an d quantified sentences will n o t be tra n s la te d w ith m aterial im p lic a tio n b u t w ith dynam ic co n ju n ctio n . I will call th e first co n ju n ct a n assignm ent, b ecau se its only effect is to s to re th e possible values o f a variable. T h e second c o n ju n c t will be called the assertion, because it expresses w h a t we a sse rt ab o u t those p o ssib le values.
T h e relev an ce of this m o v e should be clear from th e p re se n ta tio n o f D P L in sec tio n 1.1: as opposed to m a te ria l im p licatio n , dynam ic co n ju n ctio n is n o t only in te rn a lly , b u t also e x tern ally dynam ic: it m ay foreground en tities (or, in th e p lu ra liz e d v ersio n , sets of e n titie s) for su b seq u en t discourse.
1 .3 .1 . C o n d i t i o n a l s
T h e tra n s la tio n schem a for co n d itio n als p resen ted in th e I n t r o d u c t i o n corre
sp o n d s to th e following ty p e o f form ulae in o u r pluralized language:
( l w) a. I f (f, then ip.
b. ( A w A MIT,ic(</?(m))) A e v e r y f T ,w(rp(w))
(I h ave enclosed th e assignm ent in the above form ula in p a re n th ese s for b e tte r read ab ility . As I have m en tio n ed earlier, I will n o t dwell on how variables referring to possible w o rld s enter the lan g u ag e; we can assum e for th e m o m en t th a t W an d w a re ju s t o rd in a ry variables.) In te rp re tin g th is form ula sto res all the (^-worlds to W for good, a n d asserts t h a t ip holds for every elem ent w of W, as desired.
H ow th e o p e ra to r e v e ry in it m u s t be in te rp re te d will be clarified shortly. T h e tra n s la tio n s o f sim ilar sentences w ith (p o ten tially im plicit) q u an tifiers like usually, m ostly etc. a re analogous: th e tra n s la tio n s of such quantifiers rep lace e v e r y in th e ab ove form ula.
M ost im p o rta n tly , if ip o r ip have any d y n am ic effect, th o se will be preserved.
C onsider:
(5) I f Joe is sm art, he bought a bicycle.
T h e o u tp u t assignm ents th a t th e in te rp re ta tio n o f this sentence gives rise to w hen a p p lie d to a set o f input assignm ents will assign to some v ariab le W th e possible w orlds in w hich ‘Jo e is s m a rt’ is tru e ; m oreover, each assignm ent will also assign to so m e variable c one bicycle t h a t Jo e b o u g h t in some of th e possible w orlds w in th e se t th a t it assig n s to W . O u r sem antics is n o t rich enough to express th a t th e e x isten ce of such a bicycle is n o t g u a ra n tee d for th e actu al w orld (unless it is also g u a ra n te e d th a t ‘J o e is s m a rt’ is tru e in th e a c tu a l w orld), so we can n o t ex p lain w ith in th is la n g u ag e why ‘the b icy cle th a t Jo e b o u g h t’ is not available if th e su b se
q u e n t sentences a re about th e a c tu a l world. (As I have said in th e I n t r o d u c t i o n ,
th e availability of a discourse referent foregrounded w ithin a con d itio n al sentence should be relativized to th e possible worlds th a t the co n d itio n al foregrounds: see section 3.1.) If, however, th e subsequent discourse is a b o u t possible w orlds in which ‘Jo e is s m a r t’ is tru e, a bicycle becomes available for a n ap h o ric reference:
(5/) I f Joe is smart, he bought a bicycle. Then he keeps it locked into his garage.
(As it often h ap p en s in consequents of conditionals as well, th e an ap h o ric p ro n o u n then refers to th e possible worlds th a t th e first sentence in tro d u ce s, nam ely, th e ones in which ‘Jo e is s m a rt’ is true.)
N ote th a t th e so-called ‘donkey-equivalence’
3x(ip) -> ip = —¥ f>) does n o t hold for th e tra n slatio n s proposed here. T h a t is,
A \v A M IT , to(3a:(<p)(u;)) A e v e r y IT, w(ip(w)) ^ 'Jx(\/w(ip(w) —» rp(w))).
As a consequence, a ‘ donkey-sentence’ such as
(6) Mostly, if a farm er owns a donkey, he beats it
will no t b e assigned th e ‘s tro n g ’, double-universal reading ‘for m o st fa rm e r/d o n k e y pairs, if th e farm er owns th e donkey, he b eats i t ’. As a m a tte r o f fact, n o th in g m ore is really certain a b o u t w h at reading we will assign to (6) u n til we know ex actly how possible worlds will en ter th e picture. At any rate, as is often em phasised in th e lite ra tu re , speakers have very vague and varying intuitions a b o u t th e in te rp re ta tio n of this sentence: w h eth er to count farm er/donkey pairs, donkey-ow ning farm ers or donkeys ow ned by farm ers, an d how farm ers who own m o re th a n one donkey behave. (It is seldom asked how donkeys owned by several farm ers are tre a te d , b u t th a t is ju s t because it is unusual for one donkey to b e ow ned by m ore th a n one person.) Given these ju d g m en ts, it would not be wise to assign such sentences a double-universal in te rp re ta tio n autom atically. The possible ex p lan atio n o f th e vagueness of th e ju d g m e n ts aw aits fu rth er investigation in any th eo ry c u rre n tly on th e m arket (see Heim (1990)).
