Anaphora Resolution of Japanese Zero Pronouns 
with Deictic Reference 
Hiromi Nakaiwa and Satoshi Shirai 
NTT Communication Science Labor~ttories 
1-2356 Take, Yokosuka-shi, Kanagawa-ken, 238-03, Japan 
{nakaiwa, shirai }~nttkb. ntt. j p 
Abstract 
This paper proposes a method to resolve 
the reference of deictic Japanese zero 
pronouns which can be implemented in 
a practical machine translation system. 
This method focuses on semantic and 
pragmatic constraints such as semantic 
constraints on cases, modal expressions, 
verbal semantic attributes and conjunc- 
tions to determine the deictic reference 
of Japanese zero pronouns. This method 
is highly effective because the volume of 
knowledge that must be prepared before- 
hand is not very large and its precision 
of resolution is good. This method was 
implemented in the Japanese-to-English 
machine translation system, ALT-J/E. 
According to a window test for 175 zero 
pronouns with deictic referent in a sen- 
tence set for the evaluation of Japanese- 
to-English machine translation systems, 
all of zero pronouns could be resolved 
consistently and correctly. 
1 Introduction 
In all natural language, elements that can be eas- 
ily deduced by the reader are frequently omitted 
from expressions in texts (Kuno, 1978). This phe- 
nomenon causes considerable problems in natural 
language processing systems. For example in a 
machine translation system, the system needs to 
recognize that elements which are not present in 
the source language, may become mandatory el- 
ements in the target language. In particular, the 
subject and object are often omitted in Japanese; 
whereas they are often mandatory in English. 
Thus, in Japanese-to-English machine translation 
systems, it is necessary to identify case elements 
omitted from the original Japanese (these are re- 
ferred to as "zero pronouns") for their translation 
into English expressions. 
Several methods have been proposed with re- 
gard to this problem (Kameyama, 1986) (Walker 
et al., 1990) (Yoshimoto, 1988) (Dousaka, 1994). 
When considering the application of these meth- 
ods to a practical machine translation system for 
which the translation target area can not be lim- 
ited, it is not possible to apply them directly, both 
because their precision of resolution is low as they 
only use limited information, and because the vol- 
ume of knowledge that must be prepared betbre- 
hand is so large. 
The zero pronouns that must be resolved by a 
machine translation system carl be classitied into 3 
types; (a) zero pronouns with antecedents within 
the same sentence (intrasenteutial), (b) zero pro- 
nouns with antecedents elsewhere in the text (in- 
tersentential) and (c) zero pronouns with deictic 
reference (extrasentential). Regarding type (b), 
Nakaiwa and Ikehara (1992) proposed a method 
to determine the intersentential antecedents us-- 
ing verbal semantic attributes. The rules used 
in this method are independent of the field of 
the source text. Therefore, anaphora resolution 
may be conducted with a relatively small volume 
of knowledge, making the proposed method very 
suitable for machine translation systems. Further- 
more, for type (a), Nakaiwa and \[kehara(1995) 
proposed a method to determine the intrasenten- 
tim antecedents of Japanese zero pronouns using 
semantic constraints such as verbal semantic at- 
tributes and pragmatic constraints such as types 
of conjunctions and modal expressions. 
In this paper, we propose a widely applica- 
ble method to determine the deictic referents of 
Japanese zero pronouns (type (c)) using not only 
semantic constraints to the c~es but also fln:ther 
semantic constraints such as verbal semantic at- 
tributes and pragmatic constraints such as modal 
expressions and types of conjunctions. 
2 Appearance of Zero Pronouns in 
Japanese Texts 
In order to understand the distribution of zero 
pronouns with antecedents that do not appeal" in 
the text, in this section, we examine which zero 
pronouns nmst be resolved and where their an- 
tecedents appear, using a test set designed to eval- 
uate the performance of Japanese-to-English ma- 
812 
chine translation systems (lkehara et al., 1994). 
'l'he results of the examination of zero pronouns 
and their referential elements in the flmctional 
test sentence set (3718 sentences) are shown in 
Table l. There were ~, total of 512 zero pronomls 
in 463 sentences. The location of referential ele- 
ments can be divided into 2 kinds: those expressed 
in the same sentence, and those, not expressed in 
the same sentence. 'rim latter were fltrther classi- 
tied into 6 kinds. 
• The zero pronoun is not translated be(:ause the 
passive voi(:e is used. 
• The referent is the writer or speaker, I or a 
grollp~ we. 
• '\['he referent is the reader or hemmer, you, 
• The referent is human but it is not known who 
the human is. 
• The zero pronoun shouhl be translated as it. 
• The rcf(,rent is another specitic element. 
According to this study of the fimctional test 
sentence set, in 373 out of 512 instances (73%) 
the antecedent was not expressed in the sentence. 
