Formal Syntax and Semantics of Case Stacking Languages 
Christian Ebert 
Lehrstuhl fiir Computerlinguistik 
UniversitSt Heidelberg 
Karlstr. 2 
D-69117 Heidelberg 
Marcus Kracht 
II. Matheinatisches Institut 
Freie Universitgt Berlin 
Arnimallee 3 
D-14195 Berlin 
Abstract 
In this l)aper the t)henomenom of case stack- 
ing is investigated from a formM t)oint of view. 
We will define a formal  with ide~dized 
case marking behaviour and prove that stacked 
cases have the ability to encode structural in- 
tbrmation on the word thereby allowing tbr un- 
restricted word order. Furthermore, the case 
stacks help to comimte this structure with a low 
complexity bound. As a second part we propose 
a compositional semantics for s with 
stacked cases and show how this proposal may 
work for our tbrmal  as well as tbr an 
example from Warlpiri. 
1 Introduction 
Case stacking is a phenomenom that occurs in 
many Australian s (such as Warlt)iri 
and Kayardild) and e.g. Old Georgian. Case 
stacking is known to pose t)roblems for the 
treatment of case in many fi)rmal ti'ameworks 
today 1. In (Nordlinger, 1997) the problem was 
attacked by extending the fl'amework of LFG. 
Nordlinger claims that case morphology can 
construct grammatical reb~tions and larger syn- 
tactic contexts. 
In Section 2 we will introduce an ideal lan- 
guge, which exhibits perfect marking. This lan- 
guage captures Nordlinger's idea of case as con- 
structors of grammatical relations, but is inde- 
pendent of any syntactic framework. We will 
prove of this  that the case stacks pro- 
vide all the intbrmation needed tbr reconstruct- 
ing the flsnctor-argument relations and tim syn- 
tactic context a word appears in. Additionally, 
since structure lies encoded in these case stacks 
there is no need to assume any phrase structure 
lsee (Nordlinger, 1997) and (Malouf, 1999) for a dis- 
cussion on LFG and HPSG respectively. 
or restriction on word order. At the end of this 
section we consider tile computational complex- 
ity of our  and draw some conclusions 
about grammar formalisms that are able to gen- 
erate it. 
In Section 3 we propose a compositional se- 
mantics tbr our case stacking s. Un- 
like Montague semantics, where the manage- 
ment of variables is not made explicit, we will 
use rethrent systems to kee t) track of variables 
and to make semantic composition eflicently 
computable 2. Tile proposal will be applied to 
our tbrmal  and to an example t'rom 
Warlpiri. 
2 Syntax 
In this section a perfectly case marked tbrmal 
 will be defined and investigated. The 
definition of this  is based on terms con- 
sisting of functors and argmnents and tiros cases 
will be taken to mark arguments. 
In the tbllowing we let N denote the set; of 
non-negative integers and ~ the concatenation 
of strings, which is often onfitted. We shall use 
typewriter font to denote true characters in 
print tbr a tbrmal . 
2.1 Basic Definitions 
An abstract definition of terms runs as tbllows. 
Let F be a set of symbols and ~: F ~ N a 
flmction. The pair {F, ~2} is called a signature. 
We shall ofl;en write ~ in place of {F, f~}. An 
element .f E F is called a functor and It(f) the 
arity off. We let w := max{a(.f) I f E F} 
denote the maximal arity. 'l~rms are denoted 
here by strings in Polish Notation, tbr simplicity. 
Definition 1. Let ~ be a signature. A term 
over ~ is inductively dc~fined as .follows. 
2see (Venneulen, 1995) and (Kracht, 1999) on these 
issues. 
250 
/. {1' ~(.1) = o, tl,.c,. S i.,. a t('.,",,.. 
2. tl' ~(.1") > 0 a,.~ t~, i ~ ',: ~ ~(.1"), a,'~; 
terms, so 'i.'~ fl.\] .../.~(j.). 
.l.h(. set C of case mart,;ers will be the sel; 
{l,... , co}, which we assume t() 1)e disjoint fronl 
F. (-liven a term, each t'uncl;or will 1)e case 
mm'kext a(:(:or(ling to l;h(: ;~rgum(ml, t)osilJon it 
occul)ie, s. This is achieved throug\]~ tim notion 
of :~ unit, which consists of n fun(:tor ;rod ~ se- 
quence of case m:u'kers (:;dled case stack. 
Definition 2. Let t be, a term over a siflnat'arc 
fL .77to corresponding bag, A(t.), is ind'ac- 
tively dc/inc, d as ./b/lows. 
