Free-ordered CUG on ChemicM Abstract; Mzmhine 
Sa~oshi Tojo 
Mitsubishi l{ese~rch Institute, Inc. 
(e-ma,i\]) tojo@mri.co.jp 
Abstract 
We propose A parAdigm for concurrent n;~tura\[ 
lAnguAge generation. In order to represent gram- 
mar rules distributively, we adopt categorial unifi- 
cAtion grammar (CUG) Where eaclh category owns 
its functional type. We mlgment typed IAmbda 
cah:ulus with severM new combim~tors, to m~ke 
the o:rder of ,~-conversions free :for partial / locM 
processing. The concurrent calculus is modeled 
with Ch, emical Abstract Machine. We show An ex- 
Ample of A JapAnese causative auxiliary verb that 
requires A drAstic reArrAngement of case dolninA- 
tio:n. 
1 Introduction 
PArA\[le\] a.nd distributed computation is expected 
to be tlhe too.in streAnn of infbrlnAtion process- 
int. In the conventionAl generation, the rules 
for compositi(m are given from the outside ~nd 
those rules control All the behavior of the symbols 
or the objects, for ~tssembling A hierarchicaJ tree 
structure. D)r exAmple, Ml the linguistic objects, 
such a.s words And phrases must be Applied to so- 
caJled gra,mlm~r rules to form gr;mmlAtica.1 struc- 
tures or r;~tionaJ semantic represen rations, under 
A strict controller process. However, this ldnd of 
formMizAtion obviously contradicts the partiAl / 
distributed processing that would be required in 
pa,rAlle\] architecture in future,. 
In order to represent grammttr rules distribu- 
tivdy, we adopt cAtegorial grammar, where we can 
an AttAch local grAmma,r rule to e~ch word and 
phrase. WhAt we Mm in this paper is to propose 
A pAra.digm that ena, bles partial / local genera- 
tion through decompositions And reorganizations 
of ten tAtive local str u ct ures. 
In the following section, we introduce the ex- 
tended ,\-calculus. Therea.fter we introduce the 
ChAM model And we reinterpret the mode\[ il, 
terms of natural language processhGs. Then we 
show the model of membrane interaction model 
with the example of ,lap~mese causative sentence 
that requires drastic change of domination of 
cases. FinMly we will discuss the fllture of the 
model. 
2 Extended typed A-calculus 
CU(\] (Categorial U,,ificAtion (l:ra,nma,r) \[8\] is a,d- 
vantageous, compared to other phrase structure 
gl:Amlrt~rs, tot pArMlel a:rchitex:~ure, because we 
can regard categories as htnctional types and we 
c~m represent grAinlnax rules loca.lly. This means 
that we do not need externAlly-given grAmmAr 
rules but those rules reside within each word or 
each. phrase. In this section, we regard categories 
a.s polymorphic types And consider the type cAl- 
culus. In later sections we denote categories by 
I) AG (di retted acyclie grAp h) o { PA'I'R grnln m Ar 
\[5\]. 
2.1 A-calcnlus of polylnorphic type 
We use greek \]etters, for type sehelnAS. \]!'or tyl)e 
constants we use or,%.., while for type vAriAbles 
we use (-hfl,'''- a : n' represents thAI; the object a 
is of type ~t. If~v AIM fl Are 1;ypes, I, hen e~-~ fl ix 
a type. 
The purpose of' type ilfference is to infer I;he 
type of Art object fl:om A set of objects whose types 
are known. We presuppose, tha.t two type w~.rial)les 
c~ And fl Are unified wit\[, a. ltttifier O. ~/e Ilse \[' \[el/ 
this set of type-known objects. The most impel 
(:Ant two rules Are As follows: t 
1'0~ u {:c : o~01} F t : fl 
1'0~ F ,\z%/, :a.0~ , fl (1) 
\['020304 \]- t : 6t04 - ~ fi0,1 1'02030,1 \[ .5 : C~O, 1 
P0~0:&I F z(s) /304 (2) 
The rule (2) corresponds to /Lconversion of the 
or<l in a.ry A-ca.I c ul ii S \[d 1. 
2.2 Extended combinators 
In this su\])section~ we. introduce two com\])ina- 
tors theft enable us to change the order of ,\- 
co nversio:u, proposed by Stee(hnan \[6\], as a kind of 
type chAuge \[3\]. The ordinary A-cMculus requires 
~02,0~ are for 1'02 k t : cv ~ fi a, nd for \]'0:~ F s : a', 
rcslmctively. 0~ unifies ~ which ~tppears iu both type 
decla.r~tions, 
870 
a, st, ri('l, order or (:OllV(;rsioii. ilowever~ ill a. (:().(:. r 
,'eni, model> this kin(l ol'stri(:t ()r(ler i~; a. hi,l(Irat,(:(' 
a,ii (I COli i~i li~(~,iti; ('oil version s il,l'(! I'(!q u ire(I. 
