CONTRASTIVE CO-ORDINATIONS WITH FOCUSSED CLAUSES

CO N TR A STIV E CO-ORDINATIONS W ITH FOCUSSED CLAUSES

András Zsámboki

Research Institute for Linguistics, Hungarian Academy Sciences Working Papers in the Theory of Grammar, Vol. 2, No. 5

Received: October 1995

W ITH FOCUSSED CLAUSES

András Zsámboki

Theoretical Linguistics Programme, Budapest University (ELTE) Research Institute for Linguistics, HAS, Room 119

Budapest I., P.O. Box 19. H-1250 Hungary

E-MAIL: zsambokiCnytud.hu

Working Papers in the Theory of Grammar, Vol. 2, No. 5 Supported by the Hungarian National Research Fund (OTKA)

Theoretical Linguistics Programme, Budapest University (E L T E ) Research Institute for Linguistics, Hungarian Academy of Sciences

Budapest I., P.O. Box 19. H-1250 Hungary

Te le ph o n e: (36-1) 175 8285; Fa x: (36-1) 212 2050

O ne of th e m a in sem an tic roles of free focus (cf. van L eusen a n d K álm án (1993)) is expressing c o n tra st, e.g., in contrastively co -o rd in ated sentences. C o n sid er th e following exam ple, from H ungarian:

(1) Nem PÉTER eszik, hanem PÁL.2 n o t P e te r e ats b u t P au l

‘It is n o t P e te r w ho is eating, b u t P a u l’

N ote th a t th e non-focussed p a rts of th e co n trasted clauses (w hich I will call focus fram es in th e following) c a rry a presupposition. For ex am p le, th e sen ten ce in (1) presupposes th a t som eone is eating.

T h is p a p e r is d ed icated to th e problem of a special ty p e of co n tra stiv e co­

o rd in a tio n in H u n g a ria n ,3 superficially sim ilar to th e ty p e illu stra te d in (1 ), b u t in te rp re te d differently:

(2) Nem a VONAT kerül sokba, hanem ÉN voltam beteg.

n o t th e tra in is expensive b u t I was ill

‘It is n o t th a t th e tra in is expensive, b u t th a t I w as ill’

Obviously, th is sentence presupposes n eith er th a t so m eth in g was expensive, n o r th a t som eone was ill. In s te a d , it is to be used in a co n v ersatio n in w hich th e com ­ m on gro u n d (th e co n tex t) includes a fact th a t th e two clauses m ay offer a lte rn a tiv e ex p lan atio n s for. For exam ple, th e com m on base of th e two clauses in (2) m ig h t be

‘I did n o t c o m m u te ’, gmd e ith e r th e fact th a t th e tra in is expensive or th a t I was ill are p lau sib le e x p lan a tio n s for this fact. T his m eans th a t, in a sentence like (2), two p ro p o sitio n s are c o n tra ste d . Therefore, I will account for th e sy n ta c tic asp ect of th e p h en o m en o n using focus projection (cf. Selkirk (1984:C h5)), i.e., a m ech­

an ism th a t sh ifts focus fro m th e prosodically p ro m in en t elem ent to a c o n stitu e n t con tain in g it (see section 1).

From th e sem antic p o in t of view, I will address two questions: (i) W h a t is th e ‘focus fra m e ’ w hen e n tire propositions are in focus? (ii) How can we acco u n t for th e re la tio n sh ip betw een th e com m on base an d b o th co -o rd in ated clauses? As for th e q u estio n in (i), I w ill propose th a t th e focus fram e is th e com m on b ase of th e two clauses. As for (ii), an account of how th e com m on b ase is sh a re d will be

1 I am g ra te fu l to László K álm án for his com m ents a b o u t b o th th e su b sta n c e an d th e p h rasin g of th is p a p e r and for th e TgXwork h e d id on it.

2 In th is a n d th e following exam ples, prosodically p ro m in en t elem ents a re w rit­

ten w ith SMALL CAPITALS.

3 R ussian exam ples w ork analogously.

offered w ithin the fram ew ork of th e Linguistic Discourse M odel (L D M) of Polanyi (19SS) (see section 2), w hich I will provide w ith a dynam ic sem antics, along th e lines of G roenendijk an d S to k h o f (1990) (in section 3).

1. C o n tr a s t a n d F re e F o c u s

Since th e type of sentences th a t I will co n cen trate on involve b o th co n tra st and free focus, I will first exam ine these two concepts (sections 1 .1 - 1 .2 ) . In sec­

tio n 1 .3 , I will sketch how exam ples like (2) fit into the p arad ig m of co n tra st and co-ordination.

1 .1 . C o n tr a s t

B y contrast I will m ean a p a ir of inconsistent propositions, i.e., two propositions th a t can n o t be tru e a t th e sam e tim e. C o n trast has two m ain subtypes:

(a ) A p air of c o n trasted p ro p o sitio n s m ay originate from two different speak­

ers in a conversation. T his case m ight be called correction (th e second proposition is a corrective reply to th e first);

(b ) If the two p ro p o sitio n s are p a rt of th e sam e assertion, connected w ith a conjunction, th e n one of th e propositions has to be n eg ated , otherw ise the entire assertion w ould b e a contradiction. In this case, we can speak of a contrastive conjunction.

T h ere are oth er types of relatio n s betw een propositions th a t are som etim es called contrast. In p a rtic u la r, clauses can b e opposed for rh eto rical reasons, e.g., b e ca u se of the in co m p atib ility of th e ex p ectatio n s th a t they give rise to. I will refer to those cases as adversity ra th e r th a n contrast. For exam ple, th e following sen ten ces are instances of adversity, b u t no t of contrast:

(3) I am old, but you are young.'

(4) The cup is warm but the tea is cold.

In H u n g arian , co n trast h as a conjunction of its own (hanem ‘b u t ’), d istin ct from th o se of'ad v ersity (de, pedig etc.). In accordance w ith my definition of co n trast, th e se conjunctions sta n d in a com plem entary distribution:

(5) Péter nem utazott el, *d e /h a n e m a városban kószál.

P eter not left b u tad v /b u tcontr th e city-in strolls

‘P eter has no t left, h e is strolling in to w n ’

(6) Péter nem horkol, de/*hanem elaludt.

P e te r n o t snores b u t aav/ b u t contr slept

‘P e te r is n o t snoring, b u t he is asleep’

T h e first p ro p o sitio n in (5) w ould be inconsistent w ith th e second w ith o u t th e n eg a­

tio n , th u s only th e co n trastiv e conjunction is a p p ro p ria te th e re . To th e co n trary , th e p ro p o sitio n s in (6) are far from incom patible (indeed, sn o rin g entails sleeping), so only a n adv ersativ e co n ju n ctio n can be used. It expresses th a t P e te r’s sleeping w ould give rise to th e ex p ec ta tio n th a t he is snoring, b u t h e is not.

U n d e r th e above ap p ro ach , co n trast need not involve free focus. T h e sentence in (5) qualifies as co n trastiv e co-ordination, alth o u g h its clauses co n tain no free focus, unless we w ant to reg ard th e ir verb phrases as focussed.

1 .2 . F r e e F o c u s

T h e sem an tics of free focus involves th ree com ponents: th e focussed p a rt, the focus fram e, a n d the relevant domain. B o th th e focussed p a r t a n d th e focus fram e have an ov ert re p re se n ta tio n in th e syntax. T he form er is co n n ected to th e prosodic p ro m in en ce of one w ord o r p h rase, which is eith er id e n tic al o r p a rt of th e focussed p a rt. T h e focus fram e includes w h at rem ains after e x tra c tin g th e focussed p a rt from th e sentence. Finally, th e relevant dom ain h as no overt re p re se n ta tio n in sy n tax , its co n ten t is to b e co m p u ted from th e context som ehow .

