A Di phas i c A p proach to D i recti onal Locatives

A Di phas i c A p proach to D i recti onal Locatives Viv i e n n e Fon g Stallford University 1 Introduction Any th eory o f p re po s i tio n m e a n i n g s has to acco u n t for the d i ffere nt di stributions of locatives cross-lingui stically If a t y p e of locat i v e prepo s i t i o n occurs w i t h a class of verbs in one language but not with the c orre s p o n d i n g class in another this coul d a priori be due to a d i ffere nc e i n the m e a n i n g of t h e verb or of the lo c ati v e Re cent work in model-theoretic a p pro a ch e s to E n g l i s h p r ep os i t i o n m e anin g has shown how directional locatives map t h e i r a rg u m e n t s o n t o p a t h s w h i c h then map onto the temporal str u c ture of verbs ( e g Verk u y l and Z w a rt s 1 99 2 Nam 1 995ab) Verkuyl and Zwarts for e xa mp l e a n al y z e d i rec t i o n a l i ty of p a t h s as the re sult of an en ti ty moving through space y ie ld i n g a p ar ti c u l a r orde r In thi s p aper I show that direc t i o n al locatives (DLs) do n o t al ways denote paths DLs such as into and out of u s u a l l y i n t e rp re te d a s p a t h p re p o s ition s can de note orientation Also the c o r res p o n d i n g DLs in F i n n i s h c a n occur with a class of non-moti o n verbs such as forget w i t h o u t ex pressi n g c h a n ge i n location I n both these cases no movement is involved I a r g u e t h a t DLs h ave a more abstract se mantics than a pure s p a ti a l or t e m p ora l i n t e r p re t a t i o n DLs re q u i r e only that the sp atial /temp ora l structures t he y operate on h ave two d i s ti n c t phases and DLs are sensi tive t o the order i n g of these p h ases The a n a l y s i s d e v e l o p e d here entai l s a mappi n g of prepositional m e an i n g o n t o p a t h s w h i c h i s l e ss d i rect than the m ap ping assumed in Verkuyl a n d Zwart s a p p r o a c h a m o n g o t h e r s (cf also B i er w i sch ( 1 9 8 8 ) Pinon ( 1 99 3 ) ) and i n conce p t u a l sem a n t i c s (e g l ackendoff 1 990) In ad d ition t h is analy s i s e n ables us t o ret a i n t h e i d e a t h a t t h e l ex i c a l m e a n i n g s of simil ar verb types in E n g l i sh and F i n n i s h are i d e n t i c a l 2 The data The distributions o f DLs t h a t I w i l l acc o u n t for are a s fo l l o w s : (i) DLs in Fi n n i s h o c c u r w i th ( n o n - m o t i o n ) verbs t h a t e n ta i l an terior/posterior states which is u n g r amma t i c a l in E n g l i s h H e re the DLs c l e arl y do not denote p ath s ( 1 ) e n tails that after fo rge t t i n g h a p pe n s the t h i n g forg o t t e n rem ai n s for a time in the location denoted by t h e DL p re d i c a te b u t i t d o c s n o t e n t a i l or presuppose any t h i n g a bo u t i t s l o c at i o n p r i o r to the fo rg e t t i n g A s i m i l ar example w i t h another verb ( leave ) i s g iv e n in ( 2 ) ( 1 ) Tuo vi u noht-i k i rj a - n a u to-on/ a u to - s s a Tuovi forget- PA S T- 3 p book- A C C c a r- I L L ( a t i ve ) c a r- I N E ( s s i ve) Tuovi forgot a/th e book in ( l i t j n t o r i n ) a/t h e car 1 99 7 b y Vi v i e n n e Fong Aaron Lawson (ed) SALT VII 1 3 5-1 50 Ithaca NY: Corn e l l U n i versity

136 VIVIENNE FONG (2) Tuovi jatt-i k i rj a - n auto-on/* a u to-ssa Tuovi leave- PAsT- 3 p book - ACC c ar - I L L c ar- I N E Tuovi l e ft a/the book i n ( l i t i n t o!* i n ) a/ t h e car In (3) fi n d entai l s that the th i n g foll n d m u s t be finding Th e same entailment h o l d s for look for (4) ( 3 ) Tuovi l b ys- i kirj a - n l a a t i k o - s t a/ in the l o c a tio n p ri or to the * l aat i ko-ssa Tuovi find-pa S T- 3 p book - G EN box - EL A ( tive) box- I N E Tuovi follnd a/t h e book i n ( l i t o u t o f!* i n ) a/th e box (4) H a n e ts i - i avain t - a task u - sta ( Karlsson 1 9 87 ) he 100k for- 3 s G key - PA R ( titive) pocke t - E L A S/he looks for althe k e y i n (lit O l l t of ) h e r/h i s p o c ke t In none of the cases need there be a c h a n ge of location i nv o lv e d The book could be or l eft beh i n d The same is true for finding and lo ok i n g for so m e t h i n g O n e n e ed n ot remove the objec t after fi nding it Notice th a t th e eq u iv a l e n t c o n s t r u c t i o n s in E n g l i s h are u n gramm atical ( 5 ) in the car both before and after bei n g forgotten a Pa t for g o t t h e book i n l* i n t o t h e c a r (5) b Pat fou n d t h e book i n/*o u t of t h e c a r (ii) With motion verbs DL pred i c a t i o n g i ve s a path read i n g i n bo th F i n n i s h and Engli sh : ( 6 ) K i ss a j u o k s- i cat h u onee-sta # S e j li-i huonee-see n run-past- 3 s G r o o m - E L A i t remai n - PA S T- 3 s G room- I LL A/The cat ran Ollt of a/t h e room # It rema i n ed i n the room l a a t i kko - o n (7) Kissa hyppas-i l a a t i k o - s t a " S e j ii - i cat j u mp - PA S T- 3 s G bo x - E L A i t rema i n - PA s T- 3 S G box - ILL A/The cat j u m pe d out of (8) a a/t h e T h e cat r a n o u t of the roo m box # I t rema i n ed i n the b o x # I t rem a i ned i n the room b The cat j um pe d o u t of t h e bo x # I t re m a i n ed in t h e box (iii) A s modifiers of concrete n o u n s DLs h ave a s p a t i a l me a n i n g In (9) and ( 1 0) the DL mod i fi e r spec i fi e s t h e orie n ta t i o n o f t h e b r i d g e a n d t h e ro ad respec tively in (perspectival) space (9) silta S an Francisco-on br i d g e S an Francisco- I L L a/the br i d g e i n to S an Fra n c i sc o