1. tlt = .f, ~.l,.,,,. a(-~.):= {t}. 
2. s.f t -- .lt,...t,,., hl,.<..,t A(t) ::: {.I'} U 
U'/-, {s",; I ~ ~ A(td}. 
A'n oh:my.hi .f7 ~ A(t) is calh'.d a unit and q' 
C* its case stack. 
For exmnl)h:, if .l',g~ im(l x a.re flint:tots of 
arity 2, 1 mtd 0, rcs\])e(:l;ively, l;he hag A(f:l:g:c) 
is {:f, xl, g2, xl2}. The lllGtllillg ()t: :1. unit Xi2 
(:ould t)e (les(:rib(:(l t)y ':c is the fllllCt;Or of (;he 
tirsl: ~rgmnelll; t,J' the se(:on(l ;u:gmn(mI; of tim 
|;e t.lil ~ . 
Definition 3. Let t be a tcr'm ov.r a siflnat'ur, 
~.. A(t) t/,., ~:o,",',..Wo',,,li',,..,Z Z,a:t a,t(t ~X(t): : {~1 
i < 'n} (tn avbitraT'y c.nv, memlio.n of its 'a',,its. 
77tcn the st'rinfl dl ~'d2"~... ~-'5._.1 "-'5. is s..id to 
be a A(t)-string. 
Some of the A(.fxgx)-strings are (:.g. 
fxig2xl2 and g2xl:fxi2. We, m:e now l)rel)ared 
to d(:fine n tbrmM bmgm~ge over the alt)habet 
F U C t)y collecting all A(t)-si;rings for n given 
signature: 
Definition 4. Let ~ be a signat'm'e. The ideal 
ease marking  ZUAd£ ~ over this 
signature consists of all A(t)-strings s'ach k/taR 
t is a term o've'r ~. 
2.2 Trees and Unique Readability 
There is a strong corresl)ondence between bags 
and lat)elled trees sin(:e (:ase stncks can t)e iden- 
tiffed with tree addrc.sscs: 
Definition 5. A nonempty .linite set I) C N~_ 
'is a tree domain ~f the .lbllowing h, ohh 
1. cc-D. 
2. if dl d2 c- D then dl c- D. 
2. lJ'di ~ D, i c- N then dj c D for all j < i. 
Th, e. eh:me.nts qf a t're(: domain arc called tree 
addresses. A ~-labelled tree is a pai'r (1), 7) 
s'uch, that 1) is a tree domain and r: D -+ l" 
a labelling ./?re.orion s'ach, th.at th.c n'ambc.r of 
'l"',:t/',t",".~' 4 d C J) i.~ ,',:t:acth/ ~(~(d) ). 
To formalize the corresl)ondence we define a 
function 77' that assigns every b~g A(t) a ~- 
hd)(:lh:d tre(:: 
"l'({f,7,,..., f,,,7,,}):= ({'Tff I 1 < ,: < n}, 
~-: 7/~ ~ .h (1 < ,,: < ,t)) 
The function 7' reverses l;he c;l.se sl;a(;ks of ~tll 
units to get a set of tree addresses. Then the 
flmctor of the mill; is assigned to the (;rec a.d- 
dress. E.g. if the b:tg cont~dns i~ refit g32J_ the. 
resull;ing tree dolna.in will contain :L tree address 
2123 and the bflmlling flmction will ~msign 9 to 
iL 
Similarly one can define an inverse flmction 
assig\]dng a 1)ag |:o each ~Mal)ellexl tree. Thus 
l;h(:re is a l)ije(:l;ion t)etween ~-lat)(:lled trees and 
bngs. 'l'\]mrelbre difthrent 1):~gs (:orr(:spond to 
(titfer(:nt ord(:red la,1)ell(:d trees. This shows (;lint 
we h:w(: mfi(lUe r(widal)ility fi)r l)ags and sin(:(: 
every ZC.A4£ ~ string (:ira 1)(: mfiquely de(:()m- 
posed into its milts we may sl;;~|;(~ the following 
l)rol)osition. 
Proposition 6. Let ~ bc a signature. Then ev- 
ery ZC2vf£ ~ strinfl is 'aniq'acly readable. 
2.3 Pmnpability and Semilinearity 
We will first consider the prol)erty of being 
finitely pumpabh,, its detined in (Oroenink, 1997). 