A ccording to K a rttu n e n a n d Peters (1979), free focus presupposes th e ex­

isten ce of som e en tity of th e sam e type as the focussed p a r t for w hich th e focus fram e holds. T h e m aim assertio n of a sentence th a t co n tain s a free focus is th a t th e focus fram e holds exhaustively (i.e ., uniquely and m ax im ally ) for th e c o n stitu e n t in focus. V an Leusen a n d K álm án (1993) arranges th e se m eaning co m p o n en ts differently. T h ey lo cate th e ex h au stiv ity in th e p re su p p o sitio n al p a rt. T h a t is, ac­

cording to th e m , th e p re su p p o sitio n of th e sentence is th a t th e re exists so m eth in g of th e sam e ty p e as th e focussed p a rt for which th e focus fram e holds exhaustively.

T h e y p o sit th a t th e m ain assertio n is the identification of th e focussed p a r t w ith th e p re su p p o se d unique m ax im al entity. In b o th th eo ries, th e fun ctio n of th e rel­

ev an t dom ain is to re stric t the dom ain on which e x h a u stiv ity o p erates to a set of co n tex tu ally relevant entities. In some cases, the relevant d o m ain plays no role at all.

It follows from eith e r of th e above theories th a t a c o -o rd in atio n of a n egative a n d an affirm ative clause th a t have different focussed p a r ts a n d th e sam e focus fram e qualifies as a co n trastiv e co-ordination. T aken for g ra n te d th a t th e rele­

van t d o m ain is th e sam e for b o th clauses, the two clauses m u st share th e sam e p re su p p o sitio n s, because th ey share the focus fram e. W ith o u t th e n eg atio n , th e two p ro p o sitio n s m ust be contradictory, since the focus fram es have to h old tru e

exhaustively for two different focussed p arts. So the conditions for c o n trast are satisfied in such a case.

'- i f the focus fram es of th e co-ordinated clauses are not identical, th en th e tw o clauses m ay refer to th e sam e issue, b u t they are n o t inconsistent. Such co­

o rd in atio n s are no t necessarily incorrect, b u t they do not express co n trast (in th e following, the focussed p a rts w ill be enclosed in [•]F ):

(7) Nem az érett [FÉRFIAK]F tetszenek Zsuzsának, not th e m atu re m en appeal Sue-DAT

hanem az *[a g g aSTYÁNOI<]f / érett [gYÜMÖLCSÖk]f . b u t th e g ra y b e a rd s/ ripe fruits

‘It is no t m a tu re m en, b u t g ray b eard s/rip e fruits th a t Sue likes’

In th e starred version of (7), th e focus fram e of the first clause is different from th a t of th e second: it includes th e adjective érett ‘m ature, rip e ’, which th e focus fram e of th e second clause does n o t. T h is sentence could still work as a non-contrastive co-ordination (of two focus-containing sentences), if it was not conjoined w ith th e obligatorily contrastive co n ju n ctio n hanem.

A lthough, as we saw in th e previous section, free focus is n o t a necessary in g red ien t of contrastive co -o rd in atio n , those cases in which only one of th e con- tra stiv e ly co-ordinated clauses contains free focus seem infelicitous:

(8) * Károly nem volt vegetáriánus, hanem [IRMGARD]^ volt az.

Charles n o t was v e g eta ria n b u t Irm gard was it

‘Charles was not a v e g eta ria n , it is Irm gard who was one’

T h is sentence certainly satisfies th e criteria I have proposed for contrastive co­

o rd in a tio n . T h e first clause co ntains (in a negated form ) the pro p o sitio n th a t th e re is at least one person w ho was vegetarian, namely, Charles; th e second clause claim s th a t th ere is a unique p erso n who was vegetarian, namely, Irm gard. T h e c o n trad ictio n is obvious. A ccording to van Leusen and K álm án (1993), (8) is ou t b e c a u se of a presupposition failure. T he second clause presupposes th e existence of a unique vegetarian, b u t th e first clause fails to provide a context entailing this.

1 .3 . F o c u sse d P r o p o s it io n s : C o n tr a ste d E x p la n a tio n s

In H u n g arian (as íveli as in R u ssia n ), there are contrastive co-ordinations (like (2) o r th e exam ples in (9-11) below ) the properties of which do no t seem to square w ith th e concept of c o n tra stiv ity sketched in section 1.1:

(9) N em PÉTER aludt a padlón, n o t P e te r slep t th e floor-on

hanem a HÁZIGAZDA költözött szállodába.

b u t th e h o st m oved hotel-into

‘It is not th a t P e te r slept on th e floor, b u t th a t th e h ost m oved to a h o te l’

Common base: ‘th e accom m odation worked o u t w ell’

(10) N emPÉTER nem hozta el a tortát, n o t P e te r n o t b r o u g h t th e cake-ACC

hanem a CUKRÁSZ nem készült el még vele.

b u t th e confectioner no t w as-ready yet it-w ith

‘It is not th a t P e te r did n o t bring th e cake, b u t th a t the confectioner h as n o t p rep ared it y e t’

Common base: ‘th e cake is no t h ere’

(11) N emPÉTER nem kapcsolta fel a villanyt, n o t P e te r n o t t u r n e d o n th e light-ACC hanem a HÁZBAN van áramszünet.

b u t th e house-in is power cut

‘It is not th a t P e te r did n o t tu rn the light on, b u t th a t th ere is a pow er cu t in th e house’

Common base: ‘th e light is no t on ’

T hese co-ordinations show th e typical properties of c o n tra st: a negative a n d a n assertive clause are co -o rd in ated in each of them , a n d b o th contain p ro so d ically p ro m in en t elem ents. F u rth erm o re , th e occurrence of th e co n ju n ctio n hanem is a n in d ep en d en t arg u m en t for th e ir contrastivity.

O n th e o th er h a n d , th e sentences in (9-11) have a very p ecu liar fe a tu re as well, nam ely, th a t th e re are no com m on elem ents in th e co -o rd in ated clauses w hich could in d icate th e focus fram e o f th e contrast (cf. Szabolcsi (1981)). To ex p lain why th e re is no overt focus fram e in these sentences, I propose th a t each clause belongs to the focussed part as a whole:

(9) N em [PÉTER aludt a padlón\ F , hanem [aHÁZIGAZDA költözött szállodába\F . (10) N em [PÉTER nem hozta el a tortát\F, hanem [a CUKRÁSZ nem készült el

még vele]F .

(11) N em [PÉTER nem kapcsolta fel a villanyt]F, hanem [a HÁZBAN van áram­

szünet]1^ .

F rom th e sem antic p o in t of view, the propositions in th e co-ordinated clauses in (9 -1 1 ) are no t in h eren tly incom patible w ith each o th e r. I suggest th a t these

p ro p o sitio n s are com peting explanations for the common base. T h e ir in co m p at­

ib ility is linked to th is role: due to th e exhaustive character of free focus, b o th e x p la n a tio n s are presented^as u n iq u e a n d m axim al explanations for th e com m on base.

T h e syntactic a n d sem antic asp ects of th e approach sketched above corrob­

o ra te each other. T h e inform al te rm ‘exhaustive ex p lan atio n ’ corresponds to a fo cu ssed clause in th e sy n tax and a focussed proposition in the sem antics. T his is w h a t characterizes th e phenom enon illu stra te d in (2) an d (9-11). In w h a t follows, I w ill refer to th is co n stru ctio n as contrastive co-ordination with focussed clauses, or C C F C for short.