1 .3 .2 . Q u a n t i f i c a t i o n a l s e n te n c e s
As I have said in th e I n t r o d u c t i o n , the tran slatio n s of qu an tified claim s are very sim ilar to those of conditionals:
(S” ) a. Every P Q
b. ( A x A exA M X , x (P (x ))) A e v e r y X , x(Q(x)).
10 1. Formal Tools: Pluralizing DPL N ote t h a t , in te rm s o f th e definition in ( |v ii] ) above, th e form ula in (3;/b) leads to an e m p ty (c o n tra d ic to ry ) in fo rm atio n s ta te if it is know n already th a t th e re are no P s a t all. O n th e o th e r h a n d , since variables which have an em p ty value are ex cep tio n al (‘d e g e n e ra te d ’), we will be able to say th a t a sentence of th e form in (3"a) is infelicitous ra th e r th a n false in a context in w hich th ere can n o t b e any Ps. W e j u s t need th e necessary tools req u ired for th e tre a tm e n t of presuppositions to do t h a t (see section 2). T h a t is, we will say th a t a form ula like (3 "b ) h as an existential presupposition ra th e r th a n existential im port in th a t section.
As w ith th e tra n s la tio n of conditionals in (1"), th e set of all P -in d iv id u a ls becom es a n available a n teced en t for subsequent an ap h o rs. M oreover, th is set is already available in th e (local) context in which th e m ain assertion is in te rp re te d , a lth o u g h in E nglish it is n o t possible to refer back to it w ith a p lu ral p ro n o u n for g ra m m a tic a l reasons: * Every farm er believes that they m ust beat th e ir donkeys.
I believe th a t th is is due to th e sim ple fact th a t enery-phrases are g ram m atically singular in E nglish unlike in, say, French:
(7) Tons les ferm iers croient every-MPL the-PL farm ers believe-3PL
‘E v ery fa rm e r believes
q u ’ ils doivent battre leurs dues.
that they-M must-3PL beat-INF their donkeys that he must beat his donkeys.’
Since ‘ev ery fa rm e r’ is expressed analogously to all farm ers in French, th e a n a phoric p ro n o u n s in th e assertio n are p lu ral. O ne could sp ecu late th a t, since our tra n sla tio n s in tro d u ce b o th a plu ral a n d a singular variable, it is a g ra m m a ti
cal issue w hich one is considered th e g ra m m a tic al su b ject. O n th e o th e r h a n d , this does n o t ap p ly to a n ap h o rs referring to discourse referents in tro d u ced in th e assignm ent: th o se will agree w ith th e ir an teced en ts as usual:
(7) Tons les ferm iers qui ont un äne croient
every-MPL the-PL farmers who have-PL a donkey believe-3PL
‘Every farmer who has a donkey believes
qu ’ ils doivent le battre.that they-M must-3PL him beat-INF that he must beat it.’
T h e w ay in w hich we m ight w ant to in te rp re t quantifiers in our language is a type o f generalized quantification, nam ely, a relatio n betw een sets:
10PX, x(v>)l(G) = {g 6 G : g( X) + 0 & g(x) ± 0 k k O P '({ u € g( X) : [<p]{{g[x : M ] [ X : {u}]}) ^ 0},
{u e g ( X ) : [ip\{{g\x : {u}][X : {u}]}) = 0})}, ([viü])
w here O P E { e v e ry , m o s t, f e w ,...} , and O P ' is th e corresponding re la tio n over V{U).
The ldonkey-equivalence’
Vx(3y(ip) xp) = Vx(Vy(<p ->• ip))
does not hold for our tran slatio n s of quantified sentences, either. T h a t is, ( A x A ex A M I , x( 3y( P( x, y )))) A e v e r yX , x ( Q ( x , y)) ^
^ V x(V y(P(x, y) -> Q(x, y))).
As a consequence, a donkey-sentence like
(8) Every farm er who owns a donkey beats it
will not be assigned a double-universal reading (‘every farm er b e ats every donkey he ow ns’). Again, speakers’ judgm ents vary as to w h at th is sentence says ab o u t farm ers w ho own m ore th a n one donkey, so this result is desirable.
The o th e r problem often raised in connection w ith quantifiers since E v an s’
(1980) p a p e r is w hat sets should a quantificational sentence foreground as available antecedents:
(9) Few congressmen admire Kennedy. T hey are very junior.
U nder th e tre a tm e n t th a t I have ju s t proposed, th e set o f ‘all co n g ressm en ’ ra th e r th a n th a t of ‘the few congressm en who adm ire K en n ed y ’ becom es av ailab le for they to refer back to. Indeed, this is th e m ost n a tu ra l read in g of (9), th o u g h ‘all congressm en are very ju n io r’ is usually u n tru e. As A n n a Szabolcsi (p .c.) points o u t to m e, th e oth er reading can be p ro d u ced w ith co-ordination (an d a n eventual d em o n strativ e pronoun):
they 1
^ > are very junior.
