Disambiguation by Prioritized Circumscription 
Ken Satoh 
Ik)kkaido University 
N13W8 Kita-ku S;tpporo 060 J,~p~m 
ksat oh@db, huee. hokuda£, ac. jp 
Abstract 
This paper 1)r(,.sents a nml;ho(t of resolv- 
ing ambiguity by using ;~ wu'imlt; of cir- 
(:ums(:ril)l:ion, p'rio'ritizcd circwm, scrip- 
tio'm In a disa,ntbigu~tion task, human 
s/:(',ms to use various t)r(',fcrcnccs whi(:h 
have various str(mgi;h, hi llrioril,izcd cir-. 
(:umscription, we (:;m ('.xt)ress thes/', t/ref - 
erences as defe;~sibh~ (:onstr~fints with 
various strength and we infer the, most 
1)referabh ', logical models which s~l,ist',y 
stronger COllStra,ill|;S ?l,s 11111c\]1 as t)ossi - 
bh',. This ret)resenl,adon is very m~tu-. 
ral for (tis;mfl)iguation sin(:c w(; (:;m r(~. 
ga, rd a logi(:al interprelqal;ion a.s a possi- 
bh,. r('.a(ling a.nd 1:lie most prefer;d)lc log- 
ical models as the most pr('.f('.ra,bh'~ r(.'a(l- 
ings. Wc argue l,hat 1)rioritize.d (:ircum- 
s(:ril)tion is a,nol;her promising method 
for the task. We a\]so dis(:uss an im- 
t)hmmntation of l)rioritized (:ircums(:rip- 
lion by a hiera.rchi(:a.l logic program- 
lning (\]tCIA)) 1;ulgu~tge. 
1 Introduction 
'\]'his p;~pcr presents a lll(.q;llod of (tisa.ml/igu;LdOn 
t;Lsk 1)y a va.rbmt of (;ircunmcription, prioritized 
ci'rcum, scriptiou, (M(:Car|;hy. 1986; l,ifhchitz, 1985) 
and discuss its iml)h',nlental:ion by a hierarchical 
l:onstr;I,int logic progrmnming (HCIA)) bmguagc, 
sltc\[l a,s (Borning et al., 1989). 
Dis~unl)igua, I;i(/n is a v(',l'y intporl;ant t;ask in mtt- 
ura.\[ bmguage l)ro(:essing. To reso\]ve aml)iguity, 
hunt~ms se, enl to use not only syntactic (:onslxa,ints 
but a,lso wtrious lev(;ls (1t7 heuristics such as gram- 
mati(:;d 1)r(~Dren(:es (\[\[ol/1)s, t990) a,nd sema,ntic 
t)ref(',r(',n(;(',s (Wilks, 1975). 
For t~xamtlh'., SUl)pose thai: we have the follow- 
ing SCllt(HICCS. 
John just saw a man with a telescope. (M 
He bought the teles('ope yesterday. (1)) 
Although dmr(', is ;m alnt)iguil;y on mc;milig of the 
1)hrase, "'widt a teh'~scope"(ldw, teh;scot)(; ix either 
used by ,}ohn or (:arricd by the man), we might 
conclude t:hc preflwred rc~uling a.~ f'olh)ws. 
From dm above sentences. "He" wouhl be equal 
to .John l)c(:ause tho subject t;ends to be cont.in- 
ued t.o the ne.×t sentence }rod .John probably had 
a telescope at the time of seeing a ma.n fi:om |;he 
scnteiwe (b) ;u,l ilw.r|;i~ of possession. Therefore. 
from this prefl:rrcd re;~(ting, we conchuh', that the 
telescope is used as a, (levi(:(; to sec a man. 
However, this re;~ding is not tinal since at least 
the fl)llowing prcfl'~rences are involved in the above 
reading and these preferences Call be (teib.~ted 1)y 
s(;rong(;r hfl'orlm)A;ion. 
Syntactic preferen(:e: The sul)ject 1;(re(Is to I)c 
col\[\[;illltc(\[. 
Semantic prefer(m('(.': If ;~ person buys some- 
thing at time i, then he shouhl h;~ve it at 
time j where i < j. 
In or(tot to dcmons(;ratc defea.sibilil;y of t)rcfer -- 
o.11(:(! l'ltl('.s, :Ul)t)osc the following S(HItCII(:C is added 
,,ft(,,. th(, ahoy, s(..,m,n(:(,s (a) ~u.l (b). 
Bu G he gave the lnan the telescope (c) 
this morning. 
Then, we migh|; oh;rage ;~ preferred reading th~l; 
(,he mint should have had a telescope, and dmr(> 
for('., t;he t(~lcs(:ope was carried by the man at the. 
time of John's see, ing the man. In this re;uting, 
a(; legist, (;he following preference rule of mmther 
inertia of possession is used. 
ff a I)(',rson gives some.thing to tim other 
person at time i, then the other l)erson 
shouhl btve it a,t time j where i < j. 