T o make th e e x p lan a tio n pro p o sed above explicit, I will now exam ine (i) how th e focussed p a rt ex ten d s from th e prosodically prom inent w ord to th e entire clau se (section 1 .3 .1 ) , an d (ii) how th e concept of explanations can b e fit in to the sem an tics of c o n tra ste d propositions (section 1 .3 .2 ).

1 .3 .1 . F o c u s P r o j e c t io n

In th e lite ra tu re on focus, th e tech n ical devices used for explaining th e connection b e tw ee n prosodic prom inence a n d sem antic focus are known as focus projection (h en cefo rth , F P ). T h e re are two m a jo r theories a b o u t F P in th e tra n sfo rm a tio n a l­

ist tra d itio n : C hom sky (1971) a n d Selkirk (1984). B o th theories assum e a level of re p re se n ta tio n of focus extension, w hich m ediates betw een th e phonological form (p ro so d y ) and th e sem an tic m odule (m eaning). A one-to-one m a p p in g is assum ed b e tw ee n focus ex ten sio n an d m eaning, while the function from focus extension to p ro so d y is a n e u tra liz in g one. T h e th e two theories are quite dissim ilar, they share tw o im p o rta n t fe a tu re s1 connected to th e tre a tm e n t suggested in th is p ap er: (i) nei­

th e r o f them excludes th e th eo retical possibility of focussed clauses; a n d (ii) n eith er of th e m can be ap p lied to H u n g arian (or R ussian) w ith o u t m odifications.

B o th a u th o rs claim th a t th e focussed p a rt is always a c o n stitu en t. A ccord­

ing to Chom sky (1971), th e m ax im al p o ten tial focussed p a rt is th e highest V P of a clause (th a t is, an S or IP c a n n o t be focussed). This does n o t exclude the p o ssib ility of focussed clauses, b ecau se an entire clause m ight b e d o m in ated by a V P . F u rth erm o re, Chom sky (1971) posits th a t prosodic prom inence is always c a rrie d by the la st w ord of th e focussed p a rt. O n th e other h a n d , th e two lan ­ g u a g es quoted h ere (i.e., H u n g arian a n d R ussian) exhibit an o p p o site d istrib u tio n of p ro so d ic prom inence: it is m o stly th e first w ord of th e focussed p a rt th a t is p ro so d ically p ro m in en t (in th e following exam ples, em bedded foci rep resen t a lte r­

n a tiv e focussed p a r ts , only one of w hich realizes):

(1 2 ) a. He was [warned [to look out for [an [ex-convict [with [a red

s h i r t]f ]f ]f ]f ]f ]f .

b. He was warned to look out fo r an ex-convict with a [r e d] F shirt.

(7 ') a. N em az érett [FÉRFIAI<]F tetszenek Zsuzsának, h a n em ...

‘It is n o t m a tu re M EN th a t Sue likes, b u t . .. ’ . . . a z érett [GYÜMÖLCSÖK]^,

th e rip e fruits

‘rip e fr u its ’

* . .. a z [AGGASTYÁNOK^, th e greybeards

‘g re y b e ard s’

* . . . [VACSORÁZNI szeret járni]F.

dinner-INF likes go-INF

‘s h e likes to go to d in n e r s ’

b. N em az [[[ÉRETT]F férfiak]F tetszenek]F Zsuzsának, h a n e m ...

‘It is n o t M A TU R E m en th a t Sue likes, b u t . .. ’ . . . a z [ÉLTES

]F

th e elderly m en

‘elderly m e n ’

. .. az [AGGASTYÁNOK]77, th e grey b eard s

‘g re y b e a rd s’

. . . [VACSORÁZNI szeret já rn i]F dinner-INF likes go-INF

‘sh e likes to go to d in n e r s ’

T h e th re e po ssib le con tin u atio n s in (7 'b ) correspond to w ider an d w id er focussed p a rts in th e first clause.

T h is ty p e of difference betw een English, on th e one h an d , an d H u n g a ria n an d R ussian, on th e o th e r, suggests a solution involving sy n tactic p a ra m e te rs. Selkirk (1984) fo rm u lates h er theory of F P in term s of head, argum ents a n d a d ju n c ts.

P rosodic p ro m in en ce — as a reflex of th e ‘focus’ featu re — is alw ays asso c iate d w ith a w ord. T h is w ord is always a possible focussed p a rt. If it is th e h e a d or an unm oved a rg u m e n t of a phrase, th en th e p hrase itself is a possible focussed p a rt as well. A d ju n c ts are excluded from th e recursion. T his th eo ry is m u ch m ore perm issive th a n C hom sky’s (1971), yet it can n o t account for the H u n g a ria n (a n d R ussian) facts a b o u t m odified co n stru ctio n s in focus. In (7 'b ), th e e n tire m odified c o n stru ctio n can b e in te rp re te d as a focussed p a rt, th o u g h prosodic p ro m in en c e is carried by a n a d ju n c t, namely, th e adjective. So F P has to be in v estig ated fu rth e r.

1 .3 .2 . S e m a n t ic s for C o n t r a s te d E x p la n a tio n s

T his sectio n app ro ach es th e sem antics of C C F C in two steps. F irs t, I a m going

to m ake the m eaning of fo cu ssed propositions explicit. Then I will o u tlin e th e p ro b lem s arising from the co -o rd in atio n of two such propositions.

As for th e m eaning of focussed propositions, it should be g u aran teed som ehow t h a t the focussing of p ro p o sitio n s is analogous to th e focussing of o th e r ty p es of o b je cts. A generalized n o n -sy n categ o rem atic form ulation of the m eaning of free fo cu s would prove ra th e r u sefu l for carrying this out, and by applying th is tr e a t­

m e n t to pro p o sitio n s would pro v id e us w ith a null-hypothesis on w h at a focussed p ro p o sitio n m eans. In w h at follows, I will co n stru ct such a form ulation along th e lin es of van L eusen and K á lm á n (1993).

E x h au stiv ity can be c a p tu r e d using th e concept of infímum of lattice theory.

T h a t is, th e in te rp re ta tio n o f exhaustivity requires a partially ordered set. If each ite m in the sy n tac tic c ateg o ry of th e focussed p a rt is sem antically rep resen ted as a set of th o se en tities t h a t tu rn them into tru e sentences, th e n th e su b set re la tio n over th o se sets will do th e job of th e p a rtia l ordering. For exam ple, in th e case of noun p h rases, th e p a r tia l ordering will be th e subset relatio n over sets of p red icates. T h e N P Peter co rresp o n d s to th e set of those predicates th a t are tru e fo r th e individual assigned to Peter. The sem antic co u n terp art of Peter and Paul is th e set of p red icates tru e for b o th individuals, i.e., the set resu ltin g from th e in tersectio n of th e two re sp ec tiv e sets. Therefore, th e sem antic value of Peter and P aul is a su b set of the d e n o ta tio n s of b o th Peter an d Paul an d is th u s ordered a fte r them .

If the focussed p a rt is sem antically of ty p e a s.t. 3 ß .(ß ,t) — ct(i.e., it can be considered a ch aracteristic fu n c tio n of a set fp), then th ere is a poset (D a; C ) w here D a is the set of th e d e n o ta tio n s of all term s of type o , and C is th e subset relatio n over them . T h e focus, fram e a n d the relevant dom ain are b o th of ty p e ( a ,t) , so th e y can be seen as c h arac te ristic functions of some sets if and rd , respectively.

F ree focus presupposes th a t th e re is an en tity X of ty p e ct such th a t X = f \ ( i f n rd).

F u rth erm o re, th e sentence co n tain in g free focus asserts th a t fp = f \ ( f f H rd )4.