(}-.('(mil)hlaJ.or (;ha.nges I.he or(ler <~\[ .,\ vaJ'iat)le~ 
.a,s I'ol lows: 
C(Ax;q.f(.~:, y)) :~ Ayx.f(:,:, ;q). 
Anol;her re(lui relnenl, for ex<tiia.n<~es ol' I.I\](~ or(ler o\[' 
~-(;OliVersiou is 1,he \[bllowing case. ~uj)t)ose 1;haJ. 
wc, a.l'e re< I u ire(l 1,o COlli \[)ose a.II lille Ibl lowilig ty i>ed 
f :t7 > 7 
,q : +t , ,/g 
H, ~ (~ 
\]II SI.IC\]I ~1, C,{/H('J~ W(~ IIC,(!(\[ LO (to/IC,3,L(!ll;I,((\] ,(\] ~£11(\[ U, 
firM;, a, lid IAiell :\](a,) 1)ecoillOS a,l)l)li(:a,l)l(~ to .1'. Ih)w- 
ever, wil;h I;he hel I) (;\[' l, he Pollmviiig lJ (;oull)ina.1;or: 
:~J (A:</(~))(,\:q.:\](:,~))A;,,.f(q(~:+,)). 
'l?he A-va.ria.I)le in .(,I c;i.il l)e shif'l;(~(l bey+m(I i,h(! 
sc.ol)e of f so thai; we t:a.il (;Oll(;a.l,(~tlal,(} f a.il(I \[\] 
first, a.n(I, trill,% Iia.ve a l)t!('(ml(.? alll>li(:a.I)l(' :is iu 
Fig. I. 
,\ :,/ . :\] ( :,\] ) ,, 
:s(,,) ,',:,.f(:,) 
f(:/(.)) 
\]\:..j(:.) ,\:</.g(~) 
II ......... 
,\'.,:.f(:/(:,\])) a 
,I(:\](,.()7 
l,'igure I: ll-('~lnlb\]na.ior 
2.3 Cost of unifi(:atioi! 
The repeal, e(I cise of C- a.nd B (:()Jliliiiia.l;(Jt',<i is still 
l)rol)lenia.(.i(: if we consider inll)lettteulin<v , it :-'<s a.Ii 
a.cl;tla.\] s.ysl, c\[ll l)e(;a, usc: t;lie t, erlllinaLioJt o\[' I)i'(;,(;(.~ss - 
ilig is iiol; gua.ra.ntee(l. \;Ve have uio(leJe(I t.lie i)r() 
(;ess of a. i)a.rl;ia.I (lecoml)osit, iou a.s ~LI\[ a.I)sl, ra.cl, ioll 
of a.n a.l'<~llliietil; of the |ir,% or(ler l, erili. 11' this M)- 
M, ra.(;{iOli o(:ciir.4 ra.li(IOllily~ the \[)l'()(t(;~B ea.sily f'a.lls 
hil;o a, lool). In oi:(ler |,o a.vohl I, his, we a.B~ltlll(; ttie 
unilica.l, lon (:oM,. If a, ('otnt)cmnd l.erlii (a stll:,l;r(~(!) 
wer() to I)e ,:le(:onil)OSe(l Oil(re+ 1;he elenl(ml; wil.h 
Lhe longer (li,%a.liCe sh(lul(l I)e a.b<,i4::+lx:Led fi rM,. \,Ve 
Ca, II roga, i'(I l, lie whole Boni,,.~llC(! Bgru(;(,tire a,b itlOrO 
~fa.iil ul~.cl,\]ca,\[ i f i, he BI\[lil i)\[' 1, liese Ii ni \[ica.tJou (:ost;s is 
m:na, ller. We \]ntro(lu(:e I, he heuristi(: (:<)st,~ \[7\], (:Oll- 
si(lering l, he l)a, ra.lleltsiu I)e{,ween ~ynl;a('.l, tc (:a.ses 
a, li<l Sellia, iil,l(: rul(~s, a,,~ I'ollow~: 
IIO( ............. .,#)11 : ~ i 
II0(<+<,,.,<.,.)11 ~ + i 
II0( ......... +.~)11--i 
II0(<.,j ......... )11-/,, 
II0(<~.+,..,.>11, : i,: 
II0(<,<+.~)11 :- i,, 
\[I0( .......... :<,+)11 : :×~ 
II0(+.+,<,.~>ll <~ 
where 0(:,.,:/) rel)res(mt.s a. unifier ol I;w(, I)ACl's: 
()ll()>B synLa.(:I;i(; (:as(; i,<+ ;r a.u(l l, he ol;her~s seulanl, ic 
role is y. X; i~ XOlite (;()liBta..lll, la.rger l;ha.n I (t,: > I). 