T h e phenom enon in (9') seems m ysterious to me. W h a t I find m o st likely is th a t the heavily stressed personal or d em o n strativ e p ro n o u n , to g e th e r w ith the co-ordination, serve as a clue to the presence of an ellipsis: in th a t case, they or those should be in te rp re te d as ‘those w ho d o ’ in (9'). N ote th a t, in H u n g arian , w here th e presence of a subject personal pronoun is ra th e r un u su al unless it bears contrastive stress, th e ty p e of reading illu stra te d in (9') can only be p ro d u c e d w ith a heavily stressed overt pronoun and th e word is ‘even’:
(9r) Few congressmen admire Kennedy, and but
12 1. Formal Tools: Pluralizing DPL (10)
a.
K evés diák szól hozzá, és/de nagyon fiatalok.few student speak-up and/but very young-PL
‘Few stu d en ts sp eak u p , a n d /b u t th e y (th e stu d e n ts) are very y o u n g ’ b. K evés diák szól hozzá, és azok is nagyon fiatalok.
a n d those even
‘Few stu d en ts sp eak u p , and even th o se (who do) a re very y o u n g .’
Since th e tre a tm e n t p ro p o s e d here p red icts a uniform b eh av io u r of quantifiers in te rm s of a n ap h o ric referen ce (m odulo agreem ent facts), we expect th a t even n e g ativ e q u an tifiers may give rise to antecedents:
(11) No salesm an is walking in the park. T h e y are at home asleep.
As desired, th e prediction is t h a t they can refer back to ‘all salesm en ’, b u t n o t to th e em p ty set o f ‘salesmen w alk in g in th e p a r k ’. A ccordingly, th e ‘even th o s e ’- v ersio n of such a sentence is infelicitous in H ungarian:
(12)
a.
Egy kereskedő sem sétál. M indannyian álmosak.a salesman not even walks they-all sleepy-PL
‘No salesm an is w alk in g . They are all sleepy.’
b.
f i Egy kereskedő sem sétál, és azok is álmosak.and th o se even
# ‘N o salesm an is w alk in g , and th o se who do are sleepy.’
2. D e a lin g W ith P r e su p p o sitio n s
T w o very im p o r ta n t questions r e la te d to conditional an d q u an tificatio n al sentences a re tre a te d in th is paper: th e ir foregrounding featu res a n d th e ir p resu p p o sitio n al b e h av io u r, w hich I am tu rn in g to now. I s ta r t from th e very com m on a ssu m p tio n th a t p re su p p o sitio n s are to b e c a p tu re d in te rm s of th e definedness of sem an tic values. T h a t is, in both s ta tic a n d dynam ic theories, th e m o st u su al way of a cco u n tin g for th e oddity th a t a rises when th e p resu p p o sitio n of a sentence fails to h o ld (in a m o d e l or an in fo rm a tio n state) is to show th a t th e sem antic value of th e c o rre sp o n d in g form ula is u n d e fin e d (in th a t m odel or in fo rm atio n sta te ).
In o rd e r to ta lk about th e definedness con d itio n s of form ulae, we first have to develop an in te rp re ta tio n w here th is makes sense a t all, th a t is, a partial in te rp re ta tio n , in w hich th e sem antic v a lu e of a form ula is no t alw ays defined. I do th is in sec tio n 2 .1 . T h e n , in section 2 .2 , I exam ine w h a t th a t in te rp re ta tio n p re d ic ts w ith re g a rd to th e projection p ro p e rtie s of various types of com plex expression, i.e., how definedness properties a r e inherited from sim pler expressions to m ore co m p lex ones t h a t contain th e m as constituents. I will arg u e th a t th e p red ictio n s a b o u t th e b e h a v io u r of co n d itio n al and quan tificatio n al sentences are plausible.
2 .1 . P a r t i a l i z i n g t h e L a n g u a g e
T h e p a rtia l version of th e in terp retatio n function defined in th e prev io u s section will be w ritte n as [•]. It is no t surprisingly different from o th e r p a rtia l d y n am ic in te rp re ta tio n functions, such as D ekker’s (1992). T his fu n ctio n will assig n a set of assignm ents or th e value-gap V to every set of assignm ents. T h is will com plicate th e definitions, of course. P a rtiality will arise from two sources. F irst, th e in te rp re ta tio n of p red icate constants accounts for p resu p p o sitio n s stem m in g from the lexical content of a predicate, which specifies th a t th e p re d ic ate m a y be tru e or false only for a certain type of objects. For exam ple, one can a ssu m e th a t
‘m am m al’ is not in te rp re te d for individuals th a t are n o t anim als, or t h a t ‘left’
is no t in te rp re te d for individuals for which ‘was h e re /th e r e ’ is n o t tru e . Second, th e effective p a rtia lity of assignm ents, which I have ignored so far, m ay also give rise to undefined sem antic values. We will see one exam ple o f th is in th is section, namely, th e ex isten tial presupposition of quantified sentences is due to th is fact (generalized q u an tificatio n over an em pty dom ain will lead to a sem an tic-v alu e gap, see section 2 .2 ). W h e th e r o ther types of presupposition req u ire th is m ech an ism will be discussed in section 4.