W h at rem ain s to be d o n e is to in sta n tiate fp, i f and rd for th e case w hen an a n tire clause is focussed. I h av e assum ed th a t the focussed p a rt is sem antically a

4 A ssum ing an ‘e x tern allly dynam ic’ presupposition operato r 6 for w hich th e following equivalence h o ld s (cf. Beaver (1992)):

->(6(X) A Y ) = S(X ) A ~Y,

p ro p o sitio n . T h o u g h there'\is no overt focus fram e in th e sentence, we still a ssu m e for th e sem an tics th a t th ere is a function m ap p in g prop o sitio n s in to th e ir t r u t h values in th e a c tu a l world. T his is also a c h arac te ristic function th e c o rresp o n d in g set of w hich is Wact- Let th e focussed p ro p o sitio n be q. A ssum ing no re le v a n t dom ain, th e a p p lic atio n of th e categorem atic form ula yields

q =

Since TTact is a set of propositions, the p a rtia l ordering over it is sem an tic e n ta il- m ent. B eing th e infim um of Wact m eans th a t all propositions tru e in th e a c tu a l w orld follow fro m q. U sing a blasphem ous p a ra p h rase , q is th e prim a causa5 of the a c tu a l w orld.

T his fo rm u latio n of th e m eaning of focussed pro p o sitio n s is to o stro n g , b e c a u se its e x h au stiv ity ran g es over an exceedingly large dom ain of p ropositions. T h is set has to b e c o n strain e d . Tw o questions arise a t th is po in t: (i) W h a t should c o n stra in it? (ii) To w hich m eaning com ponent should th e re stric to r belong?

A d (i): I p ropose th a t the dom ain of ex h au stiv ity consists of all a n d on ly th e p ro p o sitio n s th a t possibly specify, elaborate on or detail th e com m on b ase. In w h at follows, I will refer to th e relation th a t holds betw een these p ro p o sitio n s a n d th e com m on b ase as SED (from th e initials of th e term s Specification, E la b o ra tio n a n d D etail). T h e content of the common base (henceforth, CB) m ay vary fro m context to c o n tex t, b u t th e ch aracter of its re la tio n to th e relevant p ro p o sitio n s rem ains th e sam e. W e will build this in to o u r re p resen tatio n in th e follow ing way. Let S E Dcb s ta n d for th e set of those p ro p o sitio n s th a t are S E D -re la te d to th e com m on base CB. T h e focussed p ro p o sitio n is th e infim um of th e s e t of p ro p o sitio n s th a t b o th are tru e in the a ctu a l w orld an d s ta n d in th e SED re la tio n to th e CB:

q = / \ ( W act n SED c b)-

A d (ii): Since th e re are th ree com ponents (fp, f f an d rci), th re e p o ssib ilities are open. T h e focussed p a r t can surely b e excluded as the possible c a rrie r of SE Dc b, b ecau se S E Dcb h as to be a sub-form ula th a t infim um o p e ra te s on. T h e re still are two can d id ates. S E Dcb is either identical to rd, or a su b fo rm u la of ff. T h e la tte r p o ssib ility needs fu rth e r explanation. Let us assum e th a t th e tra n s la tio n of a clause in th e discourse includes a sub-form ula th a t th ere exists a p ro p o sitio n

we could rep resen t th e m eaning of focus as follows:

S ( 3 X .X = / \ ( f f n rd)) A X = fp.

5 Cf. St. T h o m as, Sum m a Theologiae.

(namely, th e common b a se ) to which th e p ro p o sitio n of th e clause is SE D -related.

T h at sub-form ula is so g e n e ra l th at it does not change th e tru th conditions of th e entire form ula. A b stra c tin g away from th e p ro p o sitio n of the clause yields th e sem antic equivalent of th e f f :

Ap(3CB.p G SEDcb & p{wact))-

This is a characteristic fu n c tio n of a set of p ro p o sitio n s which is conceivably iden­

tical to Wict fl SEDc b- In section 2, I will present som e independent m o tiv atio n for the presence of SEDc b in the tra n slatio n of clauses as they ap p ear in discourse.

T h e distinction b e tw ee n the focus fram e and th e relevant dom ain can be ju s ­ tified straightforw ardly. T h e focus fram e is an essential com ponent of sentences containing free focus. It m u s t exhaustively hold for th e focussed p a rt. As for the relevant dom ain, it is o n ly a supplem entary device to avoid too stro n g readings.

From th is point of view, it seems plausible th a t SE Dcb should be identical to the relevant dom ain, since its purpose is also to avoid to o strong readings. N ever­

theless, I w an t to argue t h a t either th e f f and th e rd are to be conflated or else SEDcb is to belong to th e focus frame.

„ As fa r as the first possib ility is concerned, th e p ro p erties of th e focus fram e and the relevant dom ain a re largely identical. B o th com ponents are of th e sam e sem antic ty p e. Both fo cu s frames a n d relevant dom ains m ust be sh ared by the m em bers of contrastive co-ordinations. T h e relevant dom ain has no overt linguistic rep resen tatio n , so its c o n te n t is com puted somehow from the context. A ccording to van L eusen and K á lm án (1993:9), focus fram es a re also left im plicit qu ite often, in which case their c o n ten t is also to be com puted from th e context. In sum , if we were to conflate the two, m an y questions would n o t arise a t all.

If we did not conflate f f and rd, th e n SEDcb should be a sub-form ula of ff. My argum ent for this runs as follows. T he relevant dom ain m ay occur in any in stan ce of free focus, irrespective o f the type of th e focussed constituent. O n th e o th e r hand, S E Dcb is linked to a p articu lar category of focussed p arts. It only ap p ea rs when th e fp is a p ro p o sitio n , and th e n it is obligatorily there. Now, th e focus fram e is likewise category specific. It is th e result of a b strac tin g over th e focussed p art. If we w ant to e x p la in why it is present w hen a proposition is focussed, we have to include it in th e focus frame.

To assess w hether C C F C qualifies as genuine co n trast, we have to check w hether it satisfies o u r c rite ria for c o n tra st. If we disregard th e restric tio n to SEDc b, th e answer is c lea rly on the positive. T h e re cannot be m ore th a n one prima causa of one p o ssib le world: two such p ro p o sitio n s m ust be inconsistent or equivalent. If we also tak e the restric tio n to S E Dcb into account, th e n the requirem ents for co n tra st a re satisfied only if CB is th e sam e in each an d every clause. W h en entities o f o th e r types a re focussed, th e linguistic id en tity of focus frames ensures th at th e y refer to the sam e thing. A lthough S E Dcb is n o t an

overt p a r t of th e focus fram e, co-ordinated focussed clauses are still in te rp re te d in a w ay th a t th ey refer to th e sam e issue. P u ttin g th e p ro b lem in form al te rm s, one sh o u ld ensure th a t th e p ro p o sitio n al variable CB in a clause be able to b in d th e o ccu rren ce of th e variable in -a n o th e r clause. T h e p ro b lem seem s to challenge com positionality.

In th e following section, I will present some m o tiv atio n for th e p resen ce of S E Dcb as a sub-form ula in every proposition of a piece of discourse. In sectio n 3, I will a tte m p t to give a form al account of th e cross-sentential bin d in g of p ro p o si­

tio n al variables.

2. D is c o u r s e S t r u c t u r e a n d C o m m o n B a s e 2 .1 . T h e L in g u is tic D is c o u r s e M o d e l

T h e in d iv id u a l sentences in a discourse usually do no t co n tain all in fo rm atio n necessary for in te rp re tin g them . A naphors carry par excellence (referen tially ) p a rtia l in fo rm atio n , b u t in d iv id u al sentences m ay also rem ain agnostic a b o u t o th e r

— s p a tia l, tem p o ral, m o d al etc. — aspects of m eaning. In principle, a piece of discourse as a whole is in te rp re ta b le . So th ere m u st be alg o rith m s to co m p lete underspecified or m issing inform ation. This im plies th a t discourse m u st b e a s tru c tu re d entity. O n th e o th e r h a n d , the fact th a t sentences in a piece of discourse are in te rp re te d to g eth er im plies th a t discourse has got coherence on its ow n. For exam ple, topics can n o t follow one a n o th er in an a rb itra ry m a n n er, and old topics c an n o t b e ta k en up ag ain arb itrarily .