1 37 A DIPHASIC ApPROACH TO DIRECTIONAL LoCATIVES ( 1 0) Because you ve not got a good roa d i n t o London t h e n - unless its this M23 quite poss i b l y (London-Lulld) The aim of this paper is t o prov ide an analysi s of D L me a n i ng that will treat both the nouns and the verbs m od i fi ed by the D L s in a u n i fo r m way th u s achieving an i ntegrated seman tics for DLs I n a d d i tio n the d i ffe re n c e in English and Finnish with respect to the d ata in 0 )-(5 ) must be explained 3 Outline of a n a l ysis For obj ects and events which verbs denote I w i l l fi rst show that they can both be seen as ordered structures that DLs c a n operate on I w i l l motivate ordered structures for times stages o f events segments of objects and spatial traces of events In this way both the nou ns and the verbs w h i c h DLs m o d i fy are treated in a uniform way S eco n d I a d o p t the concept of an i n t e rv a l which contai n s a phase change with respect to an o rd e re d structure of times/stages o f events/parts of objects/spatial traces of e v e nts Th i rd I w i l l exp lo i t t h e p o s si b i l i ty provided by having intervals with p hase c h a n g e s to talk about the ord er i ng of the two phases with respect to each other Let us start with t i m e s a n d see how temporal p h ases are d e fi n e d I will take as given that time h a s an ord ere d structure a n d an i n herent d i re c t i on A l so time is dense The earlier than re l at i on ( --< ) bet we e n t w o t i m e p o i n t s i s tran sitive and asymmetric I argue that t h e in terval over wh i c h we evalu ate the tru t h of D L predicates con sists of two p h ases The n o t i o n of A D M I S S I B L E P H A S E - I N TE RVAL can be for mulated ac c ord ing to LObner ( 1 9 8 9 : 1 7 8 ) who defi n e s temporal p h a s es as follows: Any admissible in terval s tarts with a p h a s e of not-i a n d i s mo n o to n e i n term s of p: ie starting w i th times I fo r w h i c h 1( / ) =() i t m a y e x t e n d to l ater t i mes t with p(t )= l but m u s t n o t c o n t a i n a n y y e t later t i m e s I " w i t h p(l" ) =O agai n This is formalized i n ( 1 1 ) The i n terval ( 1 1 ] i n (i) i n d i c a t e s t i m e s i n a h a l f open interval (open on the left c l o sed o n t h e right) - ( 1 ) ( F ro m Lobner ( 1 9 8 9» ) I i s an a d m i s s i b l e i n terval i n (i) I = (i i i ] for some 1 ; -< 1 terms of / a n d I ( i n s h ort : / E A J ( t e p) iff (ii) I beg i n s w i t h a p h a se o f n o t- p : 3 t E I Vt E ] ( f--< f -+ f!( I ) ) ( i i i ) the fu n c t i o n I i s m o n o t o n e i n t h e i n terval I : for a l l t t E l i f ]I i s d e fi n e d for 1 / t h e n i f H t t h e n p( t ) -+ p ( t ) In this p a p e r I w i ll i n some cases dev i ate fro m t h e st rict l y p t o p d ev e l o pm e n t in ( 1 1 ) Lobner ( 1 9 89) a l so al lows p hase t ra n s i t i on to be from p o s i t i v e to n eg a t i v e o r vice versa; the cru c i a l po i n t in ( 1 1 ) i s t h e co n d i t i o n on monoton i c i ty

VIVIENNE FaNG 1 38 In general term s (to be made p reci se be low ) t h e admissible i n tervals for the DLs are g iv en in o rde r i n g of p h a s e s say p -< (12) G iven an p the into predicate is evaluated in th e se c o n d p h a se p w h i l e t h e o u t of pred i c a te i s evalu ated in the first p hase p What is i m p o r t a nt to n ote is t h a t the I l l ative and El ative p redicates are evalu ated in opposi ng ph ases W h e t h e r the p h as e s are ordered p --<p o r p --< p is s eco n d ar y (12) Ad m i ss i bl e intervals for DLs: a Into /Illative pre d i c a t e s take as t h e i r adm i s s i b i le i n te r v a l the monotone developmen t from p to p ( o r p t o p) w he re the truth of LOC"IN(a)(x) i s ev a l u a t e d in the s e c o n d p h a s e b Out of jelative p r e d i c a t e s t a k e as t h ei r ad m i ssible i n terval the mono tone d eve lo p m e n t from p to p ( or p to p ) w h ere the truth of LOC IN(a) (x) i s evaluated i n the fi rst p h a se now go o n to d i scuss how e v e n t s a n d o bj e c ts can be seen a s ordered struc can be g e n eral i zed to i n c lu d e eventualities and spatial configurations I w il l tures and how Lobn e r s notion of p h a s e s 4 Events and O bjects 4 1 Events Events t ak e pl ace in time Fo l l o w i n g P i ii6n ( I ( 0 3 ) a n d Krifka ( 1 989) I postulate present In (13) a mapping from events to times w h i c h p reserves any p art s t r u c t u re the function T ( Kri fk a s ( 1 989) t e m p or a l trace fu n c t i o n of an e v e n t or its run time ) localizes events in t i m e a n d + i s a pr i m i t i ve o p e ra t i o n J O I N : (13) VeVe [T (e) ;:c T (e) = T(e c el] S uppose a ru n n i n g eve n t h a s two s u beve n t s of ru n n i n g as p a r t s W h a t ( 1 3 ) s a y s i s t h a t t h e result of j oi n i n g t h e t i m e s of e a c h s u b e v e n t i s i d e n t i c a l t o the j o i n of t h e two subevents M ap p i n g t h e te m p o r a l t race of a n eve n t o n to the time l i n e w h i c h h as an ordered structure g i ve s a p re - o r d er of e v e n t s i n t i m e A p re - or d e r i s refl exive a nd transitive Thi s allows for the fact that d i ffere n t e v e n t s can go o n i n the same period of time 4 2 Objects Can objects l i ke br id g e s be t re ) t e d i n t h e s a m e w a y? l ackend o ff ( 1 992 1 996) extendi ng Marr s ( 1 982) t heory o f e n c od i n g o f o bj e c t s h a p e s s u g g e s ts that an ob j e ct can be decompo sed i n to i t h i erarc h i c a l a rr a n ge m e n t o f d i me n s i o n s where d i mensionality i s esse n t i al l y t h e n u m be r o f o rt h o g o n a l d e g ree s of freedo m within an object ( J ac k e n d o ff 1 90 2 : 29) In t h i s h i erarc h y t h e p r i m a ry d i mension of a