A ccording to th e above, we will assum e th a t th e in te rp re ta tio n fu n c tio n 1 associates each n -a ry p red icate constant P w ith two dom ains: th e e x te n sio n P + an d th e an ti-ex ten sio n P~:
P € C o n ^ d =► Z (P ) = ( P + , P " ) € V ( Un) x V ( U n ).
T h e first com ponent of Z ( P ) is P + , i.e., P ’s extension, while th e second c o m p o n en t is P ~ or P ’s anti-extension. We stip u late th a t P + fl P ~ = 0 for every P . The set U n \ ( P + U P~) , i.e., th e n-tuples th a t are in n eith er th e ex ten sio n n o r the anti-extension, will be referred to as P * .
In o rd e r to keep th e rem aining definitions simple, I will define tw o fu n ctio n s ra th e r th a n one, w ith sim ultaneous recursion: th e p a rtia l in te rp re ta tio n func
tio n [•], a n d th e function [-]+ , which assigns every form ula th e set of in fo rm atio n states in w hich [■] is defined a t all.
Qi]+ ) = A
g £ G 1 < i < n
& A ••• A (»1 s í p*)}-
“ i € s ( x i ) u „ £ g ( x n )
P red icate ap p licatio n is defined for those inform ation states in which som e assign
m ents assign a value to each argum ent and, furtherm ore, every n -tu p le t h a t we
14 2. Dealing W ith Presuppositions can form fro m th e values t h a t th e y assign to th e respective arg u m en ts is e ith e r in th e e x ten sio n o r the a n ti-e x te n sio n of P.
([ii]+) [x = j]+ = { G C V*'M : V (g(x) ? 0 k g(y) ? 0)}.
g € G
T h e id e n tity o f x and y is defined for th o se inform ation sta te s in w hich som e assig n m en ts assig n a value to b o th x an d y.
( N + ) [ - v ] + = M + .
T h e n e g a tio n o f a formula is defined for th e sam e inform ation sta te s as th e fo rm u la itself.
( H + ) [p A i/’]+ b ] + = M (G ) € [rp}+}.
I use [•] in th is definition, h e n c e the sim ultaneously recursive c h a ra c te r o f th e definitions o f [-]+ and [•]. F o r d y n am ic co n ju n ctio n as fu n ctio n com position to be defined, we m u s t make it su re th a t the first conjunct is defined for th e a rg u m e n t, a n d th a t th e second conjunct is defined for th e value of th e first conjunct.
([v -v i]+ ) = [ A , ] + = {G C Va
7
Y : / \ : g(x) =0
}.g &G
For th e sake o f simplicity, we o n ly define th e values of these ‘assignm ent fo rm u lae ’ for in fo rm atio n states in w hich th e variable th a t they in tro d u ce d has an undefined value. T h is decision, however, w ill play no role in th e following. We could as well define th e m fo r all inform ation states.
([vii-viii]+ ) [M X, x(</?)]+ = [O P X ,x (^ )]+ =
{ G e M + : V ( ü ( X ) # 0 & í ( z ) ^ 0 ) } .
g &G
L ooking a t th e values of X a n d x in term s o f requires th a t X a n d x be defined variables a n d t h a t the value o f <p be defined.
Finally, th e only clause t h a t we need for th e definition o f th e p a rtia l sem antic- value fu n c tio n [•] is this: For ev ery form ula ip,
™ M(G)“ { m (G) othertSrl;
w here [•] is th e to ta l sem antic v alue function th a t we have defined earlier.
2 .2 . P r o j e c t i o n P r o p e r t i e s
T h e next q u estion to be exam ined after this sim ple extension o f D PL is how presu p p o sitio n s are ‘p ro je c ted ’ (inherited) from th e sub-form ulae of o u r rep resen ta tio n s to th e e n tire representation. Since th e way in w hich I have p artia liz ed th e language is so rt of trivial, we do not expect su rp risin g resu lts for th e types of fo r
m ulae in ([i-vi]). In fact, the results m ostly harm onize w ith K a rttu n e n a n d P e te rs ’ (1979) observations, and p a rtly w ith Heim ’s (1983) proposal. T h e la tte r is m ore liberal in c ertain respects, which I will m ention only briefly. T h e cru cial difference is betw een th e p red icted presuppositional b eh av io u r of qu an tified sentences an d w h at Heim (1983) predicts ab o u t them , which are related to th e definitions in ([v h - viii] + ), i.e., th e definedness properties of M an d o p e ra to rs like e v e r y .
N e g a t i o n . F irst, negation is a ‘hole’ for p resu p p o sitio n s, since [~'<p] is u n d e fined w henever [ ] is. Accordingly, the following pieces of discourse are correctly p red icted to b e odd:
(13) a. I don’t regret that Joe left, ft Joe is still here.
b. I don’t regret that Joe left, f f H e ’s never been here.