P o la n y i’s (1988) ’Linguistic Discourse Model ( L D M) is a form alized th e o ry a b o u t discourse stru c tu re . Pieces of discourse are seen as c o n stru c te d fro m dis­

course constituent units (dcus) using recursive sy n tactic rules. Every dcu is associ­

a te d w ith a sem antic content, a n d every syntactic rule has a sem an tic c o u n te rp a rt th a t co m p u tes th e sem antic co n ten t of com posed dcus from th e sem antics of th e ir c o n stitu en ts.

So dcus are eith er atom ic o r composed. Every clause a u to m a tic a lly b elong to th e fo rm er category, a n d no o th e r entities belong there. E v en th o u g h discourse p articles a re n o t dcus a t all, from the point of view of th e th eo ry th ey co u n t as k in d of atom ic. T h ey come in th ree varieties: rhetorical ( because, therefore), logical (and, or, if . . . then . . . ) an d p u sh /p o p m arkers (well, anyway). T h is su b ca te g o riz atio n is sem antically m otivated.

C o m p o sed dcus are split into subcategories, too. T h e re are co-ordinations, subordinations, interruptions a n d binary structures. Since th e p ro p e rtie s o f each su b ca te g o ry are d eterm in ed by th e sy n tac tic a l/se m a n tic al ru le th a t creates th e com posed dcu in question, they will be presented to g eth er w ith th e sy n tax a n d sem an tics of LDM .

The g ra m m a r of discourse consists of context-free rules. Its basic — no m ­ in alist — in ten tio n is to re p re se n t all th e atom ic dcus as term inals an d all th e com posed ones as n o n -term in als. C om posed dcus of any subcategory can function as discourse in itiato rs.

A co-ordination can b e re w ritte n as th e sequence of an a rb itra ry num b er of dcus of any ty p e. Rules a b o u t su b o rd in a tio n are m ore restricted : th e y can be con­

stru c te d of a t m ost two dcus. A ra th e r im p o rta n t linear precedence rule applies to th e ir construction: the su b o rd in a tin g dcu always precedes th e su b o rd in a ted one.

T h e typical su b o rd in ativ e discourse o p e ra to rs are because, since, whereas. Ac­

cording to th e classification in Polanyi a n d Scha (1984), th e residual subcategories ra n g e w ith th e previous two. In te ru p tio n s only differ from su b o rd in atio n s in th e ir sem antics. B in ary stru c tu re s a re eith er subordinative (these are th e p a r excellence su b o rd in atio n s) or co-ordinative. T he la tte r ty p e includes some logical an d d educ­

tiv e types of co-ordination. T h e ir typical discourse o p erato rs are either . . . or . . . , if . . . then . . . a n d therefore. By definition, they m ust consist of two dcus.

The sem antics of th e LD M uses context frames (cfs). Every context fram e is associated w ith a dcu token (a n integer in th e case of atom ic dcus, th e sym bols C o r S, w hich indicates th e ty p e of com position). Form ally speaking, cfs are ordered n -tu p les (in p ractice, trip les). T h ere is a slot for each piece of in fo rm atio n th a t is relevant for th e c o n tex t: one for participants, one for tim e, an d one for th e properties and relations o f p a rtic ip a n ts. Polanyi (1988) uses th ese p aram eters only, alth o u g h noth in g in th e th eo ry excludes th e possibility of o th er slots, e.g., for space and m odality. T h e fram e of atom ic dcus is given by th e form al tra n sla tio n (o r a t least expressible in its term s). T h e inform ation ab o u t th e assignm ent of values to ind iv id u al variables ap p ea rs in th e slot for p articip an ts; th e inform ation a b o u t tem p o ral variable assignm ents ap p ea rs in the tim e slot; and th e inform ation a b o u t the in te rp re ta tio n fu n c tio n ap p ears in the slot for properties an d relations.

T h e fram e of com posed dcus is com puted from the fram es of th e ir co n stitu en ts a n d from th e ch aracter of th e com position.

The o p e ra tio n th a t co m p u tes th e fram e of co-ordinative dcus is called Gen­

eralized Union (G U). It o p e ra te s on a set of vectors, a n d calculates ‘th e m ost restrictiv e relevant n a tu ra l s e t’ (Polanyi (1988:617)) or ‘th e m ost specific com m on d e n o m in a to r’ (Polanyi a n d S ch a (1984:574)) for each slot. The GU also acts as a condition on co-ordinability. T h e unification cannot resu lt in a triv ial fram e, e.g., (N O W , exist). A lthough th e a u th o rs provide us w ith m any exam ples of th e result o f calculating GUs, they re m a in agnostic on how exactly it works.

(13) a. Jim took all the home ec. courses in the high school.

l(J im ,P A S T , take all th e hom e ec. courses in th e high school) b. He took the Cordon Bleu Course in France last year.

2(Jim , PA ST, take th e C ordon Bleu Course in France) a-fib. C (Jim , PA ST , ta k e courses)

If we co -o rd in ate th e sentences in (13a) and (13b) w ith th e c f th a t follow th e m , th e co n tex t fram e of th e co-ordination will be as in (1 3 a + b ). It is th e result o f th e GU of th e two ind iv id u al context fram es. In th is exam ple, two a to m ic dcus w ere com posed in to a co-ordination. B ut rem em ber th a t b o th GU a n d th e s y n ta c tic o p e ra tio n of co-o rd in atio n m ay o p erate on an a rb itra ry n u m b er of dcus, in clu d in g com posed ones.

T h e fram e in h eritan ce m echanism of su b o rd in a tio n is ra th e r sim ple: th e w hole su b o rd in a tio n always in h erits th e fram e of the su b o rd in a tin g c o n stitu e n t. B o th in ­ te rru p tio n s a n d su b o rd in ativ e b in ary stru c tu re s (p ro p er su b o rd in a tio n s) are c h a r ­ acterized by th is configuration of context fram es. B u t th ere is a n e x tra co n d itio n on th e la tte r. P ro p e r su b o rd in atin g dcus m u st s ta n d in a so-called IS-A r e la ­ tio n to th e p ro p e r su b o rd in a ted ones, while th e sam e con d itio n does no t ho ld fo r th e c o n stitu e n ts of in terru p tio n s. For the IS-A relatio n , P olanyi (1984) a d o p ts J .R . H o b b s’ definition as a startin g -p o in t:

‘A segm ent of discourse is (stan d s in th e IS-A re la tio n w ith ) th e segm ent So if th e sam e proposition P can be inferred from b o th So and S i, a n d one of th e arg u m en ts of P is m ore fully specified in Si th a n in S 0.’

Even th o u g h Polanyi (1984) does not revise th is fo rm u latio n explicitly, in p ra c tic e she qualifies a m uch b ro ad er class of relations as in stan ces of th e IS-A re la tio n . Polanyi (1984) considers (14) as proper su b o rd in atio n :

(14) a. Jim is a great cook.

l( J im , N O W , being a g reat cook)

b. He has been learning cooking for a long time.