Zero pronouns conhl be left unexpressed by con- 
verting the translation to the passive voice in 173 
instances (34%). 'Fhe other zero pron(mns, 200 
instances (39%), referred to antecedents that (lid 
not appear in the sentence. \[n 69 ()tit, of the 200 
instances (13%) zero pronouns were th.e subject of 
the sentence and referred to the writer or speaker 
I or a group we. Further examination revealed 
that only in these 69 instances did the verb that 
governed them express some modality such as - 
shilai '- want to -' or -shiyou 'Let us -' or the 
verbs were omou 'tMnk' and other such words in- 
dicating ~TI\]\[INKING ACTION'. Furthermore, zero 
pronouns that were the subjects and that referred 
to the reader or hearer you, ainounted to 28 out 
of the 200 instances (5%). In these 28 instances, 
~he verbs that governed these zero pronouns ex- 
pressed the modalities of- subekida 'should' or 
-sitehanaranai 'nmst n(it'. Similarly, modalities 
and verb types can be used to identify it or the 
'unknown human'. This tyl)e of zero t)ron(mn 
can be resolved by deducing their referents us- 
ing modality or categor:ized verl)al semantic at- 
trilmtes. 
3 Deictic Resolution of Japanese 
Zero Pronouns 
lhused on the results shown in section 2, we pro- 
pose a method to resolve Japanese zero pronouns 
whose antecedents do not appear in the texts. 
3.1 Dei('tle Resolution using Semantic 
Constraints on Cases 
~lb resolve Japanese zero pronouns whose an- 
tecedents do not appear within the texts, it is pos- 
sible to use the semantic constraints on verbs' case 
Table 1: Distribution of zero pronouns and their 
referential elements 
~~ Loc. of 'referential elements' \[ -- 
,t- II p~w I l~-yo.--7\]- ~,, in. I t~l 
elements to deduce like.ly referents. The semantic 
information used to estimate supplementing ele- 
ments is similar to the constraints on cases used 
tbr selecting the transfer patterns in a machine 
translation systeln. Figure \[ shows an examph: 
of a transtb.r pattern in a Japanese-to-English tna- 
chine translation syst, em for the ,lapanese~ verb iki- 
masu 'gC. Figure 1 shows how, if the ,lapane.se 
verb is ikimasu 'go' and the noun phr~use with a ga 
pc.riMe, which shows a subject, has the senmntic 
attribute SUBJECT, VEIIICLES OR, ANIMALS~ then 
the verb should be translated as 'go'. In this pat- 
tern, if Lit(; suhject N I beeonles a zero l)ronoun, 
the system tries to estimate the referent using se- 
mantic constraints. But, in this case., it is impos- 
sible to estimate the referent as one type, be.cause 
there are three kinds of semantic constraints. In 
the transfer pattern, the semantic constraints are 
left unfulfilled if they are not used in selecting 
the appropriate translation. So, this method fre- 
quently l)oses di\[\[iculties in pinpointing elements 
to be estimated. 
According to die results that were examined in 
section 2, this type of zero pronoun can be re- 
solved by deducing I;heir reDrents not only /ts- 
ing semantic constraints to the cases but also us- 
ing modality or categorized verbal semantic ato 
tributes. For example, in this case, it is efl'cetive 
to determine the referents corresponding to 'I' its- 
ing the verbal semantic attributes of the pattern, 
N \['S PIIYSI(JAL TRANSI,'ER and the polite exl)res- 
sion -maser. 
NI(suBJEC'rS, VEHICLES OR ANIMALS)-ga iki-mcu~u 
N\]-SUBJ go-I'OLITB 
=> N I go. 
Figure l: J apanese-toq~Jnglish transfer dictionary 
3.2 Deietic Re, solution using Semantic 
and Pragmatic Constraints 
According to the analysis of the results shown 
in section 2, we found that modal expressions 
and verbal semantic a.ttribntes are usefltl in (le- 
retraining the dei('tic referents of Japanese zero 
pronouns. Also, we can estimate the types of con- 
jun<:tions that are effe(:tive in determining the tel< 
813 
erents in a complex sentence. In this section, we 
examine three kinds of semantic and pragmatic 
constraints, modal expressions, verbal semantic 
attributes arid conjunctions. 
3.2.1 Constraints Based on Modal 
Expressions 
Modal expressions in Japanese are expected Co 
be the most powerful constraints for estimating 
deictie reference. For example, in the case of zero 
prononns in ga-cases 'subject', the referent be- 
comes the writer or speaker, I or a group, we if the 
sentence has the modal expressions, -sitai '4) want 
to -' HOPF, or -silchosii '¢ want ¢ to-' CAUSATIVE 
HOI'E; the referent becomes the reader or hearer, 
you if the sentence has the modal expressions, - 
sileha-ikenai '4) must not -' PR()IIIBIT or -subekida 
'¢ should -' OBLmA'rmN. If there are no refer- 
eat candidates found within the surrounding text, 
the referents can be determined using the previous 
constraints based on modal expressions. 
3.2.2 Constraints based on Verbal 
Smnantie Attributes 
Constraints b~sed on verbal semantic attributes 
can be divided into tile \[bllowing two types: 
(1) Constraints based on the types of verbs 
'Give and take' expressions such as the verbs 
moran 'get' and yaru 'give' and transfer expres- 
sions such as the verbs iku 'go' and h'ur'u 'come' 
can deternfine the referents of zero pronouns with- 
out modal expressions. For example, if the ga-case 
(subject) of the sentence whose verb is ,nora'tt 'get' 
becolnes a zero pronoun, the referent becomes 1. 