C o n j u n c t i o n . The value of form ulae of th e form <pA ip will b e undefined a t G if eith er [<p\ is undefined a t G or [ip] is undefined a t [i^](G), w hich is desirable:
(14) a. Joe left. He was here.
b. Joe was here. He left.
T h e first sentence in (14a) is odd if ‘Joe was h e re ’ cannot b e ta k en for g ra n te d , even tho u g h th e second sentence provides th e m issing p resu p p o sitio n . So th e p resu p p o sitio n of th e first sentence of th e conjunction m u st b e satisfied in th e in itial (‘g lo b al’) context. On th e other hand, if th e second sentence of a co n ju n ctio n contains a presu p p o sitio n , as in (14b), th en its p resu p p o sitio n m ay be fulfilled by th e im m ediately preceding (‘local’) context, created by th e in te rp re ta tio n o f th e first sentence, as we see in (14b): irrespective of th e in itial (‘g lo b a l’) context of th e u tte ra n c e of th e conjunction, th e second sentence is no t od d if th e first provides th e required presu p p o sitio n ‘Jo e was h ere’.
D i s j u n c t i o n . Since p V ip can be defined as A -'ip), th e p re d ic ted beh av io u r of presuppositions in disjunctions is as follows, -'ip a n d -'ip in h e rit th e p resu p p o sitio n s o f <p and ip, an d -><p A -'ip in h erits all those p resu p p o sitio n s. Since
—>p> is a test, th e conjunction here is effectively com m utative:
A -'ip = ~'ip A —'ip.
Finally, th e o u te rm o st negation ‘lets th ro u g h ’ all these p resu p p o sitio n s. For ex
am ple, consider:
(15) Joe left Paris or he quitted smoking.
16 2. Dealing W ith Presuppositions O ur se m a n tic s correctly p re d ic ts th a t (15) presupposes b o th ‘Jo e was in P a ris ’ an d
‘Jo e s m o k e d ’.
O n th e oth er h a n d , co n sid er th e following disjunction:
(16) The king o f France or the president o f France called.
This se n te n c e does n o t so u n d as o d d as it should if it presupposed b o th ‘France has a k in g ’ and ‘France h a s a p re sid en t’. T his is a serious problem , w hich is to be re m e d ie d by assigning different types of tra n sla tio n s to th e sentences in (15) and (16). Obviously, (16) does n o t presuppose th e existence of either th e king of France or th e president o f France (let alone both). W h a t we presu p p o se in it is th a t F ra n c e has eith er a k ing or a president. So, effectively, we should say th a t (15) a n d (16) are to be tra n s la te d w ith two different types of d isjunction.
B efo re proceeding, le t m e po in t o u t th a t th e co n tex tu al restrictio n s on using (15) a n d (16) are q u ite different. U tte rin g (15) n a tu ra lly is only possible if th e two c lau se s express a lte rn a tiv e , com peting explanations of th e sam e fact:
(17) — Joe is in wonderful shape these days. W hat could have happened?
— Either he left Paris or he quitted smoking.
The tw o alte rn ativ es in (16), on th e o th e r hand, are elaborations or in sta n ce s of one a n d th e sam e (im p licit) sta te m e n t, namely, ‘th e ru le r of France called ’, and the a lte rn a tiv e lies in w ho ru les France (a king or a p resid en t). So th e co m p etitio n is b etw een two propositions in (15), w hereas it is betw een two predicates (‘k in g ’ vs. ‘p re s id e n t’) in (16). A ccordingly, th e tran slatio n s o f (15) an d (16) sh ould differ in th a t t h e form er c o n tain s d isju n ctio n as a sentential connective, w h ereas th e la tte r c o n ta in s predicate disjunction. (How th e two tra n sla tio n s can b e p ro d u c e d is irrele v a n t here.) We co u ld in tro d u ce pred icate d isju n ctio n in to ou r lan g u ag e so th a t it h a s definedness p ro p e rtie s different from th o se of p ro p o sitio n al d isju n ctio n : ( H ) i P v <3(x1, . . . , x „ ) J ( G ) = {S € G : / \ < 7 ( x , ) / 0 &
1 < i < n
A ••• A (“ i ...«») e P + U Q +};
u i € g ( * i ) u „ e g ( xn )
([ix]+) ( P v Q ( x , . . . . , x „ ) ] + = { G C v«' M: V ( / \ s (x () ^ 0 f c g£G
A A ( » I ...
u i e g ( x i ) u n € g ( x n )
U nder th is definition,
P ( x u ... , x n ) V Q( x i , . . . , £ „ ) ^ P ^ Q ( x x, . . . , x n)
because th e form er is undefined iff eith er P ( xj , . .. , x n) or Q ( x i ,. . . , x n) is u n d e fined, w hereas the la tte r is undefined if b o th are. U nder th is ap proach, we could have the following tran slatio n s:
(IS ') Joe left Paris or he quitted smoking.
le ft-P aris(j) V q u itted -sm o k in g (j)
(16') The king of France or the president of France called.
ex A king-of-Francev president-of-France(:r) A called(;r)
T here is a different ty p e of problem atic disjunctive sentences as well, in w hich th e first disjunct explicitly denies the presupposition of th e second (see K a r ttu n e n an d P eters (1979)):
(18) Either Joe w asn’t in Paris or he left Paris already.