2 (Jim , PA ST, learn cooking for a long tim e)

A lth o u g h th e re la tio n betw een (14a) and (14b) does n o t fit well in to th e H o b b sian definition, Polanyi assum es th a t it is an IS-A relatio n . T h ere are som e p ro p o sitio n s th a t are ‘co ro llaries’ of b o th (14a) an d (14b) (e.g., ‘Jim has som e experience in cooking’) w ith resp ect to w hich (14b) is m ore specific th a n (14a) in som e sense.

Since com posed dcus can also c o n stitu te su b o rd in a tio n , th e IS-A relatio n h a s to b e defined for th em , too. T h ere is a proposition th a t can be re c o n stru c te d fro m th e c f of dcus. Its p red icate is tak en from th e slot for p ro p erties a n d relations, w h ile its in d iv id u al a n d tem p o ral arg u m en ts come from th e o th e r slots. T h is p ro p o sitio n is called th e discourse them e (D9), and it sta n d s in th e IS-A re la tio n w ith th e clcu.

For ato m ic dcus, D 9 is identical w ith the pro p o sitio n of th e ir clause. T he D 9 o f a co -o rd in atio n is th e new p ro p o sitio n com puted th ro u g h GU, w h ereas th e c h a ra c te r of th e D 9 of a su b o rd in a tio n depends on the c h arac te r of th e su b o rd in a tin g clcu.

E very LDM analysis h as a graphical re p resen tatio n as well, called the D is­

course Parse Tree (D P T ). In th e exam ple below, th e piece of d isco u rse in (15) is

represented by the D P T in (16). In (15), in d en tatio n represents su b o rd in atio n , and eq u al indentation rep resen ts co-ordination. In (16), in d en tatio n represents dom inance: the d au g h ters of a tree n o d e follow th eir m o th e r node w ith an in d en ­ tatio n .

(15) a. Jim is a great cook.

b. He took all the home ec. courses in the high school.

c. He worked as a cook in the army.

d. He took the Cordon Bleu Course in France last year.

S^Jim , NOW, b e a great cook) a ( . . . )

b ( . ..) c( • • •) d ( . ..)

T he D P T form at is n o t o n ly a visually expressive device, b u t also enables Polanyi to fo rm u late w ell-form edness/felicity conditions on how pieces of discourse can be increm ented with new dcus in term s o f adjunction. It w ould be h a rd to do th is in term s of a linear rep resen tatio n .

New u n its are in c o rp o ra te d in th e stru ctu re of th e discourse in accordance w ith th e sem antic re la tio n th ey b ear to one of its dcus. If this relatio n is of th e IS-A ty p e , th e new clause will be su b o rd in a ted to th e old dcu; if th e new clause has a n o n -triv ial com m on d en o m in ato r w ith the old one, th ey will be co-ordinated.

Syntactically, this is re a lize d by a step o f (proper or n o t-so -p ro p er) a d ju n ctio n (cf.

section 2 .1 .1 ).

However, not every o ld dcu of th e discourse is accessible to th e new clause.

Polanyi form ulates a c o n d itio n on accessibility in te rm s of dom inance. T h e new un it h as only access to th e m ost recen tly added dcu a n d th e dcus th a t d o m in ate it. Since a n adjoined u n it is always to th e right of lower segm ents in a D P T , only th e dcus o f the rightm ost n o des of th e tre e are accessible. T h e oth er nodes cannot be resum ed, i.e., their D 9s are not accessible. F u rth erm o re, N Ps th a t have been in tro d u ced in such closed-off dcus c a n n o t be picked u p by pronouns in th e new unit.

C ( Jim , PAST, le arn cooking)

2 .1 .1 . A d ju n c tio n

This sectio n aims at ex p lain in g a sy n tac tic device th a t Polanyi (19SS) uses im plic­

itly. At th e same tim e, it proposes a m odification of thfc LDM in o rd er to m ake it more tra n sp aren t, th e o re tic ally m ore app ealin g and easier to formalize.

A d ju n c tio n is a stru ctu re-p reserv in g o p eratio n on g rap h s, w hich can b e d i­

vided in to two sub-operations: (i) T h e targ eted node splits u p in to two segm ents (w hich are still one node), so th a t th e u p p er segm ent is d o m in a te d by th e sam e nodes as th e original node was, w hile th e lower segm ent d o m in ates th e sam e nodes as th e original node did. F u rth erm o re, th e u p p er segm ent im m ed iately d o m in ates th e lower one. (ii) A new node is ad d ed to this tw o-segm ent n o d e, so th a t th e u p p e r segm ent im m ediately d o m in ates it.

I p ro p o se th a t every step th a t u p d a tes discourse s tru c tu re — inclu d in g b o th su b o rd in a tio n a n d co-ordination step s — take th e form of a d ju n c tio n syntactically.

D ue to its stru c tu re -p re se rv in g ch arac te r — a n d to th e p arallelism betw een sy n tax a n d sem an tics — , ad ju n ctio n ensures m onotonicity in sem antics.

A d ju n c tio n s th a t yield su b o rd in atio n s are always p ro p er ad ju n ctio n s. T h e s u b o rd in a tin g dcu form s th e lower segm ent of th e a d ju n ctio n , w h ereas th e u p ­ p er segm ent is th e su b o rd in atio n dcu itself. T h e two segm ents form one node, especially as th e have the sam e c f :

(17) l ( x ) + 2 ( j , ) =>

As for a d ju n ctio n s th a t result in co-ordination, Polanyi eith er a d d s a new b ra n c h to th e co -o rd in atio n (this can only h ap p en w hen th e new dcu is ad jo in ed to a n alread y ex istin g co-ordination, see (18) below), which is not an a d ju n c tio n a t all, or creates a new co-ordination node w hen so needed. T his a d ju n c tio n is im p ro p er, because th e lower segm ent of th e ad ju n ctio n (th e old dcu) an d th e u p p e r segm ent (th e co -o rd in atio n dcu) cannot have th e sam e context fram e (see (19) below).

(18) C (G \J (x ,y )) + 3 (*)=> C (G U (.r,y ))

l( x ) 2(y) l ( z ) 2 (y) 3 (z)

(19) l ( z ) + 2(y) => C (G U (x ,y ))

l(x ) 2 (y)

T h e ty p e of o p e ra tio n in (18) can be tran sfo rm ed into an im p ro p er a d ju n ctio n , so th a t th e old co-ordination dcu becom es th e lower segm ent, w h ereas th e u p p e r segm ent is a new ly created co-ordination dcu w ith a new fram e:

(20) C{z) + l(x) =4>

2.2. L D M and C C F C

We have seen that the re la tio n th a t I dubbed SED plays a central role in th e analysis of CCFC. As a consequence, a necessary condition of embedding C C FC into the LDM is to in co rp o rate th e SED relation into the theory. To do this, I propose to collapse the SED relatio n w ith the IS-A relation. Given th a t b o th concepts are defined in a r a th e r vague way, there is no a priori reason why they could n o t b e the same. To assess w h eth er this is feasible on empirical ground, I will briefly consider some facts ab o u t C CFC again.

Quiescent common bases an d focussed clauses of CCFCs can be transform ed into (audible) subordinations. For exam ple, the CCFCs in (9-11) can be converted into ( 9 '- l l ') below, where th e continuations in (-a ) and (-b ) are alternative su b ­ ordinated dcus to the first sentence:

(9') The accommodaiion worked out well.

a. It is that P eter who slept on the floor.

b.

(10') The cake is not here.

a. It is that Peter did not bring it.

b.

( I T ) The light is not on.

a. It is that Peter turned it off.

b.

As can be seen, each one of th e pairs of contrastively co-ordinated clauses of (9—

11) can a ct as clauses su b o rd in a ted to a clause th at expresses their common base.

T his justifies the identification of SED w ith IS-A.