This (:onfli(:l,s with (;he 17Orlner semantic preferen(:e 
of inertia of possession by 1)uying, but the above 
preference is st, ronger tbm the former since the 
time of giving is later t;h;m the time of buying. 
rl'hlls, the folJlllCF t)reference b(~C()lll(R-; 1lO hmer 311- 
1)licablc by the new scutcncc. 
This kind of revision of reading cmmot be rcl)- 
res('.nl,ed by infl'.ren(:e in (:l;~ssical logic siu(:e in 
classi(:;d logic, once wc gel; ~ inferred result, we 
can no hmger rel:ra.(:t the result (monotonic pr'op- 
erty). Therefore, to ml(lerstand tit(,, phenolnen& 
we need other reasoning met;hods rout in f~(:t, 
901 
many researches h;tve been using general reason- 
inn f~am(:works in Artificial Intelligence. such a,s 
abduction (ttobbs et al., 1993), prol)abilistic net- 
work (Chm'niak and Gohhnan, 1989), truth lnain- 
t(mance system (Zernik and Brown, 1988), default 
logic (Quantz, 1993) and conditional logic (Las- 
carides, 1993). In this paper, wc ttropose another 
alternative, that is, circ,,.m.~cription (McCarthy, 
1986: Lifschitz, 1985). Even though circumscrit)- 
tion is one of the most pottular fornlMisn,s in the 
COllllllllllit, y of llOlllllOllOtOlliC reasoning rcs(,.ar(:h, 
it is surprishlg that w'.ry few h~ts examined feasi- 
bility of (:ircumscrit)tion for disa, mbiguation. Our 
work of disambiguation by intcrt)retation ordering 
is originated from (Satoh, 1991) and in a more 
recent work, Kameymna (Kameyama, 1994) has 
indcp(mdently propos('.d usage of circumscription 
for interpretation of pronominal anaphora. 
In this paper, we explore this direction fur- 
ther. In circumscription, we give a prefcrclme of 
der over logical interpretations and consid('.r the 
most 1)referable models. This representation natu- 
rally corrcst)onds with a disambiguation task sin(w. 
we can regard a logical interpr(~tation as a possi- 
ble remling, and disaml)igua, tion as a, task to get 
the most prcf(wal)h; reading among possil)le read- 
lags. Among variants of circumscription, priori- 
tizcd circu.mscriptio'n, is suitable to ret)rcsent vari- 
ous strength of preference rules. In f)rioritized <fir- 
cumscril)tion, we can (livide preference rules into 
hiernrchy and this hierarchy giv(,,s a t)riority rela- 
tion ov(,.r pr(~f('.rences. Therefore, we directly rep- 
resent rules in the hierarchy in prioritized circum- 
sccil)tion. 
We believe, that circumscritttion has the follow- 
ing allvantage, s in the (:ask of resolving ambiguity. 
• Since wc use a tirst-order predicate calculus for 
a basic language, we (:all rot)resent various kinds 
of inforln;ttion such as grammaticsfl rules and se- 
mantical rules in one Damework. 
• There is only one extra underlying mc(:hanism 
besides iufi'.rellC(', rules for the first-order predicate 
cah:ulus, that; is, introducing an order over h)gical 
interltretations. Therefore, re.asoning process (:an 
be un(hwstoo(l easily COlnt)ared to other lnecha- 
llisln using numerical reasoning or comt)h:x infer- 
ca(:(; rules. 
• We (lo not nec(l to assign detailed mlmcri(:al val- 
ues to t)referellce rules in ord(;r to express t)riority 
over t)r(~ference rules, but just specify a t)ref(:rence 
level of the rules. This representation can t)e re- 
gar(led as all assignment of qualitative strength 
for 1)ref(~l'ell(;(~ rules all(\[ reduces a \])ur(letl of tel)- 
resenting a ttriority over preference rules gready. 
Moreover, this prioritization is general since we 
can repr(~sent a various kind of priority besides 
specilicity. 
• It is important to retain 1)ossible readings if we 
can not w.solve aml)iguity yet. In cir(:umscrip- 
Lion, we can consider multiple preferable models, 
not nec(;ssary the single pr@rable model. So, if 
ther(~ are yet multiple possible readings as a re- 
sult of disambiguation, we can keep these possit)le 
readings as multiple i)retb.rat/le lnodels. 
In this l)aper, we also dis(:uss an implenmn- 
ration by using hierarchical constraint logic pro- 
gramlning (HCLP) language sltch as (Borning ct 
al., 1989). HCLP language is similar to constraint 
h)gic progralnming bmguage except that we (;nil 
represent a constraint hierm:dly. Thus, there is 
a corrcst/on(lencc l/ctwecn a solution of an HCLP 
language and the most t)rcferablc models of pri- 
oritized circunmcription. Ill this patter, we use 
our HCLP language based on a l)oolean constraint 
solver to get tlJ(', most t)rcferal)lc models from t)ref - 
er(mce rules rot)resented as bo(/h,,mt constraints in 
tlt(', HC'L1 ) language. Wc demonstrate how the. 