I believe th a t this ty p e of sentences should be analysed in term s of ellipsis: the second disjunct in (18) is to be tra n slated as if it was or, if he was there, he left Paris already. T h e m otivation for th is analysis comes from th e c e le b ra te d bathroom-sentence:
(19) Either there is no bathroom here, or it is in a fu n n y place.
I subm it th a t th e only reasonable way to account for th e possibility o f u sin g an anaphoric pronoun (it) in th e second disjunct to refer to a b a th ro o m (w h ile th e first disjunct denies its existence) is to assum e ellipsis a n d tra n s la te th e second disjunct as if it was or, if there is one, it is in a funny place. U nder th is analy sis, th e an ap h o ric pronoun refers back to th e referent in tro d u ced by one in th e e llip te d antecedent of the elliptical conditional sentence. If the ellipsis m echanism is th e re for th e explanation of (19), th en we can use it in the analysis of (18) as well.
If th e ellipsis-based explanation of (18) and (19) is correct, th e n ex ch a n g ing th e two disjuncts should m atter: while it seems reasonable th a t th e p o sitiv e version of th e first d isju n ct is an im plicit antecedent of th e second in (18) an d (19), we do no t expect an im plicit antecedent of this so rt in th e first m e m b e r of a disjunction. As a m a tte r of fact, exchanging the two d isjuncts in th ese sentences yields o d d sentences unless we add some indication th a t th e p re su p p o sitio n o f the first disjunct is to be w ithdraw n:
/ o/\ rn-.t j 7 r. n • r j I # he wüsu t there.
( 1 8 ) Either Joe left Paris already, or < OK, ' . , „ , , I he w asnt there m the first place.
# there isn ’t one.
'there isn’t one at all.
(19') Either the bathroom is in a fu n n y place, or < OK
C o n d itio n a ls . T u rn in g now to conditionals, ip —»■ if is defined as ~'(ip A ->ip) ra th e r th a n ->tp J ip to c a p tu re the in tern al dynam ism of conditional sentences:
(20) I f Joe has a cat, he likes it.
18 2. Dealing W ith Presuppositions
A ccording to th is definition,
[p -> V>]+ = W> A ip]+,
th a t is, th e v alu e of ip —>■ ip is undefined a t G if eith er [<£>] is undefined a t G or [ip] is u n d e fin e d at [<p](G). T h u s , we co rrectly predict th a t th e p re su p p o sitio n of th e co n seq u en t m ay be s a tisfie d by the an tec e d en t (in th e ‘lo c al’ in fo rm atio n s ta te th a t re su lts fro m in te rp re tin g th e an teced en t) even if it is n o t a t G: [ip] m ay be defined a t [<^](G) even if it is n o t in the ‘g lo b a l’ context G:
(21) I f Joe was in Paris, he left Paris by now.
O n the o th e r h an d , if th e a n tec e d en t does n o t guaran tee th a t th e p re su p p o sitio n o f the co n seq u en t is satisfied, th e n the in itia l context m ust g u a ra n tee it:
(22) I f Joe is in a good shape, then he left Paris.
Since in te rp re tin g the tr a n s la tio n <p of th e first clause of (22) does no t provide th e p re su p p o sitio n o f the second clause, the tra n s la tio n of th e second clause will be defined a t [<p\(G) only if it is alread y in G. T h u s (22) as a w hole presu p p o ses th a t J o e is or w as in Paris.
As a m a t t e r of fact, we w ill not tra n s la te conditional sentences using m a te ria l im p licatio n , b u t, since th e projection p ro p e rtie s of co n ju n ctio n are th e sam e as those o f im p licatio n , th e in h eritan ce p ro p e rtie s of th e tra n sla tio n s th a t I have proposed in th e previous se c tio n are th e sam e. T his is th e ty p e of p resu p p o si- tio n al b e h a v io u r adopted by K a rt tunen a n d P e te rs (1979) a n d Heim (1983) as well, except t h a t Heim (1983) po ten tially allow s for ‘local a cc o m m o d a tio n ’, i.e., a m echanism t h a t ensures t h a t presu p p o sitio n s which should b e satisfied by th e
‘glo b al’ c o n te x t are som ehow in tro d u ced on ly locally. Such a move w ould be m o tiv ated by a so rt of a p p a r e n t counterexam ples th a t som etim es a p p e a r in th e lite ra tu re (e.g ., van der S a n d t (1989)), b u t w hich sim ply ex h ib it th e effect o f focus o n th e p re su p p o sitio n al b e h a v io u r of u tte ra n ce s:
(23) I f Joe has a son, his kid must be happy.