It seems, then, th a t C C F C can be embedded into the LDM, if we assum e th a t every subordinated dcu co n tain s th e sub-formula th a t its proposition is IS-A- related to th e proposition of th e subordinating dcu. Since every dcu is a possible subordinated dcu, the tra n sla tio n of every dcu has to contain the sub-form ula th a t th ere is a proposition th a t its D e is IS-A-related to. This sub-formula is identical w ith the sub-formula corresponding to th e SED th at I have added to the tran slatio n of clauses to account for p ro p o sitio n al focus. In this sense, Polanyi’s LDM is an

in d ep en d en t m o tiv atio n for doing so. T his way of rep resen tin g / ^ - in h e r ita n c e challenges com positionality, since th e D 9 of th e s u b o rd in a tin g dcu m u st cross- sen ten tially ‘b in d ’ th e pro p o sitio n th a t th e D 9 of th e su b o rd in a te d dcu is IS-A- re la ted to. C om m on-base in h eritan ce in C C F C s also challenges com p o sitio n ality . A panacea for b o th will be presented in section 3.

A d irect em b ed d in g of C C FC into P o la n y i’s LDM , how ever, does n o t seem viable. If one in te n d s to IS-A -relate th e p ro p o sitio n of th e focussed clause to th e com m on base, one should create a su b o rd in a tio n w here th e quiescent co m m o n base is th e su b o rd in a tin g dcu an d the focussed clause is th e s u b o rd in a te d one.

T h e a ssu m p tio n of vacuous dcus is not ap p ealin g a t all. F u rth erm o re: In case of co n trastiv e co-o rd in atio n s, not only th e com m on base should su b o rd in a te th e first clause, b u t one also h a s to assum e th e existence of a n o th e r su b o rd in a tio n b etw een th is su b o rd in a tio n a n d th e second clause. T h e co -o rd in atio n w ould b e tra n sfo rm e d into a double su b o rd in a tio n (cf. (21) below). T h is is heavily c o u n te r-in tu itiv e .

(21) C S ( CB)

l ( z ) 2{y) S(CB> 2<y>

0(CB) U x)

To su m u p , th e fram e-in h eritan ce m echanism of th e LDM provides C C F C w ith th e desired cfs. Since th e su b o rd in atio n dcu in h e rits its D 9 from th e s u b o rd in a tin g dcu, b o th focussed p ro p o sitio n s are IS -A -related to th e com m on base. O n th e o th e r h an d , th e s tru c tu ra l p ro p erties of C C FC can n o t b e acco m m o d ated in th e ex istin g LDM m achinery.

2 .3 . I S -A a n d G U

S u b o rd in ab ility a n d co-ordinability are expressed in term s of IS-A a n d GU. If an IS-A re la tio n holds betw een the D6s of two dcus o r th e a p p licatio n of GU to two dcus resu lt in n o n -triv ia l context fram es, then th e two dcus can b e s u b o rd in a te d or co-o rd in ated , respectively. Due to th e fram e in h e rita n c e m echanism of th e LD M , the D9s of a su b o rd in a tio n dcu an d th a t of its s u b o rd in a te d dcu also s ta n d in an IS-A relatio n . I will show th a t th e D 9 of every c o -o rd in ated dcu is also IS -A -related to th a t of its co -o rd in atio n dcu. F irst, I will show th a t th e D 9 of each c o -o rd in a te d dcu (except for th e ones w ith dow nw ard m onotone N P s) is IS -A -related to th e D 9 of th e co -o rd in atio n dcu, even in th e H obbsian sense. In th e second ste p , I will show th a t th e IS-A re la tio n of Polanyi holds even betw een th e D9s of c o -o rd in a te d dcus w ith dow nw ard m onotone N Ps and the D ° of th e ir co -o rd in atio n dcu.

Polanyi considers H o b b s’ definition of IS-A as th e core of th e sem an tic rela­

tio n in su b o rd in atio n . So if tw o propositions s ta n d in a H obbsian re la tio n , th en th e y also s ta n d in a P o lan y i-ty p e IS-A relatio n betw een th em . T h e su m m ary of H o b b s ’ definition is th a t (i) th e propositions th a t are IS -A -related have a com ­ m o n entailm ent; an d (ii) a n arg u m en t of th e second p ro p o sitio n of IS-A is m ore specific th a n th e corresponding argum ent in th e first. (In ad d itio n , (iii) th e above a rg u m e n t has a c o u n terp art in th e common en tailm en t as well.)

F irst I w ill show th a t p o in t (ii) holds betw een a co -o rd in atio n dcu a n d any o f its co n stitu en ts. The GU com putes ‘the m o st specific com m on d e n o m in a to r’

fo r each slot o f th e context fram e s of the co-ordinated dcus. B ut even ‘th e m ost specific d e n o m in a to r’ can a t m o st be as specific as th e slot it has been generalized fro m . If every slo t is a re p re se n ta tio n of a ty p e of arg u m en t, th e re m u st b e at le a s t one slot — or a p a rt o f a slot — th a t is m ore specific in th e fram e of th e co -o rd in ated dcu th an in t h a t of the co-ordination itself. O therw ise it is n o t a co -ordination. So I am left w ith the first point.

In order to prove th a t co -o rd in ated dcus have n o n -triv ia l en tailm en ts, I first h a v e to m ake it explicit how th e reconstruction of D9s works in th e case of co­

o rd in a tio n . As fo r the slot fo r p ro p erties and relations, GU a b stra c ts over th e m ost specific com m on m eaning p o s tu la te of the p red icates in question (all th e b e tte r if th e s e m eaning p o stu la tes define th e common p red icate of th e co-o rd in ated clauses).

A s for the slot for individuals, I suppose th a t GU a b stra c ts over th e m o st specific co m m o n p ro p e rtie s of the in d iv id u als in question (all th e b e tte r if these p ro p e rtie s d efin e an in d iv id u a l).6 T h erefo re it is not crucial th a t th e reco n stru ctio n should p ro v id e a D 9 w ith the a p p ro p ria te type of quantifier. I assum e th a t P o la n y i’s G U works as follows: if all N P s of the co-ordinated dcus were non-dow nw ard- m o n o to n e, e x isten tia l q u an tificatio n would do in th e D e of the co -o rd in atio n dcu (cf. (22) below ).7

(22) First co-ordinated clause:

Every lion runs.

Second co-ordinated clause:

Som e zebras galop.

D e o f their co-ordination dcu:

‘Som e (savannah) an im als move f a s t’

It is conceivable th a t th e existential quantifier does n o t work in case of down- 6 T he a lte rn a tiv e of this k in d of operation is n o t too appealing. If GU a b stra c te d

over th e biggest set of com m on referents, m uch of th e generalization would be lost.

7 I call an N P downward m onotone if if th e tests for quantifiers th a t are dow n­

w ard m o n o to n e in th e ir second argum ent ju stify it.

w ard m o n o to n e N P s. Indeed, som etim es th ere is no quan tifier th a t w o u ld do.

C onsider:

(23) First co-ordinated clause:

A t m ost five ladybirds creep.

Second co-ordinated clause:

No may-bug crawls.

D e o f their co-ordination dcu: ???

I do n o t know how to solve this problem in term s of re c o n stru ctio n . I know , how ever, how to solve it in term s of IS-A. F irst, I prove th a t th e D 6s of dcus w ith non-dow nw ard-m onotone N Ps are IS-A -related to th e D 6 of th e co -o rd in a tio n dcu.