;fi)ove example of the disalnbiguation is tre;~ted in 
tlm HCLP language. 
2 Prioritized Circumscription 
In this section, we briefly review prioritized cir- 
cmnscritltion. For simI)licity sake, we modify the 
definition of prioritize(l circumscril)tiol, by (Mc- 
Carthy, 1986; Lifschitz, 1985). The difference is 
that we let all t)rcdical;es vary and lnaximize pref- 
erence rules whereas Lifschitz mininfize abnormal 
predicates for prefercnc(', rlth~s. 
Let cI)(x) and ~P(x) be formulas with th(! same 
nulnller of fre(~ w,.riables x. We say (,hat ¢) and ~P 
are similar. ¢1) > ~I/ stands for Vx(~II(x) D (P(x)). 
We extend this notation to tuples of formubm ep, ~IJ 
wllQFC (I) 22: {\[)\[ .... {~,f,, alld ~1 / = @1 ..... ~\[,'., all(l 
and ~ are similar (each (I)j and @5 ~tre similar): 
(D > ~1) stands for A<' _ .~::~(I'j > ~Pj. We also write 
i1)> ~PA~P >(l) asCD =9 and 4)>~PA~(qJ_> (It) 
as ~P > ~P. 
Let a tuph', of formulas 4) be broken into disjoillt 
parts q51 , (1)2 .... , (1)a:. Let ~Iri be similar to 4;< We 
(te~ll('. q* ~ ~ d,Q" t, (A i .1 (\[~j = @.i ~i =: A'i::Iv j--1 D ~ /)it. 
We also wril;e (1) ~ vii A ~(~It _ ~I)) as • ~ iP. 
Definition 1 Let A(P) be a formula, and (D(P) 
be a tuple of formulas wh, ich, is brokcn into 
4il(P),4,2(P) ..... (1)~:(P) where P is a, tv, ple of 
predicates used in these formulas. 
The ,~ynl, act, ic d@',nition of prioritized circum- 
scription i.s as follow.s: 
A(P) A -~p(A(p) A 47(p) >- ~(P)), (1) 
"tl~ll,(~f'(" 
1. p i.s a, t'uplc of predicate variabh',s ca, oh, of 
wh, ich, ha,s the same arity as th, e correspond- 
ing predicate constant in P, 
2, A(p)((D(p)) is a formula obtained b!l replac- 
ing evcry occurrence, in A(4L respectively) of 
a predicate con.st(m,t in P by the, correspond- 
infl predicate varia, ble in p. 
902 
At:cording 1,o l:he result of (\]Afschil,z, 1{)85). wc 
give a, model theorel,ic tlclinil,ion of l:hc ~d)ovc \[of 
nmla, (1) ~t,~ folh~ws. 
Definition 2 Wc dcfi~,~ ant, o'rdc':" > ovc'r Ioqica, I 
i'.,l, crprcl, ation,,~ a,,s folio.,,<" 
M~>M 
.wh,¢,rc 
I. M' a,',,d M have lb.c .~a,'m,c do'm,o,i,~,. 
2. cm"U/ co'n,.,#,an,/, a,'n,d, fu,'n, cl, io'n, .s!/'m, bol k,a,.s /k,e 
,sa, w,c i',,tcrprclatio'n, in, M/ a,'H,d M. 
,7. q,(p) >- *l'(q) i,s t'r.,, in, M' (o'r. cq.iva, lc'.,tlfl. 
i,, M) :,,,. M'\[p\] ,,.,~ p ,,,,a M\[P\] ,,.~ q .,/,,.,.,: 
M'\[P\] (M\[P\]) ",:.s o. t,,.pl,: of tb,, <,:t,m,sio',,,.s .fo'v 
M' (M. '.,xst.:cl, i vcly ) of prcdica, t,#s i'.. P 
in l,he a, bovt! order, ~t grealcr ilttcrprel,a,t,ion is 
more prtd'cral)h;. 'l'he a,lmvc, order h~tuidvcly 
me,ms I,ha, l: logical int, cq)rtfl;~d,iotts which m~txi- 
ma,lly sa,lis\[y a, subsel, ot7 ~li ~ ;brt~ prNTcrM,lt!, a,nd 
if l,htu'(! arc iul,crprel,a,l,ious which mLl,isf~g lit(', mmm 
ft)rllllll~ts ill q)l. l,hcll iltt,crl)rt'.l,;tt;iOllS which ma,xi- 
maAly smisfy ~t subsel; of ~1)2 i~rc prcfvra,blc, aml... 
a,nd if l here arc intc.rprtfl;a,I;ions which sal,isf'y dtc 
sa,me t'orn)ul~ts in (1) z' ~, I:h(m it, l,('.rl)rel~tl:ions which 
m;~xitmdly sM,isfy ~t subs('.l, of il) \]'~ ~ue l>r(4'(~ral)h'.. 