3 Chemical Absl;ract Ma(:hin(., 
(;l~, m, ic.I A t,,~.~racZ M.ch, inc (Ch A-\\]l, for sh(,rt) Ill\] 
\[.~ a, pa,ra,(I igt. ol + (:(.,n(:u rre. L ..\<a,h:ttl m+. In this l)a: 
per, we \vi II tneti t, ion ou r I ) ri tic\] pies on it a,t;tl r:-+l la,. 
g.a,ge l)r~.:<+ssi .(+~ wi lh r(+g+u.(n t,(+ tlm ( ',h A M .lodel. 
W( + ;rt,gBllttl(+ +AI(> l)rO('(~,<4,S 0\[' l+a,tti_l:a,l la, ngtmg(, 
r,.!cog.it, i(m a,,<+ folh)ws. Wh(,u(+v(+r a, liltKui,-it;h: t)b. 
ject i,<+ r(>(:o<c,;idz,'.+,rl, it, is thr()wl/ i.tu t, he ,soh+l,i+m 
<:Z (JhAM, att(I a(',t,'-i a,,,+ a, ?no\[could. \:(~rl),,-+ a, lld 
H()IIlO other ~+LtlXil\[+l.l'y VOI'i),9 itlt;l+O(tllC(+% 7121712\[)7"lLI:C,'+'. 
:l'hese melnl)ra,tm+ l:..~(:onles (;heir '~(:()pe,~+ \['(:,r (:a++e 
(or role) (Mlui,a,tic)u; nattMy, ca,oh verl) ,'-,0ar(:tl(>,<+ 
for + inole(:ule,4 (u(>utJ i)hr++se,s) LhaJ; are nec(+.s,~+a.ry 
I,o sa, ti~f'y (~a.ctl verb's (:a.,,~e (rol(;) fr;.u.e, ,,vit;Nitl it,~ 
meinbra,n(x In ~()t+l,'+ oc(a,si,:m,<L+~ \]l' tnultij)le verbs 
e×i,sl, iu one ,senl, cm('x~, t;hey ,uia,y (:onlli(:t a,<+ to, whi(:h 
verl) (h+tuilta, t;es which nou t+ l(h ra,se. In such a+ c:-t,se, 
Lwo uleml)raN('s ('.a,n itll;era,(;t a,;lld ('a, tl (?XC\]Ia, IIgC. 
,'40Ill(! niolo('tL les. 
\'Ve LISO ,41+,$2~,43+... \['OF IIlOIII\[)I'+IAI(+,~. ~/+\[101\] a 
IIl(!lll\[)l'illl(~ ,S+' CO/II~-I,\[JI,~ ;~ IllOl(~clll(\] (~ wo (lel\]ot, e a,,~ 
Lerl)rel;ed a,s al+ inclu,<d<m rela,tiou (D) iu tlhi~ ('a,(,. 
:I'W(') IIl(Hllbl'~-I+ll(!B C'd,II iti\[,(!ra,cl, w\[10ll I, Iley (;()tit&f(:(; 
wii.h I;he .,)ta.l,i(m <11', +'" '+, It+~. lr th(,+(, i., ,. U(,,u 
ing molecule (t;tlat which is Not yet (:onca, I;,.,na,t(,d 
with c,l:h+,r m(~le('ule.,<+) +>u otl,:' ,si(I,a+ it, (~,a,. m,.,ve 
i, hr,:)ugh the porou,s nlenil)ra, r\]es. Va, leuce,s for (:un- 
C;'Lt,(uI;-/tiOII of (;a, ch tlloleCtll(? i-tr(,, +:(+l)re,s(Hl{,(;(I I)y 
typ(+(I hz'n+bd, a va,ria.,bles. IJ (.le rnettil)ra.(> c(m 
I,a, ins only one (:omp()sit;e .stru(:Lure, a,n(I il; ,,-;t;ill 
ha,s ,~u rpl u,(+; va,l(m(;es, we (:a,t:t rega, r(l that, whole t he 
m<'till)ra,n(~ ha.4 t, ho,<+e surplus va, l(m(;os as f,: .l l (, ,.v s . 