T h e a p p a re n t problem w ith (23) is th a t th e p resu p p o sitio n o f th e consequent ( ‘Jo e has a k i d ’) is satisfied by th e context c re ate d by the a n teced en t (because
‘J o e has a s o n ’ entails ‘Jo e h a s a child’), w hich would m ean th a t th e c o n tex t o f u tte rin g th e conditional a s a whole need n o t satisfy it. However, th e en tire sentence in (23) m ay p resu p p o se th a t Joe h as a child. T h e correct e x p la n a tio n of th is p h en o m en o n is th a t son in th e antecedent m ay be u n d e rsto o d as focussed an d , in th a t case, th e fact th a t J o e h a s a child is ta k e n for g ra n te d by th e a n teced en t already. T h is is p re tty obvious if we tra n slate (23) into H u n g arian , w here focus is m a rk e d s y n ta c tic a lly (w ith w o rd order):
(24) a. Ha Jóskának van egy fia ,...
if
Joe-DAT
isa son-POSSD-3SG
‘If
Joe has a son (*rather than a
g ir l) ... ’ b. Ha Jóskának fia va n ,...son-POSSD-3SG is
‘If Jo e has a SON (rath er th a n a girl). .. ’
A H u n g arian sentence th a t s ta rts w ith (24a) will not p resu p p o se t h a t J o e has a child, w hereas one th a t s ta rts w ith (24b) will. In sum , I believe t h a t ‘local acco m m o d atio n ’ is no t needed to explain th e projection b eh av io u r of co n d itio n als.
Q u a n t i f i c a t i o n . Finally, th e definedness conditions th a t we w ould p re d ic t for universally quantified sentences if we agreed to tra n slate th e m w ith th e universal quan tifier definable in our representation language w ould be as follows. If we tra n s la te d a sentence of th e form Every x that <p, t/> as
Vx(v> -A VO = - ’(c* A ip A
th e n its sem antic value would be defined a t G iff some g 6 [ex](G) assig n s a value to x for which \fi\ is defined, an d [if] is defined at th e value of [<p\ ap p lied th e set of th o se assignm ents. T h a t is, th e value of th e tran slatio n o f Every dog barks would be defined w henever ‘dog’ is defined for a t least some individuals, a n d ‘b a rk s ’ is defined for some of th em as well. (T he sam e p resu p p o sitio n is p re d ic te d for qu an tified sentences in general.)
T h is pred icted pro jectio n behaviour is acceptable in general, b u t it differs sh arp ly from H eim ’s (1983) result, according to which all quantified sentences should have universal presuppositions. W ith her m echanism , ‘b a rk s ’ sh o u ld be defined for all dogs in order for Every dog barks to m ake sense. Sim ilarly, ‘every n a tio n h as a kin g ’ should hold in an inform ation state in w hich eith er E very nation cherishes its king or No nation cherishes its king can be u tte re d felicitously. As a m a tte r of fact, it is h a rd to tell w hat these sentences presuppose, i.e ., how m any n a tio n s m u st have a king to u tte r them felicitously. It seem s th a t th e sam e kind of vagueness is involved here as w ith generic sentences in general: th e se sentences p resu p p o se the generic statem en t ‘nations have kings’ ra th e r th a n th e universal sentence ‘every n atio n has a kin g ’ (or th e existential sentence ‘some n a tio n h as a k in g ’, w hich th e tran slatio n w ith V in th e current fram ew ork would y ield ).
M a x i m i z a t i o n a n d q u a n tif ie r s . Let me now look a t th e p ro je c tio n p ro p erties o f th e in te rp re ta tio n o f quantificational sentences proposed in th is p ap er.
M X , x(ip) in h erits th e presuppositions of ip, so Everyone who knows th a t Joe left p resu p p o ses ‘Jo e left’. O n th e o ther h an d , Everyone who beats his donkey will yield an undefined value only if nobody has a donkey a t all. Sim ilarly, since O P X ,x ((^ ) also inherits th e presuppositions of <p, Everyone knows that Joe left
20 2. Dealing W ith Presuppositions p resu p p o ses ‘J o e le ft’, bu t Everyone beats his donkey only presu p p o ses ‘som ebody h as a donkey’.
In term s o f p resu p p o sitio n al behaviour, th ese results a re th e sam e as if we w ere to tra n s la te quantifiers in th e conventional way, w ith th e im provem ent th a t we d o n o t p re d ic t universal p resu p p o sitio n s ä la Heim (1983). T h e big difference lies in th e ‘e x iste n tia l im p o rt’ o f quantification: since Everybody who has a donkey will assign an e m p ty set to th e variable th a t I have called X above if n o b o d y h as a donkey, th e sem antic v alue o f Everybody who has a donkey beats it will be u n d efin ed r a th e r th a n false in th a t case. T his clearly corresp o n d s to th e in tu itiv e in te rp re ta tio n o f th is sentence. Som etim es n eg ativ e quantifiers m u st b e p rev en ted fro m having th is so rt of ex isten tia l im p o rt, so No one who has a donkey beats it m u st b e tra n s la te d as ‘it is n o t th e case th a t anyone who h as a donkey b e a ts i t ’.
A ccordingly, th is ty p e of sentences will not have any foregrounding effect, either:
th e y do no t allow plural a n a p h o rs to refer back to the people w ho have a donkey.