1 39 A DIPHASIC ApPROACH TO DIRECTIONAL LoCATIVES road/river/ribbon/bridge i s a li ne Moreover any 1 - dimension al axis can have a direction or orien tation Verkuyl a n d Zwarts ( 1 992) defi n e this notion of dimen sionality of an object as the number o f s p a t i al orde r i n g s that can be imposed on the material parts of that object A bridge can be s e e n as one-dime n sional because it can be partitioned i n to a set of p a r ts that i s ordered by one spatial rel ation where one slice of the bridge fol lows another ( Ve r k u y l a n d Zwarts 1 992 :496) This gives a I -dimensional view of the o bj ec t w i t h a l i near order Here I first i n troduce a spatial t ra c e of an o bj ect 0 an alogo u s to the temporal trace in ( 1 3) In ( 1 4) the fu nction (1 is t h e I -d i men sional spatial ordering of an object 0 which local i zes 0 in space and preserves any p art structure present ( 1 4) (Spatial trace fu nction ) : "10"10 [17(0) E8 17(0) = 17 ( 0 ::; 0) ] Adopting the idea t h a t a o n e - d i m e n s i o n a l o bj e c t can be part i tioned into a set of parts ( Verkuyl and Zwarts 1 992) t h e s p a t i a l trace fu n c t i o n can give the p arts of the bridge (S1o S 2 etc) : s"=a(br) S econd I po s t u l a t e that an object con strued as bei n g I -d i mensional can have an orientation or direction T h i s w i l l be d i sc u ssed b e l o w 4 3 Phases for objects Obj ects like bridges are e a s y to v i e w as c o n s i s t i n g of p h a s e s The v i e w i n g of objects as 1 -dimensional entities and the s p a t i a l trace fu nction ( see ( 1 4 ) ) a l lo w u s to look at a bridge as con s i st i n g of p ar t s a s d i sc u s s e d a bo v e T h e p a r t s of the brid ge which are outside of a region - for ex am pl e S a n Fra n c i sco - c a n be 1 p h ase (call it p) and the p art of the bridge that is within San Fra n c i sco is t h e other (p) (see ( 1 5) ) In other words ph ases are defi ned in t e r m s of l ocations occupied by the p arts of the bridge as it spans out i n s p ace p p ( 1 5) We derive the orderi n g of p h a s e s from k n o w i n g t h e l o c a t io n of S an Francisco i n rel ation to p arts of t h e b r i d g e and a g i v e n n arra t i ve pe r s p e c tiv e B ridges are i n h eren tly a-direction al A b r i d g e h a s no i n t ri n s i c fron t/bac k or le ft/r i g h t coordinate sy stem of i t s own a n d w hether i t c a n be c a l led a bridge i n to S an Francisco or ou t of San Fra n c i s c o d e p e n d s on the n arra t o r s/spe a k e r s p e rs p ec ti ve i n fixing the point of origin o f the b r i d ge With a b ri d ge Oll t o f S a n F r a n c i s c o the point of origin is fixed at S a n Franci sco and the p a rt of the b r i d ge that is lo c a t ed in S a n Francisco is ordered hefore t h e p a rt located o u ts i d e of t h e c i t y Wi th a bridge i n to S an Franci sco the p o i n t of or i g i n i s fi xed o u t s i d e of S a n Fra n c i s c o and the p art of the bridge that is l o c a t e d in S a n Fra n c i sco i s ordered ({fter t h e part located outside of the city Imagine a bridge t h a t strad d l e s t h e S a n Fra n c i sco B a y w i t h o n e end i n S an Francisco Let p be t h e l o c a t i o n p red i c a t e a p p l y i n g to S an Franc isco L O C - IN(san franc i sco) :

VIVIENNE FaNG 140 ( 1 6) p(sx)=1 i ff: 3bx [sx=a(b) 1\ LOC - IN(san fra n c i sco ) ( b) ] A n d suppose w e order t h e p h ases p and p as fol l o w s : p -< p Th i s i s depicte d ( 1 7a) with the ax is poi n t i n g to S an Franci sco ( 1 7) in a into San Francisco: p San Fra m ; i s(;o I s" b out of San Francisco: p San Franci sco ----r-----r-- " Now the orderin g in ( 1 7 a) g ive s t h e adm i s s i b l e i n te rv a l I ( i n terms of p and s) over which we can eval u ate silta Sail Franciscoonlbridg e into San Francisco ( see ( 1 8) We have an i nterval in w h i c h t here is a monoton i c p h as e change from "p to p a nd the truth of directional locative pred icate c a n be eva l u ated in the second phase ( 1 8) I i s a n admissible i n terval in terms of jl ( L O C - I N ( s a n fr an c isc o» and s iff (i) I = (s ; s e ] for some i -< 8 (ii) I begin s with a p h ase of n o t - p : 3s E I Vs E I ( s -< 8 p( 8 ) ) (iii) the function p i s m o n o t o n e i n t h e i n terv a l I : f/ t h e n for all s s E I i f p i s defi ned fo r if S -< 8 t h e n p( 8 ) p ( 8 ) I w i l l assume here t h a t t h e s em a n ti c s of both t h e Fi n n i sh and English expres sions are the same hence I w i l l d e fi n e the tru t h cond i t i o n s j u st for a bridge i n to S an Francisco i n ( 1 9 ) ( 1 9) a a bridge into S an Fra nci sco b 3a (brid ge(a» and (i) I i s an i n terval w h i c h is an orderi n g of t h e ran ge of (T ( a ) a nd contains one phase c h an g e ( p -< p ) w i t h res pe c t to the l oc a t ion of some p art of the bridge i n San Fra n c i sco: and (ii) 3 s E I V y E I (y -< s -4 - L OC - 1 N (ysan fran c i sco» 1\ 3s E I VZ E I ( s -< z L O C - I N ( z san fr a n c i s c o» Condition (i ) i s sati sfied by h av i n g a w e l l - d efi ned ad m i s s i b l e i n t e rva l a s given in ( 1 8 ) t ha t is t here is o n e a n d o n l y one p h ase c h a n g e Con d i tion ( i i ) says that if one p art y of the bridge i s earl y e n o u g h i n t h e orderi n g i t s h o u l d be located outside