Lcl; A I)c ~r \['Ol'ltlllla. Wc s,~y (:hal: a, logicM in- 
l;erpr(,.l;Mion M is the "m,o,st prcfc~'a, blc 'm, odcl M, I,k,c 
cla,~.~ of mml, cl,s of A w.r.t.. > if t, h0.re is no nIo(tcl 
M' of A in l, hc class such l:h,td, M' > M a,ml uo(; 
M > M'. 
According t,o t, hc result of (Lifschil,z. 198,5), wc 
ha,re l,hc followhlg ('OITt',S\[)OIII\[(:IIt;C I)(:l,ween syII.- 
La,cl.ic deli ldl,itm mM scnl~mlic dctinil,ion. 
Theorem 1 A Iogica,1 in.l, crp'.ct.,l,io~, M i,s a, 
"m.odcl o,f (1) iJf M i,s I, hc "mo,sl, l)'r@:rablc modal 
w,r.t. > h~, tlw cla,,~,s of'm, odcl,s of A. 
3 Disambiguation by Prioritized 
Circumscription 
\]11 order l,o Hse prioril;ized (:ir(:umscripl:ion for a, 
disa,lt~l)iguMion (,a,sk, wc nud~t: I he tol\]owil~g (;of 
resl)OlMtmce lint,worm I'ornmla,s in tim (h:linilion 
t)t' l)rioril,izctl circunmcripl,ion ~elItl iit\[orlmtl,ioll itl 
IHI.t.llI'}L1 \[al,llgll}l, gt'.. Ill l,he syn(;a*:dt: th,.linil:ion of 
l)riorilized circulnscriplion in S0.cl.ion 2, we t:orrt> 
st)trod A wilh int'ormat.ion al),:tul: given scnl:ences 
tutti t~ckgromtd knowh~dge wlfit:h is ~dwa,ys trut'. 
in ~my sil,md;ion. And, wc rcga,rtl ~I} a,s ~ hi)h: o\[ 
|)r(q~H't,,llCC, l'llh~s. Nol,c I;\]t;t,l, t)l'(!\[~H'Cllt:t~ l'lt\[Cs ~-l,i'c, 
plll, into hicraxchy ~mcording l,o ,St,F(!llgl;h of \]-II'('.t'~',I'- 
Cllt:l.! I'Illcs. :\['hcIl, l;\[IC IIIOSI, pl"cfcr~dJc models cor- 
rcsl)ond wil;h l;hc most l)refcra,1)lc rcmliugs since 
C;-Lt;h tltodc\] s~4islies Sl,l'onp~(!r 1)rt4't',rtm(:e ruh~s a,s 
much a,s pt)ssil)lt' m.l l,herct'ore, t ht! syl~l,a,t:l,ic def- 
iniliou bt!ctmms a Slmt:ilit:M, ion o\[ l.he l~refcra,lflc 
rea,ding,~ by Fhc, mtm I. 
In l,hc subst!(lucnl, std),sct:l:ions, w(' lirsdy fix mt 
C, Xl)erimtml~d h)gica,l represenla, l,ion of S(!lli;elt(:es. 
I)a.t;l(grt)und kuowlcdgt: m.t prt:ferences. Then. we 
l,rea\], l,hc c×~mq~lc, in Set:don it by the logic;d rep- 
l'(~s(~tll,~LI,iO t|. 
a.1 Logical Representation of Sentences 
and Background Knowledge 
Wc uso ;m axla~pbfl, ion of KowMski's evenl, caJcu- 
lus (Kowalski and Sergot, 1986}. Howcwu'. l;hc 
ith'.;r of dis;unbiguat,ion in i;ltis 1)~rper does not tie- 
pond ou ,t p;trl,icut~tr represcnt, al;ion. We ~tssutne 
{,\[lg-'L\[, CH.ch SClli,CIICC exl)ressc, s }gll eVCltI,. For CX~Llll- 
pit:, a, SClJt,encc' "John g~tw~ the l:ch'.scol)C t;t) t, ho, 
lnmt'" is rcprc.scnLcd a,s the \[o\[lowing fornmlm 
,u:t( I,\], ( ;ivc ) A actor(E, J,,h,'.,) A 
okjcct( t';, 51'clcscopc ) A "rccipie,~.t( E. M .,~,) 
A (:OII/\[)I('.X sCIII;CIIC(! is Slll)\[)OSe(| t,O \[)C. dCCOlll- 
posed inl;o ~ seL of siluple senI,e:u(:es which is t, rmm- 
la,i,cd into t,hv. n, bovc rcprc.sentat,ion. Ambiguities 
a,rc expressed by disjunct;ions. For exmnplc., t, hc 
scntel.:C "gohn s;tw a man wil;h sr l;t~'lcscope" is 
c×pressed a.s follows. 
l,i'm,c( l':, T) A re:i,( I,, ,5cc) 
A a,:t,,r(15..I.h...) A ,,lU,,,:t(15. M ..*,.) 