P (a) |= 3 x .P (x )

T h is is tru e irresp ectiv e of th e type of P , a an d x. T h e fo rm u la rem ain s tr u e even if P in th e e n tailm en t is replaced w ith a superset of P . T h e re la tio n b e tw e e n th e D e of a co -o rd in ated dcu an d th a t of th e co-o rd in atio n itself is ju s t a n in sta n c e of th is. Since e v ery th in g th a t follows from th e logical consequence of a fo rm u la follows fro m th e form ula itself, p o in t (i) of th e H o b b sian definition is satisfied as long as we consider cases w ith non-dow nw ard-m onotone N P s.8

S tep two: P o la n y i’s IS-A relatio n accounts for cases w ith p u re d o w n w ard m on o to n e N Ps. It is easy to find a su b o rd in atin g clause for eith er one o f th e co­

o rd in a te d clauses in (23), cf. (24) below. Since the D e o f th e s u b o rd in a te d dcu is IS -A -related to th e D e of th e su b o rd in atin g dcu, th is m ean s th a t P o la n y i’s IS-A re la tio n easily accounts for th e D e of co-ordination c/cus like

(24) a. Insects hardly move these days.

b. A t m ost five ladybirds creep.

c. No May-bug crawls.

P o lan y i’s IS-A re la tio n does not account for clauses w ith N P s of m ixed m o n o to n ic ­ ity, a lth o u g h it seem s possible to co-ordinate them :

(25) a. A lion often has no difficulty catching its prey.

b. Every lion runs.

c. No zebra galops.

T h e co-o rd in ab ility of (25b) an d (25c) can easily be e x p lain ed in term s of IS-A . T h e D es of b o th are IS -A -relatcd to th e proposition ‘lions a re m uch faster th a n z e b r a s ’, O ne can m an ag e to find analogous argum ents in th e com m on e n ta ilm e n t to satisfy po in t (iii) as well.

8

w hich is a possible D e of th e co-ordination itself. T his in te rm e d ia te proposition is, o f course, IS -A -related to (25a).

T h e next ta sk is to replace GU w ith IS-A b o th as a condition on co-ordinability a n d as a n o p e ra tio n to com pute cfs. T he co-ordinability condition will sound as follows: an old dcu of th e discourse and a new u n it can be co -o rd in ated if th e set o f p ro p o sitio n s th a t the D e of b o th dcus is IS-A -related to h as a t least one n o n -triv ia l elem ent. Let the m o st inform ative elm enet of this set b e th e D e of th e new co -o rd in atio n dcu. T his replaces th e GU operation.

T h is move h a s th e following im p o rtan t consequences:

(A ) T h e GU o p e ra tio n can b e dispensed w ith.

(B ) C CFC can b e rep resen ted as a co-ordination (cf. Figure 3). T h e m ost in ­ form ative p ro p o sitio n th a t the D e of eith er dcu is IS -A -related to is exactly th e com m on base. In th is sense, C C FC provides in d ep en d en t m otiv atio n for replacing GU w ith IS-A.

T h a t is, the new definition accounts for co-ordinations th a t could n o t have been c a p tu r e d otherw ise.

C (m o st in fo rm ativ e 2 6 (IS -Aj, fl IS-Aj,)), alias (CB) l( z ) 2(y)

Figure 3.

3. D y n a m ic D is c o u r s e S e m a n tic s

T h e ta sk of th is section is to give a form al account of the non-com positional p ro p e rtie s of b o th C C F C an d th e LDM. I will present a dynam ic sem antics for d isco u rse s tru c tu re along the lines of G roenendijk an d S to k h o f’s (1990) D ynamic Predicate Logic (D P L). T his sem antics does no t account for all th e effects of the L D M , b u t the tre a tm e n t of C C F C will be preserved by the form alization.

In section 3 .1 I will o u tlin e some p ro p erties of dynam ic sem an tics in general a n d o f D PL in p a rtic u la r. Section 3 .2 is a b o u t th e central id ea und erly in g th e d y n am izatio n of th e LDM , w hich I will form ulate in a dynam ic discourse sem antics in sectio n 3.3.

3 .1 . D y n a m ic L o g ic s a n d D P L

T h e definitive p ro p e rty of d y n am ic sem antics is th a t it conceives o f th e m eaning of a sentence n o t as its tr u t h conditions, b u t as th e way in w hich it changes

th e in fo rm atio n s ta te of th e h earer. T h a t is, th e m eaning of a sentence is a fu n c tio n m a p p in g in fo rm atio n sta te s before its u tte ra n c e to in fo rm atio n s ta te s a fte r u tte rin g it. T h e various ty p es of dynam ic sem antics differ in th e way th e y rep resen t in fo rm atio n states. Som e sem antic system s ch aracterize such sta te s by th e fu n ctio n s th a t assign values to free variables (or ‘discourse re feren ts’). D P L a n d H eim ’s (1982) ‘File C hange S em antics’ belong to th is ty p e. O th e r theories rep resen t in fo rm atio n states by p airs of in te rp re ta tio n fu n ctio n s a n d assignm ent fu n ctio n s (such as B eaver’s (1992) K PL ). These functions m ay be fully specified fu n ctio n s co m p atib le w ith an in fo rm atio n s ta te (as in D P L ), or m ay be p a rtia l fu n ctio n s specified only for a su b set of ‘salien t’ expressions (such as th e discourse referents in H eim ’s theory).

D y n am ic P re d ic a te Logic accounts for certain p h en o m en a re la te d to an ap h o ric relatio n s, su ch as cross-sentential anaphoric binding an d donkey a n ap h o ra, b u t it can only d eal w ith extensional, first-order form ulae. T h e language into w hich n a tu ra l-la n g u a g e sentences are tra n sla te d is th a t of first-o rd er p re d ic ate logic. O n th e o th e r h a n d , conjunction is n o t in terp reted in a c o m m u tativ e m an n er, an d th e tra n sla tio n s m ay contain free variables th a t are in te rp re te d as if th ey were b o u n d by q u an tifiers in form ulae to th e ir left.

T h e in te rp re ta tio n of a D P L form ula is a re la tio n betw een assignm ent fu n c­

tio n s. In each p a ir th a t belongs to such a relatio n , th e first m em b er is a possible in p u t in fo rm atio n sta te , w hereas th e second m em ber rep resen ts th e corresponding o u tp u t s ta te . For som e expressions th e in p u t an d the o u tp u t sta te s are identical.

T h ese can only im pose conditions on th e in p u t in fo rm atio n states. T h e y are said externally sta tic, an d they are called tests (e.g., conditionals are of th is ty p e).

In th e in te rp re ta tio n of o th e r expressions, th e in p u t a n d o u p u t assignm ents can be different. T h ese expressions can change sta te s of in fo rm atio n , an d are called externally dynam ic (in p a rtic u la r an existentially quantified form ula is ex tern ally d ynam ic, b e ca u se it in tro d u ces a new variable binding). T h e re are also several ways o f conjoining two expressions: in some cases, th e second sub-form ula is in ­ te rp re te d w ith resp ect to th e o u tp u t state created by th e first. In th is case, th e resu ltin g expression is internally dynamic (dynam ic co n ju n ctio n belongs here).

O therw ise, it is said internally static (as, e.g., disjunctions).

3 .2 . T h e C e n t r a l I d e a

P olanyi (1988) form ulates a w ell-form edness condition in term s of D P T s, nam ely, on th e accessibility of old dcus to new ones. A ccording to P o la n y i’s condition, th e accessible dcus are th e m ost recently adjoined dcu a n d th e dcus th a t d o m in a te it. T h is affects b o th possible ways of continuing discourse th em es a n d a n a p h o ra resolution. T h e co n tin u ab ility of a discourse them e m ean s th a t it can re a p p e a r in — o r affect th e co m p u ta tio n of — a newly ad d ed c o n stitu en t. So, clearly, th e possib ility of a d ju n ctio n a n d continuability are co n n ected w ith each o th e r.