A DIPHASIC ApPROACH TO DIRECTIONAL LoCATIVES of S an Francisco and a later part z if it i s l ate e n o u g h in the orderi ng should be in S an Franci sco Th i s cond i tion e n s u re s t h a t the bridge that we are talking about is neither wholly outside of S an Franc i sco nor whol l y i n side but rather the bridge has to straddle the two regions Conversely bridg e out of San Franciscolsilta San Fra n c is co sta would have the ordering of p h ases p -< p if we k e e p p as the l o c at i o n p red icate applying to S an Francisco The ordering i s differen t bec a u se the p er s p ec t ive is switched - see ( 1 7b) where the axis poi nts away from S a n Fra n c i sco So we would evalu ate the truth of the Elative predicate at p (see ( 1 6» which is now the fi rst of two phases (20) a a bridge out of S an Franc i sco b 3a(bridge(a» and (i) I is an interval w h i c h i s an o r d e r i n g of the range of a(a) and con tai n s one phase change ( p -< p) w i t h respect to t h e l ocation of some part of the bridge in San Francisco; and (ii) 3sEI Vy EI(y -< s -7 LOC - I N (ysan fr a n c i sco» /\ 3 s E I VZ E I(s-<z -7 LOC - I N (zsan franc i sco» I n thi s account t he m e a n i n g of DLs i s not tied to t h e idea of fic tive motion (cf Matsumoto ( 1 9 9 6 a 1 996b) Talmy ( 1 9 9 6 ) L a n g a c k e r ( 1 9 8 7 ) among others) Fictive motion is i nvoked by the a u t h o r s m e n t i o n ed fo r l i n gu istic expressions that do not express a real p hys c i a l motion of the S u bject but rather some sort of subjec tively conceptuali zed notion of moti o n For e x a m p l e in t h e e x am p l e s below (from Talmy ( 1 996» the road/the mou ntain ra nge is d e p i c t e d as mov in g (2 1 ) a Thi s road goes from Modesto t o Fre s n o b That m ou n t a i n range goes from lvlexico to Canada But note that the exam ples in (9) and ( 1 0 ) d o not i n v o l v e motion verbs A l so as modifiers of nouns the o r i e n t a t iona l read i n g o f the DLs in (9) and ( 1 0) cannot be attributed to stative verbs i n d u c i n g the stative/orien tational i n ter p retat i on (cf Nam ( l 995ab» Con sider the examples bdow w h e re d i reclional locatives l i k e across and throu g h c an give a stative read i n g w h e n t h e y oc c u r w i th stative verbs : (22) a The c a t i s s i t t i n g across t h e street b C hri s saw t h e cat t h ro u g h t h e w i ndow S i nce the d a t a in (9) and ( 1 0 ) i n v o l v e ne i t h e r verbs of motion nor stative verbs this acco u nt of D L s p r ov i d e s an i n terpreta t i o n t h a t i s c o n fi ned w i t h i n the domain of objects Finally the proper i n terpretation of n O l l n p h ra s e s with DL m o d i fie r s will h ave to take i n to account t h e use o f t he se e x p re s s i o n s For example w h i l e a road that has a p hase in S an Francisco a n d a p h ase o u t s i d e o f i t C a n be called a roa d into San Francisco t he same road if i t leads to a t o l l - bo o t h b e fore e n teri n g S a n Fran c i sco is 141

VIVIENNE FaNG 1 42 not u sually termed a road into the toll-hooth p re s u m a bl y becau se roads are u sually not seen a s help in g one to (merely) end u p at a tol l - booth S i m i l ar ly a ribbon into the city m ay seem a nom al o u s but if a c on t e x t is p ro v i d e d where the ribbon has some function/u se for example for a n t s to crawl o n then the phrase i s accep t able Below I show th a t the presen t a n a l y s i s based on p h ases relates orientation and path structure in a u n ifo r m way 4 4 Phases for motion verbs I h ave already discussed how e v e n t s take p l ace in time a n d h o w events can be mapped onto times given the temporal trace fu n c t i o n B u t in additi o n motion events are closely related to space as wel l An entity in motion moves throug h time passing through po i n t s in s p ac e In other a n a l ys e s o f m o t i o n events (Bierwisch 1988 Verkuyl and Zwarts 1 99 2 Pinon 1 993 Nam 1 99 5ab inter alia ) th e spatio temporal mapping of motion eve n t s is what d efi n e s the c an o n i c a l notion of Path In Verkuyl an d Zwarts ( 1 992) for e x amp l e a pr ep osi t i o n a l phrase headed by to i s i n terpre t ed as a n a te m p o r a l s p a ti a l pa t h P" = ( P l p ; P ) Motion events i nvolve a GO fu n c t i o n w h ic h p ro v id e s a te m p or a l structu re ( t b ti ) The application of the G O fu n c t i o n to the s p a t i a l path w i l l be a mapping from the atemporal spatial Path i n to the temporal Pat h creati n g a new sp a t i otem p or al p ath ( t bp I ) (tipi) ) But in t h e present analysis i t would be wro n g to assume t h a t the DLs under consideration refer to p a t h s d i re c t l y s i n c e w i t h obj ec ts and non-motion verbs no c ha n ge of location is i nvolved W h a t we need fi rst is the spatial trace of a motion event I use a simpl i fi ed sp at i a l trace fu n c t i o n (J"" w h i c h l oc a te s events i n space and preserves any p art s tr uc t u r e presen t : (23) ( S p atial trace o f eve n ts ) : s x=(j"e (e x) where VeVe [O " ( e) - (J" ( e ) = (J"F ( e H e )] T for e v e n t s The a p p l i cation of the spa t i a l mapp i n g w i l l re s u l t in a space/ti m e mapping of motion even t s (the same resu l t a s that of Verku y l and Zw arts ( 1 992» G iven that we h av e a n o r d eri n g of space/t i me coord i n ates the a d m i s s i b le in terval for motion ev e nts i s defined i n term s of t h e c h a n ge in location of the e n tity We already h ave a t e m p o ral t r a ce f u n c tio n temporal function to the moving through t i m e ro o m for example the p a rt o f t h e spatiotemporal t r a c e of t h e occurs o u t s i d e th e room c a n be one phase ( c a l l i t "p) and t h e part t h a t i s w i t h i n the room c a n b e another ( p ) Th e orderi ng of p hases i s "p p For motion into a motion even t that (24) Order of phases f o r d a n c i n g i n to the room : p -< p "p The truth con d i ti o n for i n to the p ro01l1 ( Pat) is eva l u ated at p :