,<+;,~ I + ..',:+:y.++...U,,',,~(,.,:, :+\], +::) 
1 
>, z ?s .< .,+ + I: ~ +,,.,'/.t,:.,+(:,:, .V, z) 
Now, w(+ wilt at)ply our .oti(:>lt,4 a,h.ov,.', to t, he 
a,ct, u a l \[)rol)l(,lU o\[ ,4e n Ix'n (',(, <t'~(+ll(',l;a,i;ioII. 
871 
(yore- = read) 
Ken-wa Naomi-ni hon-wo yom-u. 
Kc'n-wa Naomi-hi hon-wo yom-ase-'ru. 
Ken-wa Naomi-hi hon-wo yom-are-ru. 
Ken-wa Naomi-hi hon-wo yom-a.se-(r)-are-ru. 
- wa 
-too 
hon 
#om- 
-ase- 
-a?'e- 
: nominative case marker 
: dative case marker 
: accusative case marker 
: noun for 'book' 
: root of verb 'read' 
: auxiliary verb for causative 
: auxiliary verb for passive 
: present tense marker 
Who reads? 
Kc~ 
Naomi 
Naomi 
Ken 
Table 1: Agents alternation by agglutination of auxiliary verbs 
4 Example: Japanese causative 
sentence 
In th.e Japanese language, the causative ~nd the 
change of voice a.re realized by agglutinations of 
those auxiliary verbs at the tail of current verbs. 
These auxiliary verbs as well a.s ordinary verbs 
can dominate some cases so that these agglutina- 
tions may change the whole syntax \[9\]. Namely 
the scope of the operation of these auxiliary verbs 
is not the operated verb but the whole sentence. 
In order to illustrate these role changes, we show 
the ~dteruation of the agent of tlhe main verb in 
Table l with a short tip to Japanese lexicon. 
As an example, we will take the sentence: 
Kcn-wa Naomi-hi h.on-wo yom-ascru. 
(Ken makes Naomi read the book.) 
First, we give I)AG's for each lexical items in 
l)'ig 2. The last DAG in Fig. 2 represents that the 
verb 'yomu (rex(l)' requires two roles 'the re~der' 
and 'the object to be rend', and one optional ro\]e 
%he counter-agent' who hears what the reader 
reads. In that tigure, 'W I =' means that each 
word is recognized in the general world however a 
verb 'yomu' in trod uced a special membrane sl as a 
subworld of W. Each DAG means a polymorphic 
type of the lexical item. 
Assume that there is a. parser that constructs 
partial tree. st:ructures, as recognizing each word 
from the head sequentially. Then, when the first 
:fbur words are recognized, they can form a con> 
plete sentence of (3). 
I= {read(lClo~,NIo,2,Vlo~): \[ cat 6' \]} 81 (3) 
Because all th.e three nouns are adequately con- 
eateuated by 'read.', a sentential representatio:n is 
m.ade in the subworld of .st. in (3), Oi's a.re the 
records of unification, thaJ; contain the costs and 
the original types; they becom.e necessary when 
they are backtracked, and in that meaning, those 
bindings are transitive. 
Now, let us recapitulate what ihas occurred in 
the membrane, sl. "\['here were four lexical items in 
the set, a:nd they are duly organized to a sentence 
and sl becomes a singM;on. 
.sl = {K:N, N:N, B:N, 
,\zyz.rcad(x, y, z) : N --, N -~ N -+ S} 
,~ - {,'~.l(l;', N,.)} 
Then, the problematic final word '-aseru 
(causative)' arrives; its \])AG representation is as 
in Fig. 3. The DAG in Pig. 3 requires a sententiaJ 
lbrm (category ,S') as an argulnent;, and in addi- 
tion, it subcategorizes an item of category N as 
an agent of l;he su bsentence. 
Now, the process becomes ~s in Pig. d. All 
through the process in Pig. 4, C- and B- 
combinators are used repeatedly as well as ordi- 
nary type inference (l) and (2). The second men:,- 
brane s2 requires an agent role (the variable x' of 
'make). There is a record in 0t that it bit agent, 
so that the comparison should be marie between 
01 and 04(= O(~r,j)). llowever, because both of 
0t and 04 unifies nominative case and agent role, 
the costs are. equivalent. In such a. case, linguistic 
heuristics will solve the problenl. In this cas G the 
agent of make shouJd be the nominative of the 
whole sentence, and the co-agent o\[' make is (;he 
datiw~ of tlhe whole sentence, so that K and N are 
bit by newly a.):rive(I utake, t1 remains bound to 
rcad, because there is no A-variable of that type 
iu ?)ta,~e. The process is depicte.d in fig. 5. 