Definition 7. A hm, g'aage L is finitely 
pumpable 'ill there is a constant c such th, at 
for any w C L with, \['w\[ > c, there arc a finite 
number k and strings uo,... ~'tt k and vt,... ,'ok 
s?tclt that w -- uov\]u\] ?J2?t2""Ok'lt k and for each 
i, l < Iv/\[ < (: and for any p > 0 the string 
P P P 'aoV 1 'll d 't)2'a 2 • • • 'Dh'u,t; belongs to L. 
Proposition 8. Let ~ bc a signature. Then 
ZC.Ad£ ~ is not finitely \])'alttpabld. 
251 
Pry@ It is easy to observe that the puml)able 
parts cannot contain a functor since that would 
lead to I)mnt)ed strings containing the same 
units more than once. Hence the number of 
units cannot be increased by pumping and all 
pumpable parts must consist of case markers 
solely• But since the length of an ZC.Ad/2 f~ string 
consisting of a fixed munber of units is l)ounded 
each pumpable string could be pumped up such 
that it exceeds this bound. Thus ZC.M£ a is not 
finitely 1)umpable at all. \[\] 
Now we are concerned with semilinearity. 
Definition 9. Let M C N n. Then M is a 
1. linear set, {f for some k C N there are 
u0,...,u~ ~ N '~, such, that M = {u0 + k N}, 
~i=i niui \[ ni C 
2. semilineav set, if for" some t~: C N there 
are linear sets M\], •. • , Mk C _ N 'z , such th, at 
M=U i=1 
A lan.quage L over" an alphabet E = {wi I 
0 _< i < n} is called a semilinear  
if its image under the Parikh mapping is a 
semilinear set, where the PariMt mapping ~IJ : 
E* ~ N n is defined as follows: 
<o,... ,o) 
wi ~ e (i) .fi)r O < i < n 
or/3 ~ vI,((~) -F'I'(fl) for all ~,fl C E* 
wh, ere e (i) is the i + 1-ttL 'unit vector', wh, ich, 
consists of zeros except for the i-th component, 
wh, ich, is 1. 
Note that - given a term t - the Parikh image 
of all A(t)-strings is the same since these are 
just concatenations of difthrent permutations of 
the units in A(t). 
In the tbllowing we make use of a proof tech- 
nique used in (Michaelis and Kracht, 1997) to 
show that Old Georgian is not a semilinear lan- 
guage. We cite, a special instance of a proposi- 
tion given therein: 
Proposition 10. 
M be a subset of 
the properties 
1. For" any I~: E 
l~) 1(k) 
Let P(k) = ,~k 2 + 2~-----~-k and 
N n, where n > 2, which has 
N+ there are some numbers 
E N for wh, ich the n-tuple 
(k, P(k),l~ k) I (k) \ belon(ls to M. ~''" ~ '~--11 
2. For" any k C N+ th, e value P(k) provides an 
upper bound .for th, e second component l\] 
of any n-tuple {k, ll,... ,l~z-1) E M (that 
means ll _< P(k) ./'or" any such n-tuple). 
Then M is not semilinear. 
In order to investigate the semilinearity of 
ZC,A'I/£ a we choose distinct symbols f, x C F, 
such that f/(f) = w and ~2(x) = 0. We shall 
construct terms si by the following inductive 
definition: 
1. s0:=x 
2. Sn := f(sn-l,x,... ,:c) fbr n > 0 
It is easy to observe that by virtue of construc- 
tion sn consists of n leading functors f and that 
in each iteration the number of x increases t)y 
- 1). 
Lemma 11. Let F U C = {f,\],:c,2,... ,w, 
fl,-.. ,.flFI-2} be an enumeration of the alpha- 
bet underlying ZCA,4£ ~, where f\],... ,f1I,'1-2 
are the remainin.q fl, nctor's in F - {.f, z} Then 
the Parikh image of some A(sn)-strin9 5n is 
2--60 
= (.,, 2n 2 + -5--" 
(w--1)n+l,n,... ,n,O,... ,()) 
~-1 IFI-2 
Furthermore, ~ 2 '- ~n + ~n imposes a,n upper 
bound on the second component oof vIl(Sn). 
Proof. The first part of the leunna can be 
proved in a straightforward way by induction 
on n. The claim on the upper bound ibllows 
ii'om the observation that the nmnber of occur- 
rences of case marker 1 can be maximized t)y 
repeated embedding of terms in the first argu- 
inent position. \[\] 
Proposition 12. Let ft be a signature. Th, en 
27CAd£ f~ is not semilinear. 