T h e obvious shortcom ing o f th is tre a tm e n t is th e sam e as w h at we have seen w ith V: an e x iste n tia l ra th e r th a n generic p resu p p o sitio n is p re d ic ted for quantifi- c a tio n a l sentences. It would ta k e a full-fledged view of genericity to fo rm u late th e req u irem en t th a t [ M I , i ( ^ ) ] a n d [OPA-, x(<^)] are defined if [</?] is defined ‘gener- ic a lly ’ for the in d iv id u als in AT’s value. As w ith th e problem o f donkey-sentences d iscu ssed in sec tio n s 1.3 .1 a n d 1 .3 .2 , I believe th a t the solu tio n lies in in d ep en d en t fa c to rs c o m p licatin g the p ic tu re draw n here.
3. R e sid u a l P rob lem s
T h e following p ro b lem s, w hich a re clearly cru cial to the issues discussed in this p a p e r, have b e e n raised in th e previous sections b u t have n o t b een solved.
3 .1 . M o d a l i t i e s
In fo rm a tio n s ta te s o r contexts o f D P L (and its extension in th e previous sections) ex p ress p a rtia l know ledge a b o u t individuals in th e actu al w orld, given a com plete know ledge of th e w orld (the m o d el). In a c tu a l fact, an in fo rm atio n s ta te should also c a p tu re a p a r tia l know ledge a b o u t th e a c tu a l world itself. T his could b e im p le m e n ted by conceiving of in fo rm atio n sta te s as sets of possibilities, i.e., p airs of th e fo rm (y, w) w h e re g is an assig n m en t and w is a possible w orld, which also acts as a m o d el w ith its own universe a n d its own in te rp re ta tio n function. M oreover, an in fo rm atio n s ta t e does n o t co n tain ju s t in fo rm atio n a b o u t th e actual world, b u t also ab o u t various alternative worlds, such as h y p o th etical, co u n terfactu al, p a st a n d fu tu re w orlds. It sh o u ld b e possible to u p d a te p a rtia l knowledge ab o u t v ario u s a lte rn a tiv e worlds se p a ra te ly in an in fo rm atio n s ta te to tra n sla te m odal,
p a st-ten se etc. sentences. U nder this approach, the variables referring to p ossi
ble w orlds in form ulae range over those partial possible worlds in th e in fo rm atio n s ta te ra th e r th a n com plete possible worlds. Various p a rtia l possible w orlds m ay be foregrounded in an inform ation sta te p re tty much as discourse re fe re n ts (par
tial individuals) can. T his is th e kind of ap p aratu s th a t should be dev elo p ed to successfully tre a t th e m odal character of conditional sentences and th e p h e n o m en a re la ted to m odal sub o rd in atio n .
3 .2 . G e n e r i c i t y
W henever collections of individuals (or possible worlds) are involved in a n a tu ra l- language u tte ra n c e , th e linguist faces th e problem of genericity. I use th is term in a ra th e r b ro a d sense, referring to all sorts of cases w hen a p re d ic a tio n ab o u t a collection of individuals is vague as to th e extent in which ind iv id u al m em bers of th e collection can b e m ade responsible for the tr u th of th e p re d ic atio n . T he conditions determ in in g w hether genericity arises in a sentence involving collections a re no t w ell-understood. T he exam ples below illu stra te some cases w hich, for som e reason, involve generic m eanings in th e above sense. In (25a), a p ro p e rty is p red icated a b o u t a collection; for lack of an explicit d istrib u tiv e q u a n tifie r (such as every), such sentences allow exceptional m em bers in th e collection, w hich do n o t have th e given pro p erty (this is generic predication in th e narrow sense). In (25b), th e collection is seen as th e agent in a p articu lar event; u n d er o ne reading, it is left vague w h at role each m em ber plays, if any, in achieving th e re su lt in question (collective predication). In (25c), a certain ty p e o f event is s a id to occur regularly, i.e., th e re is a collection of tim e intervals somehow evenly d is trib u te d in each of which th e event occurs at least once (habitual predication). T h is is sim ilar to (25a) in th a t exceptional tim e intervals are allowed.
(25) a. Ravens are black.
b. The boys carried the piano upstairs.
c. Joe goes to the library.
I argued in earlier p ap ers (e.g., K álm án (1990)) th a t, in spite of th e diversity of th e cases in which genericity arises, th e generic aspect of m eanings sh o u ld be given a uniform tre a tm e n t. True, generic m eanings can n o t be c a p tu re d in te rm s of inference properties: it is no t possible to specify w hat th e above sen ten ces entail a b o u t th e p ro p o rtio n of black ravens, boys who actually helped carry in g th e piano u p sta irs or tim e intervals (say, weeks) in which Joe has been to th e lib rary . O n th e o th e r h an d , if we look a t these m eanings from a different perspective th a n th eir inference p ro p erties, we can cap tu re ra th e r precisely w h at inform ation th e y carry.
T h e inform ation carried by generic expressions can be b est c a p tu re d in term s o f th e possibilities of accommodating presuppositions in an in fo rm atio n state.