A DIPHASIC ApPROACH TO DIRECTIONAL LOCATIVES (25) 1 43 p (s x t x ) = l iff: 3 ea s x=ae ( e x ) 1\ t = T (e) 1\ L O C - I N ( room ) (Pat)(et )] The in t erpre ta ti on of a se n te n ce like Pat d a n ce d i n t o t h e ro o m a b s t r actin g away from te n se is given below: (26) a Pat dance i n to t h e room b 3e(Dance(Pate» and (i) I i s an i n t e rva l which i s a n order i n g of the range of ( T (e) a (e)) and contains one ph ase change ( p -< p ) with respect t o the location of Pat in the room at some time; and (ii) 3 (st) E I V(ab) E I «ab) -«s t ) -+ -LOC - I N ( Patro0111( ab» ) 1\ 3 ( st ) E I V ( x y) E I «s t ) -«x y ) -+ LOC - I N ( Pa troom (xy» ) I do not c l aim that all d a n ci n g moti o n s h a v e a t raj ect o ry y ie l d i n g this o r d e r i n g Dancing can wel l trace r a n d o m l i n e s/c u rves i n s p ace and yet not h ave a traj ectory t h at gives a c h a n ge of l o c a t i o n from p to p Ho w e v e r all we need is this: if d a nc i n g involves a tr aj ec t o r y w e get the r i g h t structure s for d e fi n i n g possible ph a ses; and DLs can o n l y be i n terpreted given t h i s partic u l ar structure Therefore the a n a l y sis p redic t s that when d a n c i n g has some o t h er confi g u ration the even t is i n c o m p at ible with DL i n t erp r e ta t i o n A related issue ( a l so rai sed by Lo b n e r ( 1 9 89» i s t h a t g i v e n the d e fi n i t i o n of ad missible i n tervals as b e i n g m o n o t o n e in term s o f p a danc i n g even t ( fo r e x am p l e dan ci ng a tango) t h a t i n v o lv e s go i n g in a n d o u t of t h e room or t h a t i nvolves back tracking w i l l have to be ruled o u t i n t h i s mode l In s u c h cases the entire event is correctly p re d ic t e d to be i n c o m p a t i b l e w i t h the descri ption d an c i n g into the room But i f w e allow the even t t o b e broken d o w n i n to small enough c h u n k s that is i f we relativize the p o i n t s i n s p ac e/ti m e w h e re t h ere is a t r aj e c to r y i nvol v i n g one p hase change then t h a t smaller eve n t c h u n k can be descri bed with t h e DL Witness the well-formed d esc ri p t i o n w i t h a D L p red i c a t e in (27 ) in a co n t e x t where a couple dances the t an g o all over t h e h o u s e g o i n g in and out of vari o u s roo m s : of positions (27) While p erfo rm i n g t h e t a n g o i n t h e h o u se t h e c o u p l e d a n ce d i n t o t h e k i tchen L e t u s look b r ie fl y a t d a n c i n g o u t o f t h e room Keep i n g t h e p h a s e s p a s l o c a t i o n i n side the room and p a s l oc a t i o n o u t si d e t h e roo m the orderi n g of phases i s p -< p A n d t h e tru t h con d i t i o n for o u t o f t h e room i s eva l u ated a t p ( 2 8 ) O rde r of p h as e s p room for d an c i n g out o f t h e """- P ro O I11 : p -< p S l t l The o rder i ng of s p a t i a l posi t i o n s a n d a l so t h e ord e r i n g of p h a s e s are d e p ende n t on t h e p r o g re ssi o n of the m o t i o n e v e n t t h ro u g h t i m e O n e lo g i c a l c o n sequence o f the spatiotemporal mapp i n g o f m o t i o n eve n ts p u r s u e d h ere i s t h a t t w o exp ress i o n s

VIVIENNE FaNG 1 44 such as dancing in to the ki tchen and d a n c i n g o u t of the ( s a m e ) kitchen cannot describe the same event i n a g iv e n time i nterval That i s at a given time t the kitchen cannot be both a p ha se p and a p h a s e p i n our model Rather the two expressions must be i nterpreted either as ( i ) des c r i b i n g consecu tive even ts: for ex a m p l e dancing into the kitchen at time t and d a n c i n g out of the k i tchen at t i me t ( t -< t) ; or (ii) describing two se p ar a te events (with d i fferent p articipants) that take p l ac e at the same time t given our a s s u mp t i o n that t h e m a p p i n g of even t s onto time gives a pre-order o f events i n time ( s e c t i o n 4 1 ) O n the other hand recall that the a x i s repre s e n t i n g t h e sp a t i a l ord e ri n g of parts of objects has two p oss ib le directions dependi n g on the p e r s p ec ti v e taken bridge into S a n Franc i sc o A and a bridge out of S an Francisco can describe the same bridge de pend i n g on the p ersp ect i v e t ak e n T h e br id ge has no te m p oral map ping and so p e r sp e c t i ve shift c a n occur at any p o i n t B u t perspec tive sh i ft cannot be invoked for the manner-of-motion eve n t s descri bed above Th u s the presen t anal ysis captures the difference between the use of D Ls as mod i fi ers of nouns and as modifiers of motion events 4 5 Event structures We now come to verbs t h at h ave p os t e r i or or a n t e rio r e n tailed s t a t es such as for g e r a n d fi n d resp ec t iv e l y How do we m o t i v a t e t h e a p pr o p r i a te ph a s e s over which to interpret Finnish DLs when t h ey occ u r w i t h these verbs? Thi s class of verbs l i ke motion verbs denote events t h a t can be given a tempo ral trace But they differ from motion verbs in two i mportant ways F ir s t they do not denote motion so there is no movem e n t t h ro u g h space and t h u s there will be no sp at i al trace of the argument of t h e D L p r e d i c a t e S econd these verbs are culmi nated events (Moens and S teedman 1 9 8 8 S teedman 1 99 7 ) A verb like forge t i s a typical c u l m i n ate d event with an e n t a i led con seq u e n t s t a t e S o these v e r b s h ave a di ffere n t l exic a l a s p ect u a l r e p resen t at i o n from m o t i o n verbs w h i c h ar e proce s se s The p h a ses for i nterp re t i n g DLs w i t h verbs l i ke fo r g e t and fin d can n o t be defined i n s p ati al terms in t h e same way as fo r o bj ec t s a n d m o t i o n events be ca u s e there is no s p at i al trace over time/space I n stead I arg u e that Fin n i s h DLs can also be i nte rp ret e d i n p h a s e s defi n e d in terms o f a s pectu a l d e v e l o pmen t or tran sition The a sp ec t u a l structure o f a verb l i ke forge t for exam p l e consists of the event and a con seque n t state The c u l m i n at i o n o f t h e e ve n t can be seen as t h e tran s i ti o n point from one state of affa i rs to a con seq u e n t s t a t e We c a n consider the consequent state of a forgetti ng eve n t a s a p h a s e p w h ere t h e re i s no lon ger any pote n t ia l change of location of the t h i n g forgotte n so th e con seq u e n t state mai ntains the p os i t i on of the book S upporti n g evidence for t h i s i n terp re t a t i o n of the se m a nt i c s of forget comes from temporal adverb i a l s w h ich s p ec i fy t h e t i me t h a t t h e result of the action obtained (Dowty 1 97 9 : 2 5 1 ) a s shown in (29) for bot h Engl i sh a n d Finnish : (29) a I forgot the cake in the o v e n for two hours