A(dc' ,'~,ct ( t . I , lcscotm ) 
V(timu( E', 7') A m:t(E', llo, vt:) 
A.,d,.'( l',/, M.,'n,) ' :' A ob,~ ccl,(\['; . Tclt:scopc) )) 
The laM: CoIIjllIICt; c.xpre.sst~s mnbiguity in l,he 
l)hra,sc ' "wilah ~t I clcst:opc." (used ~ts ~L devit:e or car- 
tied by 1,11(': ma,n). 
In tahiti,toll I:o l, he SClH;tttl,i(: rel)l'CSCld,a.l,ion, we 
also use synl,acl,it:M informal>ion fl't)n~ a, tmrser 
so l;ha\[; gr~tlttln~d,i(:aJ 1)r(~ft~r(,,lt(;(: rlll(',s (:~tH H(', ex- 
l)rcsscd. For ex~mq)le, we show some of tim gr,m> 
mal,it:;d inforlmtl:ion of l, hc s(HII;tHIcc "',John gatve 
dm I clcscopt~ l;t) l,he ma, n'" ;ts follows. (We assunm 
t,hM, stml;ct|cc munl)cr is 1). 
s'Mtj (\], ,/ok,'Jt) A 'vt:'r b( l, G'i'u, ) 
Adi:r~ t:t obj (I, 7'clt:~scol)c ) 
Ai'n, di'rcct obj (1.. M,vn,) 
Ai'n,_thc._,~tm, te'.,cc( 1, ,h)It,~, ) 
Hy usi Ig dtcsc l)¢Lsi(: t)rcdic;tl,es, w('. t:ml rcpl'(',SC, lll, 
l)~u:kground klmwh;dgt: which m:c ~dwa,ys wdid. 
For cxmnpb. I)a,cl(ground knowlcdgc~ "q\]' a,l has o 
al l imt,. i, ~md a,l is not equal t,o ~2, I;hcn we dots 
not, ha,vc o atl; I;imc {'" c;ut t)e t'.xprcssed in l,he fol- 
lowi nl~; formula ~ • 
VcV,/~V6f,\] Vo, 2 VoVc 1 ( 
(/,'i'm,c(c., 'i) A ¢u'L(c, Ii.,'vt') A ,u:t,,','(c. a,1) 
Aol, jc.l.(c o) A ~cq(aq, a,2)) D (2) 
((/,i.'m.c(c.1, 'i) i a, ct(Cl~/la,.m!) 
Aat:/,o'/'(, 1. ",2 )) D nobj cot (cl. "))) 
a.2 Logical Ret)resentatlon of Preferences 
Wo rcl)rcselll, a, prcfercnt:c rlLlc ~-ts ~t formula, in ,,1) in 
I,hc synl,;u:dc th'.lilfil;iou of prioril;izcd circuinscrip- 
l,iott ~tI~t ha.ndle ,~ priorit, y a, nlong; \[)l't:ft~rences by 
tWo ignoi'c joint ownership for simplicity. If' wc 
w.uhl like t:o cousider the possibility, wc cml i'cprcscnt, 
the \['Ol'l|lUlat ~ts I,lt(~ st,roll\[g(~st; t)r(J'ercnl;t~. 
903 
imtting stronger preferences into a stronger hier- 
archy of l)references. 
For example, consider the following two gram- 
marital preferences. 
1. If "He" appears in a sellteltce as the subject 
and the subject in the previous sentence is 
male, then it is 1)referal)le that "He" refers 
to the previous subject. 
2. If "He" appears in a sentence as the subject 
~tnd someone in the previous sentence is male, 
then it is preferable that "He" refers to the 
one in the t)revious sentence. 
Suppose that the former is stronger than the lat- 
ter. This priority of the t)references means that 
the formula: 
(isa(a, Male) A subj(i, a) 
Ain~th, e_sentence(i + 1, He)) D eq(a, He)(3) 
shouht be satisfied as much as possible for every 
a and i, and if it is maximally satisfied then the 
following forinnla: 
( isa( a, Male) A in_the_sentence(i, a) 
Ain_thc_sentcnce(i + 1, He)) D eq(a, He) (4) 
shouhl be satisfied as much as possible for every 
a and i. 
We can represent semantic preferences as well. 
For exalnple, a preference "If al sees a2, then a2 
and al are not equal" means that the following 
expression shouhl be satisfied as nmch ~s possible 
for (;very e, (t,1 and a2: 
(act(e, See)A actor(e, a,1)A object(e, az)) D (5) 
=eq(a2, a,1 ) 
Note that the Mmw; is a preference rule because 
there is a possibility of reflexive use of "see". 
3.3 Example 
Now, we are ready to treat disamhiguation of the 
sentences used in Section 1 by prioritized circum- 
scription. 