Proof. Let n = w + IF I and consider the linear, 
and hence semilinear, set R := 
- 1) + 1)e (2) + 
w+2 
hie(0 I m c 
252 
Then (;lit fllll pre, iniage Lh> of 17, under the 
Parikh niap consists of all strings which con- 
tain nu((w -1) + 1) occurrences of the symbol 
x (where 'n,2 is any number) and any number of 
occurrences of the symbols f, l,... ,w, and no 
other symbols. We define the  Lj7 as 
the set of all strings belonging to Lst and the 
ideal case marking s. Then LM con- 
tains all A(s,)-strings. 
Considtring the Parikh iniage M of LAf we 
gel; 
M = ,I,\[CAd = m ,I,\[ZCaaC 
= cq ,I,\[IC54Z; 
because of the (lefinition of Llz as the flfll pre- 
image of 1{. But then the set A// fultills the 
conditions of Prot)osition l 0 (tuc to \]xeillilla 1\]. 
Hence M is not sere|linear. Since 17, is sere|linear 
1)y definition and semilinearity is closed under 
intersection ZCAd£ t? is not sere|linear. \[\] 
2.4 Computational Complexity 
In this sul)section the COml)utai;ional (:onll)lex- 
ity of ZCJ%4£ ~ is (:onsidere(t. r\]Jh(', results are 
achieved by defining a 3-tat)e-rl)uring machine 
accet)tor (det)ending on a given signature) that 
recognizes Zg3d£ ft. 
Proposition 13. Let tt be a ,sig'natv, rc. 7Turn 
IcM£ c #)TS ME(,.,v&7 log % 
ZCM£ ~ C DSI'ACE('n,). 
l'roo\]: In the following we lc, t 'n denote the 
hmgth of the inlmt string. The 9~u:ing machilm 
algoril;hln can be subdivided into three main 
parts: 
1. The intmt string is segmentext into its units: 
The algorithm steps through the input and 
adds set)aration markers in 1)etween two 
units. This can be done in O(n) time. 
2. The llllits are sorted according to their 
case stacks: More tbrmally a 2-way straight 
rnc,#c sort is pertbrnmd. This sorting algo- 
rithm is known for its worst case optimal 
complexity: it peril)tins the sort of ti: keys 
in O(klogk) steps. In our case the keys 
are milts and thus their mnnl)er is clearly 
tmml(led by ~t.. Tim additional square root 
factor comes from the comparison stel). 
One can show tha|; the maximal length of 
a (:ase sta('k occuring in an ZOJ~£ ~I string 
of Mlgth 'n is l)ounded above by O(v/77,). 
Hence a comparison of two units takes at 
most O(v/77,) steps. Thus the overall com- 
t)lexity of the sorting part is O(nv/77 log 'n). 
3. The sorte<l stquen<:e of units is (:hecked: 
The algorithm successively generates case 
stacks according to the fimctors it has read. 
Each case stack is compared to the refit of 
the inlmt. If they coincide the algorithm 
advances to the next unit on the input and 
generates the next case stack. After all case 
stacks have been gel/erated the whole int)ut 
string must have been worked through, in 
this case the algorithm a(:cet)ts. This (:an 
l)e done in O('n,) time. 
Summing u t) the COml)lexities of these tln'ee 
l)arts shows that the time COml)lexity is as 
claimed in the proposition. 1;'urthel'nmre, the 
algorithm uses only the cells needed by the in- 
lint plus at most t;:- l (:ells tbr additional set)- 
aration markers (due to the first part), where 
t,: is the nunlber of units the inlmt string con- 
sists of. This shows thai; |;he space (:omph~xity 
ix linenr. \[\] 
2.5 Discussion 
A first ('on('lusion we lllay draw ix that cases 
btve the ability to (:onstruct the context they 
apl)em: in. ZCML ~ strings encode the same 
structural intbrmation as ordered labelled trees 
do thereby allowing unconstrained order of 
milts. Additionally each such string can be read 
unambigously. This was shown by means of 
a bijtction l)etween bags and ordered labelled 
trees. 
The fact that ideal case marking hmguages 
are neither finitely punq)at)le nor sere|linear 
means that they fall out of a lot of hierarchies of 
formal s. As (Weir, 1988) shows, multi- 
component trcc adjoining 9ramm, aTw a generate 
only sere|linear s. Consequently, ideal 
case marking s are not MCTALs. How- 
ever, (Groenink, 1.997) defines a class of gram- 
mars, called simple literal movement grammars, 
aand henc.c line.at con|ca;t-free rewrite systems, which 
are shown to l)e weakly equivalent to MCTAGs in (Weir, 
1988) 
253 
which generate all and ouly the PTIME recog- 
nizable s. Ideal case marking s 
should therefore be generated by some simple 
literal movement grammar. 