1 45 A DIPHASIC ApPROACH TO DIRECTIONAL LOCATIVES b Unohd-i-n kaku - n u u n i - i n k ahde - k s i tu n n i - k s i forget-pa ST- l P c a ke AC C oven- I LL two-t R A C n s l ative) hour-tr A - I forgot the cake in the oven for two hou r s Prior t o forgetting ho w ev e r there i s sti l l pote n t i a l for ac t i n g o n /d o i n g somethi n g with t h e book so to speak L e t u s cal l t h i s a n ter i o r p h ase --- p S o t h e culmination o f forgettin g i s a tr a n s i t i o n between a p h a s e wi th pote n t i al for c h an ge a n d a second phase with no po te n t i a l for c h a n ge We now h ave an i n te rv a l I that has exactly one phase change w i t h respect to the as pe ctual structure of forgetti ng The phases can be defined in terms of the temporal trace of the aspectual p roperties of the verb 1 will simp l y l abel the aspectual seman tic property of verbs as A ( see (30» The temporal trace fu nction T rel ates w h at i s a p r i or and a con sequent state of affairs as time- points on a time- l i ne And because the eve n t of for get t i n g is a culminated process the time of forget t i n g i s r epres e n ted as a poi n t on t h e time line (the culmination poi n t ) w i t h i n the i n t er v a l i n which we c a n talk about the aspectual property of the verb ( see ( 3 1 )) - (30) tx=tca) p "p t2 (3 1 ) culmination I" l: The Illative pred i c a te i s eval u ated a t p ( see ( 3 2» T h e tru t h c o n d i t io n for Pat forgot the book c ar- I L L AT I V E abstrac t i n g a w a y from t e n s e i s g i v e n i n ( 3 3 ) ( 3 2 ) p (t ) = l i ff: 3 Ax [ t x = T ( A x ) 1\ L O C - I N ( bookcar t )] x (33) a Pat forget the book car- ILLAT I V E b 3e(Forget(Patbooke» a n d ( i ) I i s a n i n terval w h ic h i s a n orderi n g of t h e range of T(A) a n d contains one p hase c h a n ge ( "P -< P ) w i t h respect to t h e po t e n t i a l c h a nge of location of the book: and (ii) 3 t E I ( L O C - I N (carboo k t ) 1\ VtE I ( H t --t L O C - I N ( carbookt ) ) ) Forge t does n o t pres u ppose a n y t h i n g a bo u t t h e l o c a t i o n o f the book p r i or to the culmination of t h e eve n t W h a t ( 3 3 b i i ) says i s t h a t g i ven a t i m e t w i t h i n the admissi ble interval when the book i s loc ated in t h e c a r we k n ow that fo r all t i m e s following t the book will be in the c a r Conversely t h e as p e c t u a l structure of a verb l i ke fi n d consists of t h e event and an anterior e ntailed state of affai r s t h at is t h e book m u s t be in th a t location p rior to being found The c u l m i n a tion of the eve n t can b e seen a s t h e tra n s i tion point from this anterior s tate to a n o t h er state of a ffa i r s I n te r ms of poten t i a l for c h an g e prior to finding t h e book t h ere is no p o t en t i a l for c h a n g i n g t h e location of t h e book but after finding it there i s a pot en t i a l of remov i n g it G iven t h a t th e c u l m i n ation of the

VIVIENNE FONG 1 46 finding event is the tran sition p o i n t we c a n see two p h ase s the fi rst p hase p where there is no potential fo r c h a n ge and the s ec o n d p h as e p where there is potential for change (34) a Pat find the book c ar- ELAT l V E b ::le(find(patbooke) ) and (i) I is an i n t er v al w h i c h i s an ord er i n g of the range of T(A) a n d contains one phase change (p --< p) with respect to the po te n t i a l change of location of the book; and (ii) ::l t E I (LOc - I N (c ar bookt) 1\ vte I ( t --< t LO C - IN(carbookt ) ) ) Forget o n l y occurs w i t h IlIative/Al lative pre d i c a te s and fi n d only with Ela tive/ablative predicates Th i s fal l s o u t from o u r model l i n g of t h e phases based on the i nherent entailment p ro pe r t i e s of the verbs The I l l ative predicate only gets an interpretation in a second p hase p when p is well-defi ned by the posterior entail ment property of forget The Elative predicate o n l y gets an i n terp ret a t i on in afirsl phase p when p is w e l l - d e fi n e d by the e n tai l m e n t property o f fi nd I n summary Finnish DLs c a n b e i nterpreted i n the p h as e s determined b y the temporal trace of the lexical a s p e ctu a l structure of v e r b s I assume that English DLs on the other hand can only a c c e s s p h a s e s t h a t are defi n ed s p at i al l y or spatio temporally and therefore d o not occur w i t h verbs l i ke fo rge t and fi n d which do not have mappin g s of s tr u c t u re s in space s Predictions S upporting ev i d en c e for t h i s treatment of F i n n i s h DLs comes fr o m the occurrence of DLs with v ari o u s classes of verbs that sh are s i m i l a r a s p e ctu a l structures as the verbs forget an d fin d First c o n si d er as pe c t u a l verbs l i ke ruveta b e g i n and lakata s t o p A spectual verbs that des c ribe the o n se t of an ev en t (e g be g i n start ) des c ri be the action of turning the event on ( i e a tran sition ter m i n a t i n g i t s off- state and startin g an on- state of the sam e t y pe ) ( ter Meulen 1 99 5 ) In Lobners ( 1 9 8 7 ) phase-semantic account begin a n d stop refer to a n i mpl i c i t t i m e parameter to ( wh i c h may differ from the time of u t t e ra n c e bec a u se of ten se operators for example) a n d these verbs tell somethi n g a bo u t the c lose fu t u re how t h i n g s go on from to with respect to the proposit i o n e m bed d ed (Lobner 1 9 8 7 : 7 3 ) The relev a n t t i m e i n terval has two phases p and p w h i c h contain t o For sto p (p t O ) t h e fi rst p h a s e i s p and h as started before to If to is the l a s t p o i n t of t h i s ph ase t h e n stop ( p t O ) is true I n Finnish a s p e c tu a l v e rb s l i k e ruveta a n d lakata t a k e verbal c o m p l e ments that are suffi xed with DL Case To beg i n read i n g has an a n terior p h ase where no reading occurs and a t r a n s i t i o n poi n t s t a rt i n g the read i n g ph ase So the phases here are defined over the tempora l -aspec tu al m a p p i n g of beg i n (35) Toi n i rupea-a l uke- ma-a n Toi n i begi n - 3 s G read - INF- I L L Toini begins re ad i n g ( l i t To i n i begi n s i n to rea d i n g )