We consider the following l)ackground knowl- 
edge which is always true. We denote the con- 
junctions of the following ;~ioms as A0(P) where 
p d~.f (eq, is, time, act, actor, object, 
recipient, device, sub j, in_the_sentence). 
1. If al is equal to a2 then a2 is eqnM to az. 
ValVa2(eq(al, a2) D eq(a2, al)) 
2. If al and o,2 are equal and a2 and aa are 
equal, then al and a3 are equal. 
ValVa2Va3 ((eq(al, a2 ) A eq(a2, a3 )) D 
eq(al, a3 )) 
3. if al is equM to a2, then a2 is an actor of al's 
action, too. 
VeValVa2((cq(al,a2) A actor(e, al)) D 
aetor(e, a,:~ )) 
4. if a use o as a device at time i then a has o 
at tilne i. 
VeViVaVo((ti,ne(c, i) A actor(e, a) 
Adeviee(e, o)) D 
3e I (time(el, i) A act(el, Have) 
Aactor( el, a) A object(el, o))) 
5. If al has o at time i, and al is not equal to 
a2, then a2 does not have o at time i. 
This is same as (2). 
We consider the following preferences. 
1. If ax sees a2, then ax and a2 are not equM. 
• (P, e, =(5) 
2. If a is lnale and a is the snbject of i-th sen- 
tence and "He" is in the next sentence, then 
a is equal to :'He". 
• 2(P, e, a,i) =(3) 
3. If a is rome and a is in i-tll sentence and 
"He" is in the next sentence, then a is equM 
to "He". 
¢Pa (P, a, i) =(4) 
4. If someone gives o to a at time i, then a has 
o at time i + 1. This expresses inertia of 
ownership. 
= 
(act(e, Give) A object(e, o) 
Arecipient(e, a) A time(e, i)) D 
?e I (act(el, Have) A actor(q, a) 
Aobjeet(el, o) A time(el,i + 1)) 
5. If" a buys o at tinle i, then a has o at time 
i + 2. This preference of another inertia of 
ownership is weaker than the former prefer- 
ence 1)ecause time interval is longer than the 
fornler t)reference. 
/b~(P, e, a,o, i) = 
(act(e, B,,v) A actor(e, a) 
Aobject(e, o) A time(e., i)) D 
?el (act(el, Have) A actor(el, a) 
Aobject(e~, o) A time(ca, i + 2)) 
We assmne that ~ is a formula which should; be 
satisfied in the first place, O~ in the second place, 
(pa ~ in the third place, q54 in the fourth place and 
• ) in the fifth place. 
Example 1 We con.sider the following sentences. 
John just saw a man with a telescope. 
He bought the telescope yesterday. 
A logical representation of the above sentences ix 
as folh)ws and we denote it as AI(P). 
ti?ne (El, 2) A act(E1, See) A actor ( El, John) 
Aobjeet( E1, Man) A isa(.lob, n, Male) 
Aisa(Man,, Male) A subj ( 1, John) 
Ain_the_sentence ( 1, John) 
Ain_t he_sentence (1, Man) 
A(de'vice( E1, Telescope) 
V(actor(E~, Man) A time(E~, 2) 
Aact( E~, Have) A object( E\[, Telescope))) 
904 
Atim,'(I':2,0) A act(E2, Buy) 
Aacto'r( E2, He) A object,( E2 , Telescope) 
Ai'n,_thc_sc'n, tcncc( 2, He) 
NoLe thaL we represent "just" as Lime 2 and "yes- 
terday'" a.s time 0. 
In t, he synLa(:tic deiinil;ion of the lliOSl; prefer- 
M,le reading (I), we let A(P) be &(P)A At(P) 
and /~: I)e 5. 
We show an intuitive ext)l;ulation of inferen(:e of 
geLLing tl,e most t)referM)le reading as \[i)llows. 
F'rom the preference 2, "lie" preferably refers t,() 
,lohn. NoLe LhaL although t, he t)reference 3 seems 
Lo l)e alq)li(:able, iL is noL acLually used since the 
stronger prefcre, nce 2 overrides Lhe preferen(:c 3. 
Thell, from Lhe preference 5, John had l;he tele- 
scope el: Lime 2. Frolll Lhe t)reference l, .lohn is not 
equM to the, mau. Then, the man (:aunol: have l:he 
Leles(:ope, at Lime 2 front l;he l)a(:kground knowl- 
edge 5 and l;herefore, t;he t:eh;seope was used as a 
device fi-om the disjuncLiol~ iu A1 (P). We ca.n a(:- 
l,ua.lly prove tha, t &:vice(l':l,telescop(:) is l,rue in 
t, he most 1)referM)le remlings. 
Example 2 Suppose we add the following sen- 
/once t,o the p'rcvious scnl, e'n, ces. 
But, he gave the telescope to the man 
this morning. 