We note fltrthermore that the (theoretical) 
time complexity is significantly better than the 
best known for recognizing context-free gram- 
mars. In fact, we implemented a practically ap- 
plicable algorithm which constructs the corre- 
sponding tree out of a given IC.Ad£ n string in 
linear time (in average). 
3 Semantics 
We are now going to propose a semmltics tbr 
s with stacked cases. The basic prin- 
ciple is rather easy: we are going to identify 
variables by case stacks thereby making use of 
referent systems. 
3.1 Referent Systems 
The semantics uses two levels: a DRS-level, 
which contains DRSs, and a referent level, 
which talks about the names of the refbrents 
used l)y the DRS. Referent systems were intro- 
duced in (Vermeulen, 1995). We keep the idea 
of a referent system as a device which adnfinis- 
trates the variables (or referents) under merge. 
Tile technical apparatus is however quite difli;r- 
ent. In particular, the referent systems we use 
define exl)licit global string sul)stitutions over 
the referent names. 
There is one additional symbol o. It; is a vari- 
able over names of referents. If we &SSUlne that 
a flmctor g has meaning g a simple lexical entry 
for g looks like this: 
/g/ 
I o:o I 
o - g(1 , a(g) o) 
Here, the upper part is the ret~rent system, and 
the lower part an ordinary DRS, with a head 
section, containing a set of referents, and a body 
section, containing a set of clauses. This means 
that the semantics of a functor g is given by 
the application of g to its arguments. However, 
instead of variables z, !/, etc. we find 1~o, 2~'o, 
etc. The semantics of a 0-ary functor z and a 
case marker, say 2, are: 
/2/ \[o2-o 
When two such structures come together they 
will be mcr.qcd. The merge operation (9 takes 
two structures and results in a new one thereby 
using the retbrent systems to substitute the 
nmnes of referents if necessary and then tak- 
ing the union of the sets of clauses. E.g. the 
result of the merge/g/ (9 /2/ is 
/g2/ 
I 0:0 
- g(12 o, 
Tile meaning of o : 2r'o is as follows. If some 
structure A is merged with one bearing that ref- 
erent system, then all occurrences of the vari- 
able o in A are replaced by 2~o. As the re- 
sulting rcti;rent system we get o : o. This is 
exactly what is done in the merge shown above. 
We shall call a structure with referent system 
o : o plain. Merge is only defined if at least on 
structure is t)lain. 
3.2 Semantics for .ZC.Ad£ 
To see how the semantics works we shall repro- 
duce an earlier example ~md take the ZC3dZ; f~ 
string g2xlfxl2. Motivated by the definition of 
the ideal case marking  we shall agree 
to the conventions that 
1. Case markers may only be suffixes 
2. Case markers may only be attached to 
flmctors or case marked flmctors 
By these conventions the string under consid- 
eration must be parsed as (g2)(xl)(f)((xl)2). 
They force us to combine tile fimctors with 
their case stacks first and afterwards combine 
the units. We shall understand that this is a 
syntactic restriction and not due to any seman- 
tics. 
The composition of g and 2 was already 
shown above and is repeated on the left hand 
side, using that ft(g) = 1. The result of com- 
posing x and 1 is shown to the right. 
254 
/g2/ /xl/ 
o:o \] I o:o 
"-'O 2~o -- g(12 ) 1~o -- x 
Merging these two structures we get 
/g2~1/ 
o:o 
~3 
2~o -- g(12~o) 
1~o----" x 
Together with f this gives 
/g2xl~/ 
o:o 
2~o ---- g(12~o) 
l~o--x 
o = f(l~o, 2~o) 
By coml)osing the strucl;ures for x an(1 1 we get; 
the structm:e /xl/shown above. We merge this 
one with that for 2 and get 
/~12/ 
o:o 
t ° 12~o -- x 
The merge of l;h(; two sl;rucl;ures abov(; tinally 
gives 
/g2~,fx12/ 
0:0 
12~o -- x 
2~o -- g(12~o) 
1~o----" x 
o ----" f(1~o,2~o) 
We shall verify that the wflue of o is a(:tually 
the same as the value of f(x, g(x)). Notice first 
that in the body of the DRS we find that 12~o 
and 1~o have the same value as x. We may 
theretbre reduce the body of this structure to 
2~o - g(x) 
o -- f(x, 2~o) 
Finally we m~\y replace 2~o by g(x) in the sec- 
ond line. We gel; then 
o - f(x, g(x)) 
whi(:h is the intended result. 