A DIPHASIC ApPROACH TO DIRECTIONAL LoCATIVES p read " p t2 (36) begin t1 To stop readi ng on t h e other hand presupposes a p o s teri or p hase o f reading then the point of s to p p i n g i s a t r a n s i t i o n p o i n t w h i c h i s fol lowed by a phase where there is no readi ng (37) Toini l akka-a l u ke-ma-sta Toini stop- 3 s G read - I NF-ELA Toini stop s re adi n g ( l i t Toi n i s to p s o u t o f rea d i n g ) Notice that the I ll a t iv e occurs with be g i n and t h e Elative o c c u r s with stop Thi s i s similar t o the pa tte rn i n g with fo r g e t a n d fi n d I n the discussion above I argued that the I l l ati v e pred i c a te o n l y gets an i n t e rp re t a t i o n i n the second of two phases (phase p ) when p is well-defi n ed b y the e nt a i l me n t p roperty of forget (en tailing a posterior s t a t e of affairs ) Here the I l l ative pred i cate gets an i nterpretation in the second of two phases (ph ase p) w h e n p is wel l - defined b y the temporal as pectual mapping of b e g i n w h i c h descri bes the start and cont i n u ation thereafter of a reading event Th e El ative p red icate gets an i n terpretation in the first of two phases when t h e first p h ase is wel l -defi ned by the t emp o ral a s pe c t u a l m a p ping of find and stop S econd verbs o f exhort a t i o n like keho ituio e nco u r a ge neuvoa advise kieltiiii forbid and varoittaa w arn are i n tended t o br i n g about a c h ange in an other person s ac ti ons or i n te n t i o n s Notice o n c e again t h e d i fferent selections of Illative or Elative p red icates by these v erb s : (38) Sointu k e h o i t t - i Sointu encourage-pa s T- 3 p S ointu e n c o u r a g e d To i n i - a l au l a- m a - a n Toi n i - PA R s i n g - I N F- I LL To i n i to si n g (39) Sointu n e u v o - i Toi n i - a Hihte-mti - a n Sointu advise-pa s T- 3 p Toi ni - PA R l e ave- I N F - I L L Sointu a d v i s ed Toi n i to l e ave (40) S ointu kiel s-i To i n i - a poltta-met- sta S ointu forb i d - PA S T- 3 p To i n i - PA R s m o ke- I N F- E L A S oi n tu forbade Toi n i to smoke (4 1 ) S o i n t u varo i t t - i S ointu w arn - PA S T- 3 p S ointu warned Toi n i To i n i - a Toi n i - PA R l a h t e - mii- s t a leave- I N F - E L A a g a i n s t l e av i n g T h e dis tri b u t i o n o f Elative versus I l l ative pred i c a t e s h ere c a n b e u nderstood i n terms o f the i nterpretations o f speech act verbs a n d t h e i r complemen t s I will merely sketch out th e po ss i b l e i n terpretation s in order to i l l u strate t h e idea o f phases here; 1 47

VIVIENNE FaNG 148 for more detailed discussion see Wi e r z b i c k a ( 1 9 8 8 ) and R o hr b au g h ( 1 995) among others For kieltiiii forbid and varoittaa warn the speaker removes an initial set of options available to the addressee bu t the verbs d o not carry any expectation s as to what might happen next The verb suffixed with El ative Case i n (40) and (4 1 ) is a predicate that refers to the i n i ti al o p t io n (for our purposes the first phase) In the case of kehoittaa encourage a n d n e u voa ad v i se t h e s p e aker considers a future action of the addressee (cf Wierzbicka 1 9 8 8 : 3 6ff) b u t t he initi al set of options available is irrelevant The Illative v erb a l p re d ica t e in ( 3 8 ) and (39) refers to this future action (in the second pha s e ) Third i n Finnish there is a d i ffe r e nce i n mean i n g between the verbs jiiiidii (which I gloss as remai n ) and pysyii stay Th i s is refl ected i n the locative pred icates that the verbs select: jiiiidii takes DL pred icates (42) while pysyii does not (43) (42) Neva-n suu j a-l Ttiyssi n a - n rauha-ssa Neva-GEN mo u t h remai n - PA S T- 3 S G Ttiyssi n l-l- G EN treaty- INE v e n ah i i s i-! le Russian- PL-ALL(ative) - In the Treaty of Tay s s i n ti the mo u t h of the Neva went to the Russian s ( Per haps the Neva changed ha n d s ) (43) Neva-n suu pysy-i Tli y s s i nli-n rau h a - ss a Neva-GEN mouth s ta y- PA s T 3 S G Tiiy s s i n a - G EN treat y - I N E ve n al ais-i -!lao Russian-PL- A D E(ssive) - In the Treaty of Tay s s i n ti the m o u t h of the Neva s t aye d i n the possession of the Russians (There was no c h an ge of h a n d s ) In (42) there i s a possibil i ty t h a t t h e R u s s i a n s m i g h t n o t h ave h a d claims on the River Neva before the treaty and after the t reaty they defi n i te l y did This i s cap tured by the DL p re d i c a t e ( t h e A! l a t i v e ) On t h e other hand (43) w i t h pysyii does not presuppose an y c h a n ge c o u ld h ave taken place and s o we cannot p o stu l ate any phases where there m i g h t be a c h a n ge As S t i c h DL p red i c a t e s do not occur with such a verb 6 Conclusion The meanin g s of E n gl i s h DLs h ave a l w a y s been n oted to encode a m ean i n g of change (Dowty 1 97 9 l ackendoff 1 990 Wu n d e r l i c h 1 99 1 ) The q u e st i o n for such an i n t erp re t a t i o n i s h o w ori e n t a t i o n m e a n i n g s c a n c o m e abou t Finnish DLs can be seen as lacking a c h ange m e a n i n g a n d t h erefo re they c a n occur with ve rb s that do not denote change (Fo n g 1 99 7 ) The q ue s t i on for t h i s a p p r o a c h is h o w these locatives can occur with motion verbs to d e n o t e c h an g e of locat i o n I h ave shown t h a t the d i p h a si c approach to t h e i n terp r e t a t i o n o f DLs presen t ed here gives a u n i fo rm treatmen t of t h e m e a n i n g of DLs in cases w here Fin nish and