A logi(:al representation relate(t I;o this Sclll;ence is 
as follows. We denot;e the fornml;t as A~(P). 
t,i', 1,,¢" (I'23, \]) A (l, dl;,( E3, (-~i',,e) A acl:or(\],':~, l\] e ) 
Aobjcct( \]'\]3, Telescope) A recipient( Ea, Man) 
Note thai; we represent %his morning" a.s time 1. 
In l;his case, we h;t a(P) be A0(P) A A~(P) A 
A2(P) in the synta(:t:ie definil;ion. The, u, reading 
of "'widl ~t t;elescol)e" is (:hanged. From l:he pret: 
erence 4, Lhe 1,H-Ln shouhl have had Lhe l;eles(:ot)e 
a(; I;ilne 2. if the, (;eles(:ol)e were used as a de- 
vice el; dnle 2, John wouhl Mso have Lhe Leles(:ot)e 
aL dm same time a(:(:ording to background knowl- 
edge 4 and it (:ontradiets background knowledge 5. 
Then, the weaker t)referen(-c 5 is rel;r~cl,ed Lo ~woid 
contradiction and the stronger preference 4 is sur- 
vived. Therefore, in l;he mosL t)refera,1)le rea,ding, 
Lhe ll\[;l, li h~ul Lh(,' telescot)e at l;inle 2. 
4 HCLP language 
Now. we discuss an imt)lementation of priori- 
tized (:iv(:ulns(:ritfl:ion by IICI~P. FirsLly, we briefly 
review ~t hi(,r;Lrchi(:M consLrainL logic l)rogr~ttn - 
ming(HCM )) language. We follow t.he definition 
of (l~orning el; M., 1989). 
An HCI,I ) program consisLs of rules of (;lie form: 
h: -bl ..... b.., 
where h is a predicat, e and each of hi ..... b,,, is a 
predicate or a constraint or a 1M)eled (:(restraint. 
A lal)eh'.d (:onstrMnl; is of the form: 
label C 
whe,'e C is ~t constraint in specitie (lomaill and 
label is ~ label whi(:h expresses st, rengl,h of the 
(:onsl;rainL (/. 
The oper;d, ionM smmmties for HCLP is similar 
Lo CLP exeet)t manipulating a (:Ollstraint hierar- 
chy. In \[\[CLP, we a(:cmnulate labeled consLrMnts 
to form a constraint hierarchy by each 1M)el while 
exe(:uLing CLP until CLP solves all goMs mM gives 
a, reduced required constrMnts. 'Phen, we solve 
constraint hierarchy wiLh required const, rMnLs. 
To solve (:onstrainL hierar(:hy, we firstly lind a 
m;~ximal subseL of constraints for the strongest 
level which is (:onsistent with the require(l con- 
strMnl;s. Then, we try to find a inaximM subset of 
consLraints in the se(:ond strongest, level with re- 
spe(:l: to t, he union of the. required consLrMnt, s and 
Lhe lnaximal (:onsisl;ent subset for l.h(; sLrongest, 
level .... and so on until a maximM consisl;ent sub- 
set of COltsLraints in the k-th strongest, level is 
added. The.n, an assignment which satisfies t;1,e 
final seL of consl;r:tinl;s is eMled a sol,.tio'n,. 
O a.,t be assignm,;nts C0'(and 
t)e a se.t of constraints in the strongest, level of 
tl,e hierarchy sat, istied t)y 0(amt o), and C~(and 
~2 C¢) l)e ~L set; of (:onstrMnts in the secon(l strongest 
level of t.he hierarchy satisfied by 0(and a) .... , an(l 
C~'(,md C a:).~ be a set of (:onstrMnt.s in f.he t,>f.il 
strongest level of Lhe. hierarchy satisfied by 0(an(t 
(7). 
0 is locally-predicate-better (Borning el, el., 
1989) Lluul (~ w.r.L, t, he (:onstrainl. hierarchy if 
there exists i(t < i < k) such that for (,'very 
j(:l < j < .i c:; : ,,na c:; c 
We can prove thaL if 0 is a solution, t, hen there is 
no assignment ~r which satisfies the required (:on- 
strMnLs and is locally-predicate-better than 0. 
Note l;hal; t;ll(: definition of loeally-t)redicate- 
l)etter (:onlpm'~to," is similar to the definition of 
the orde, r over logical interpretation in the t)ri - 
oritized cir(:umscription. The difference is that 
locally-1)redicate-better (:omparator (:onsiders as- 
signment:s for variabh,,s in constraint;s in IICLP 
whereas t, he order over h)gical interpret.aLton COil- 
siders ~msignmenl;s of truth-value for formulas in 
1)rioritized circumscril)tion. 
5 Implementation by HCLP 
language 
In order to use, HCLI ) l,~nguage h)r iml)lemen- 
~ation of prioritizcd (:ireunmcripdon, we need 
Lo change t'ornnflas in 1)rioritized circumscription 
into (:onsl:raints in tlCLP. It is done as follows. We 
introduce a domain closure axiom so Lhat we only 
consider relevant constants used in the given sen- 
ten(:es. Then, we inst;mtiztte universM-quandfied 
variM)le, s in background knowledge mM free vari- 
ables in preferen(:es wit, h the relevmlt (:onsL;mts 
and iul~rodu(:e Skolean fimctions for existential- 
qua.ntified variables. 