872 
w I= It(= l~;~,.-~,~a): \[ cat N 
case )to??t 
cat N W I = N(= Naomi-hi) : 
case dat 
w I= ~(= z~o..-.wo): \[ eat N 
ea, sc aec 
s~ I = ~\x~l~.?'~'~ad(:,, y, =)(= yo,~-) : 
val 
rg 
rfl 
L 
aT(\] 
L_ 
cat S 
form \[form fintie \] 
cat N t role agcnt 
<.:at N 
role objeel <:at N \] 
role co-agent 
optio~ality + 
l?igure 2: lnitb~\[ I)AG 
A:,,~j~.,,,,,.,~:~,(x, y, ~(v)) : 
val 
arg 
arg 
aT f\] 
cat S J form \[form fintic \] 
cat N \] 
role agent 
cat N \] 
role co-Agent 
optionality I 
cat 5' 
subcat role agent 
role t 
Figure 3: I)AG t'o1: 'ma~:e' 
s, I = r~:ad( l~'lo ~, NIo=, I~lo=) 
Az:q.s~ I = 'read(z, !/,/~) 
,e, 1 
II .\:,:'y'~'.s~ I- .~ak~(x', :,/, ~') 
.\] 
II ~,~/~'.~21 = .~akKKI0~, y', z') 
.\] 
II ~z'.s= I = ',,~,al.<(~Clo~,NIo~,Z) 
.1 
II .~= I: ,o.ake(KI0~, NIo~, .Xy.','~ad( N, e:, 13)) 
\[?igur(, 4: Process 
873 
W 
\[ S 1 ('-') road 
' :_2/ ?_, 
! /1, xyz.makc 
/ __ __ __ j' 
w 
,~U rear 1 
I I I I 
/ .... S 
~2~ kc 
,.,._ ..... 2 
W 
f sl I \2__--, 
s2 l /~makc \] 
/ \ \ read I 
0 0"0 i ,<: /\ i 
d 
N B} 
l:'igm'e 5: Mei\]i I) i:a, nes inte:r~tction 
5 Conclusion 
Introducing free-ordered typed A (:a.lctJhls, to- 
gcthcr with the Notion o\[' uniticazion costs in 
t;ype, s, wo ha.ve shown the structuring of ha.ru- 
ral lmlgu~gc synt~x, by dlstril)~ltively \]:el)resented 
tyl)oS in ra.lidol~i orders. \~\[e adopted a :rood01 of 
Chemical Abstract Machine for the i)artiall con- 
currenl; COlnl)tll;a.iJio\]t luode\]. 
AJUhough we in t:ro(luced the concept of cosl, s 
a.n(I termina.tio\]i was a.ssur<~(l, the effi(;i(;n(;y of con- 
strucdng a. p~rsing tree wott\]d 1)e far slower than 
sequential processi:ng. Ilowever oHr ob,i(~ctiv(~ is 
not to propos(; ~ faster algorithm, but is to show 
t h e possi bility of dis tril) uted i)rocessin g o f n at Ilra.l 
lai\]guages. We could show theft \]l¢~tu\]'al language 
syntax is solf-organiz¢fi)le, in that each linguistic 
ol)jeclJs (1o ;ii()l; :need I;o be l)OUJ'O(I into hnot(Is', viz., 
0,xl;(;ri7 ailly gi yen gra.llllila, i:. 
\[5\] S. M. Shieber. An Introduction, to 
Un~/ication-Based AppTvaches to Grammar. 
CSI,I, St~nford University, 1986. 
\[6\] M. Steedma, n. Corn bin;~tors m~d gram ma.rs 
- in (/atcgorial Crammars and Natural Lan- 
guage Structures, pa.ges d 17 442. D. Reidel, 
i1088. 
\[7\] S. Toj(~. Ca.tegoria.l analysis of sentenc(~ g(m- 
era tion. In The Logic Programmir~,g Conj'cr- 
encc (1;PC '9l), pages 22!) 238. Institute of 
New G(mera, tion Cotnl)uter (ICOT), 1991. 
\[81 \]l. UszkoreiL Ca.tegoria.1 unifi('+don gram- 
ma, rs. In Proc. of COLING '86, pages 187 
\] 9<1, 198(\]. 
\[9\] T. (hinji. Japanese Phrase ,5'trucl,'urc Cram- 
mar. \]). \]{,eJdel, 21987. 
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874 