A DIPHASIC ApPROACH TO DIRECTIONAL LOCATIVES English behave the same (ie w i t h motion verbs and objects) In addition I have shown that Finnish differs from En g l i s h in allo w i n g the in terpretation of DL predi cates in non- spatial domai n s What D L s are sensitive t o i s t h e order of things: whether states of affairs precede or follow events whether the p o i n t of view regards one pi e c e of object as precedin g o r following another Acknowl edgements I wish to thank Arto Antti l a Cleo Condorav d i Marti n a Fal ler B rett Kessler Paul Kiparsky Rob Malouf S ta n ley Peters Chri s P i fio n and especially Henriette de S w art for comments s u gge s t ion s a n d h e l p I a l s o thank the audi ence at S A LT VII for their comments Refe rences Bierwisch Manfred 1 9 8 8 O n the G rammar o f Lo c a l P re p o si t ion s I n Syntax Se mantik und Lexikon e d M a n fred B ie r w i sc h Wo l fg a n g Motsc h and IIse Zim mermann Berl i n : A kademie- Verl ag Dowty David R 1 979 Word MeaninR and Mo ntarue G rammar D o rd re c h t : Reide l Fong Vi v i e n ne 1 99 7 A Te m p o ra l I nt erpret a t i o n for Loc a t ive Case Proceedings of WCCFL 1 5 : 1 45-1 59 Jackendoff Ray 1 990 Semantic Strucwres C a m b r i d g e Mass : M I T Press Jackendoff Ray 1 992 Parts and B o u n d aries In L exi c a l and Conceptual Semantics ed Beth Levin and S teven Pi n k e r C a m br i d g e M a s s : B l ackwel l Jackendoff Ray 1 996 The P r o p e r Treatme n t of M e a s u r i n g O u t Telicity and Per haps Even Q u anti fi c a t i o n i n E n g l i s h Natura l L an R ltag e and Linguistic Theory 1 4:305-354 Karlsson Fred 1 9 8 7 Fin n ish G rammar Porvoo : We rn e r S oderstrom Osakeyh tio 2nd editi o n Krifka M anfred 1 9 8 9 Nom i n al Refere n c e Te m p o r a l Co n s ti t u tion a n d Quantifica tion in Even t S e m a n ti c s I n Seman tics a n d Con textual Expressions ed Renate B artsch Johan van B e n t h e m and Peter van Emde B o a s Dordrec h t : Foris Langacker Ronald 1 98 7 FOUlldaTiOll s (d Cog n itive G rammar S ta n ford Cali for nia: S tanford U n i v e r si t y P re s s Lobner S ebasti an 1 9 8 7 Quan t i fi cation a s a M ajor M od u l e of Natural Language Sem a ntic s I n Studies i n D iscourse R ep res e n ta tion Theory and the Theory of Genera lized Quantifiers ed Jeroen G roe n e n d ij k D i c k d e J o n gh and Martin S tokhof Dordrecht: Fo r i s LObner S ebastian 1 911 9 G e r m a n sc/toll-erst-iloch: A n I n tegrated A n al y sis Lin guistics and Philosophy 1 2 : 1 67-2 1 2 Marr David 1 9 8 2 Visio n S a n Fran c i sc o C a l i forn i a : Freem a n 1 49

1 50 VIVIENNE FONG Matsumoto Yo 1 996a How Abstract is S u bj e c t i ve Motion? A Comparison of Ac cess Path Expressions and Cover a ge Pa t h E x pre s sio n s In Co n c eptual Structure Discourse and Language ed A d e l e Gold berg Stanford : CSLI Publications Matsumoto Yo 1 996b S u bj ective M o t i o n and E n g l i s h and Japanese Verbs Cog nitive Linguistics 7 : 1 8 3-226 Moens Marc and Mark S teed man 1 9 8 8 Temporal O n tology and Temporal Ref erence Computa tional Ling u ist i cs 1 4 : 1 5-2 8 Nam Seungho 1 995a The Sem antics of Locative P rep o s i tio na l Phrases i n English Doctoral dissertation UCLA Nam Seungho 1 995b The S emantics of Paths and S pa ti a l Orientation s Proceed ings of the 1 0th Amsterdam Colloquium 5 5 1-566 Pinon Christopher 1 1 99 3 P a t h s a n d Their Names Proceedings of CLS 2 9 : 2 87303 Rohrbaugh Eugene G ra n t n 1 99 5 Scalar I n terpreta tion in Deontic Speech A cts Doctoral dissertation U n iv e r s i t y of Tex a s at A u sti n S teedman Mark 1 997 Te m p o ral i t y I n Handbook of Lo!!ic a n d Lang uage ed J ohan van Benthem and A l i c e ter M e u l e n A m s te rd am : El sevier S cience Talmy Leonard 1 996 Fictive Motion a n d Ce p t i o n I n Language and Space ed Paul B loom Mary A P et e r so n Lyn n Nadel and Merri ll F Garrett Cambridge Mass : MIT Press ter Meulen Alice G B 1 99 5 Represen ting Ti m e in Natural Lang uag e : The Dy namic Interpretation of Tense and A spect Cambridge Mass : MIT Press Verkuyl Henk J and Joost Zwarts 1 992 Tim e and S pace in Conceptual and Logical Semantics : the Notion of P a th L i ng u is ti cs 3 0 : 4 8 3-5 1 1 Wierzbicka Anna 1 9 8 8 The Semantics of Grammar Amsterdam: John Ben jamins Wunderlich Dieter 1 99 1 How do Prep o s i t i onal Ph r a s e s fi t i n to Compositional Syntax and Semantics? Li ng u is ti cs 2 9 : 5 9 1-62 1