905 
For ex~mll)h'., we lu~ve the following fl)rmula l>y 
inst:anl,i~tting t)r(',f('rence 4 in Section 3.3 with Ea 
for c and t;h(', m;m for a ~md th(: t(;lescol)( ~. for o 
,rod 1 for i and introducing a. Skolem functioll f: 
(act(E 3 , Give) A objcct(Ea, Tcle.scopc) 
Arccil)ic'~,l,( E a, Ma,7~,) A timc( Ea, 1)) D 
(a.,t(f(Ea, Man, Tclc,scop( , 1), Ilavc ) 
Aactcrr(f(Ea, Man, Tclcsco't)c, 1), Mw~r) 
aot, jcct( f ( \[~'a, Man, Telescope, 1), Tclc scW)c ) 
AI, imc( f ( Ea, Man, Telescope, 1), 2)) 
By this trm~slal;ion, every forlnula t)e(:om(',s ground 
a,nd we r(.g,'trd a, ditf(,r(mt ground atom as gt (liffcr- 
ent; propositional synlbol. '\]'11(',71, every fornlula, 
in t)rioritiz('d circumscription can 1)e rcg~r(h,'d ~ts 
a 1)ooh'mt (:onsi:raint in HCLP. We tra, nsla.te ~dl 
formulas in the syntactic detinitiol~ of l:h(.' back- 
ground knowledge and t:he s(',nten(:(',s in \]~',X\[Llll- 
ples 1 &71(l 2 into boolean (:OllSl;l'a, ittt, s ill oTlr IICM ) 
la, ngu;~ge (Sat;oh, 1990). Then, fi'om 1,\]m two s('7~- 
ten(:('s in I~\]xa, ml)le 1, our IICLP l~mgu~tgc givc's 
th(' following result as ~c part of a solution: 
timc(E~,2) - true 
a.to'r( l¢~, ,\]oh,'t~,) = true 
,b.jcct( E~, Man) -- true 
a,,/,( 177. Scc) true 
de'vice( ET , ~l'clc scope) = true 
which m('~ms l;ha, t the t, eh',scope is used as a (h'~vi(:e. 
And, our ItCLP language gives l;|t(? following 
result for tim S{',IlI;(*,IIC(',S in Exa, nll)le 2: 
tim, c(ET, 2) = true 
a,(q~o~" (El, .lob',,) true 
ol).\]cct( l,\]l, Ma,'n,) = l;rTte 
a,¢'t ( E:t, Se.c ) = l;ru(~ 
d~ vicc( l')~, Telescope') = fiflse 
,,,:to r(l¢'~, M (,,',,) = true 
ti'm.~(E~. 2) - true 
(tcl,( lb'tl , \[\] (t,'OC ) t rtt(', 
obje r't( \]5'{, TclcscW)e ) = true 
which lllCa,llS thai: the mint ha,s t, he t(~lescot)(~ (a, ll(1 
il; is not used a,s ~ device). 
6 Conclusion 
We belicw; tim, l: dw, following are conl:ribul,ions of 
this 1)~tmr. 
1. We (~xa.mine ;t fi~asil)ility of priorit:ized (:ir- 
(:Uln,script;ion for specifying taw. most 1)refer - 
al)le re~u(ling by cons|de.ring a. (lisaml)igtt~ution 
t;~sk in the (:on(:rct(~ exemq)h~s a.nd show 1;1l~-~1; 
We cmt represent the task quit.e natur~flly. 
2. We discuss an iml)hmw.l~tatAon of (lis~m> 
biguation wil:hin gm HCLP la, ngua,ge by 
showing ~ correslmndc'ncc between a, prior- 
it:y oww preference rules in prioril:ized cir- 
(mms(:rit)t, ion m~d a (:Olmtr;fint hi(',rar(:hy in 
ltCI,P. 
As a~ fut:ur(,' r(:s(',a, rch, we ne('J I;he lbllowing. 
1. We wouhl like to cxa.min(~ a comt)ut:a.i:iomd 
(:Oml)h'.×ity o| dismnbiguation by tI(,'I,P. 
2. it is bett(;r 1;o learn preferences mltom,'*tic**lly 
in sl:(',a(t of specifyillg preferences by user. 
One, at)l)ro~Lch for h'~Lrning is to buihl ml ill- 
(;(:ra(:i:ive syst, em su(:h t, luL(: the system shows 
t,o a user a set of possible readings for given 
sc'nt(m(:(,s and the user gives ~m order over 
possible readings, if'hen, the, syst;(,m wouht 
be abl(', to l(,~trn pref(,ren(:(~,s 1)y gener~tlizing 
the order. 
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