After |;lit semantics of the mdts has been com- 
lmted the order of merge is mdml)ortant. If we 
(:hoose to merge these semantics in an order dif 
ti;r(;nt from the one above, we get the same re- 
sult. 
a.a An example from Warlpiri 
To show how this proposal may work for naturM 
s we give an example fi'om Warlt)iri 4 
in which (:as(; stacking oc(:urs. We have to 
deal wit, h l;he t bur case markers ergative (ERe), 
past tense (PST), absolutive (ABS), and locative 
(Loc). 
,lapanangl;:a-rlu Iuwa-rnu marlu 
Japanangka-ERg shoot-PST kangaroo-ABS 
pirli-v,.qka-rlu 
rock-LOC-ERG 
,lat)anangka shot the kangaroo (while) on the 
ro ck 
\¥e extend the t)roposal by taking into ac- 
count that cases may not only flmction as argu- 
mind; markers but have a semantics, too. This 
actually does not make much of a diflhrence 
for l;his calculus. We propose the tbllowing se- 
mantics for the locative and the past tense case 
lllarker 
ILocl /psi/ 
o : LOC~o I ° 
located (o, LOC o) 
o:o 
past'(o) 
St), when the locative is attached, it; says that 
the thing to which it; attaches is located some- 
where. Here, o represents the thing that is 
locaLe(l, while I,OC~o is the location. The 
past tense semantics simply says that the thing 
which it attaches to happened in the past. 
We construe the meaning of the ergative as 
being the actor and the meaning of the absolu- 
tive as being the theme s. 
dThis examl)h; is taken front (Nordlinger, 1997), p.171 
'~In fact, ergative and absolutive should mark for 
grammatical flmctions, but since linking of grammati- 
cal functions and actants is quite a complicated matter 
(see (Kracht, 1999)) we make this simplification. 
255 
/ERe/ 
o EI\],G~ o 
actor'(o) --" ERC~o 
Again, we shall agree 
/ABS/ 
o : ABS'-'o 
2~ 
theme'(o) - AB8~o 
nl using the conventions 
stated in subsection 3.2. First we have to attach 
the case markers to compose the resulting struc- 
tures afterwards. The semantics of the proper 
noun Japanangka is taken to be a plain structure 
with body o "-- japanangka'. The composition of 
this structure and the ergative semantics yields 
/,Japanangka-ERG / 
o:o 
ER.G~o ~ japanangka' 
actor'(o) -- En.G~o 
We assmne that the nominals /pirli/ and 
/marlu/have the following lexical entries: 
/pirli/ /marlu/ 
o-o 
{o} 
rock'(o) 
o:o I 
{o} 
kangaroo'(o) 
Thus the semantic composition of pirli, LOG 
and ERG gives: 
/ pirli-LOC-ERG / 
o:o 
rock'(LOC~ERC~o) 
actor'(o) -- EROde 
Iocated'(ERC~o, LOC~EnO~ o) 
Similarly we can compose marlu with the abso- 
lutive case: 
/marl'a-aBS/ 
o:o 
{ABs o} 
kangaroo'(ABS~o) 
theme'(o) -- ABS~o 
The semantics of the verb is shown on the left 
hand side and its composition with /PST/ on 
the right hand side. 
/ l'a al 
I o:o I 
°1 sheet'(o) 
Iluwa-PST/ 
o:o 
shoot'(o) 
past'(o) 
Finally by inerging tile structures/Japanangka- ERe~, /ma,+a-*BS/, /pi 'li- 
LOC-ER,G/ ill rely order, we get tilt following 
result. 
o:o 
{ABS~o, LOC~ER.G~o} 
ERG~'o -- japanangka' 
shoot'(o) past'(o) 
actor'(o) ----" ERG~'o 
theme'(o) -- ABS~o 
kangaroo'(ABS~o) 
rock'(LOC~ERO~-'o) 
Iocated'(EI{C~o, LOC'-'Elm'-" o) 
It says that there was an event of shooting in 
the past, whose actor is 3apanangka and whose 
theme ix something that ix a kangaroo, and that 
there is a rock, such that Japanangka is located 
on it. Note that the only syntactic restriction 
were the conventions stated in subsection 3.2 
and thai; we (lid not make any fllrther assump- 
tions on syntactic structure or word order. 

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