In the case of verb kuru 'come', the referent be- 
comes an element other than i, tbr example you. 
These kinds of verbs inrplicitly indicate tile rela- 
tionship between the writer/speaker and the ref- 
erent of the ga-case (for example, the empathy 
(Kuno, 1978) or the side of the territory of in- 
fbrmation (Kmnio, 1985)). Based on these prop- 
erties, tire deictic referents of Japanese zero pro- 
nouns (:an be estimated. 
(2) Constraints based on the types of verbs 
and modal expressious 
I,;ven if the referents of zero pronouns (:an not be 
determined using modal expressions or tile types 
of verbs, the referents can sometimes be deter- 
mined using a combination of modal expressions 
and the types of verbs. For example, it1 the fol- 
lowing Japanese expression, the ga-case becomes 
a zero pronoun. 
(1) hon-wo gon-da 
¢-SUBJ book-OI3J \]read-PAST 
I read a book. 
In this sentence the experience of the 
writer/speaker, 1 is suitable for the reference of 
the zero pronoun. As shown in this sentence, if 
the ga-c~use in an expression with a verb whose 
semantic attribute is ACTION and modal expre.s- 
sion is -ta PAST, becomes a zero pronoun, it will 
be translated by a truman translator ~s 1. In a 
similar way, if the ga-case in an expression with 
a verb whose semantic attribute is ACT1ON and 
modal expression is -darou 'will' FSTIMA'FION, be- 
comes a zero l)ronottn, the referent is you. Such 
constraints using both verbal semantic attributes 
and modal expressions can be used to determine 
the deictic reference of 3 apanese zero pronouns. 
To write constraints based on types of verbs eflbx:- 
tively, we used the 97 verbal semantic attributes 
(VSA) proposed by Nakaiwa (1994). 
3.2.3 Constraints based on Conjunctions 
Sometimes the deictic referents of Japanese zero 
pronouns can be determined depending on the 
types of conjunctions. The constraints based on 
the Japanese conjunctions can be divided into the 
following two types. 
(1) The eonstralnts on <:as(; sharing depend- 
ing on the types of conjunctions 
Minami (1974) and Takubo (1987) proposed that 
(lilt'event Japanese conjunctions cover or share 
different cases, l,'or example Minanfi divided 
Japanese conjnnctions into three kinds, A, B and 
C. A complex sentence which includes A type 
Japanese conjunctions, such as tsu-Lsu 'while' and 
nagara 'while', shares one ha-case ('l'opie) and one 
ga-ea,se (Subject). In the case of B type Japanese 
conjullctions, stlch a8 lzodc 'because' or tara 'iF, 
one ha.-c~e is shared but not the ga-case. In 
the case of C type J a I)an esc conj u actions, such as 
kcredo 'but' or kedo 'but', neither the ha-case nor 
the ga-case are necessarily shared. According to 
this classification, if two ga-cases in a complex sin> 
tence joined by an A type Japanese conjunction 
were to become zero pronouns and the referent 
of one of the two zero pronouns wins determined 
by the constraints proposed previously, then the 
referent of the other zero pronoun is the same ref- 
erent. These characteristics of Japanese c(mjunc- 
tions can be used to determine the refit'rents of 
zero pronouns. 
(2) Constraints based on conjunctions, 
inodal expressions and verbal semantic at- 
tributes 
Sometimes co-occurrence of conjunctions, verbal 
semantic attributes and moda.l expressions in a 
complex sentence determines the meaning of the 
sentence, and sometimes they determine the deic- 
tic referen(;e of zero pronouns in the sentence. For 
example, in the following Japanese expression, th(~ 
subject of the verb ika-nai 'go-not' becomes a zero 
pronoun but the referent can be determin(;d as the 
writer or speaker, you. 
(2) tokoya-ni ika-nai to, 
¢-SUBJ b~'ber-IND-O13 J go-not if 
If you don't go to the tmrber, 
kami-ga boubou-ni-naru 
hair begin to look unt2dy 
your hair will begin to look untidy. 
814 
This sentence has the meaning that the writer 
or speaker advises that if you do not do some- 
thing, a situation will arise. The meaning type of 
a complex sentence can be determined using the 
rules that the eOBjlIIICtiO\[I is tO 'if' and in the sub 
clause ga-case beeoInes a zero pronoun and tile 
meaning; o\[' the verb is ACTION with negation and 
in the main clause the meaning of the verb is A'P- 
'PlLIBU'FE with tnoda\] expression ni-uaru 'become' 
AT'I'ItlB U'\['\],', '\['ltA N S FE \[1.. 
'\['he meaning type of a complex sentence can 
he determined using the tblowing ruh'.s: when the 
con.imletion is 'if' ~md the sill) clause ga-c;~se be- 
(;on~es a zero \]\]FOlIO/Ill, and the meanil~g of the verb 
is aCTION with negation, and in the main cla.use 
the meaning of the verb is ATTRIBUT\],; with modal 
expression, then ni-naru q)eeome' is an example 
of A'\["PI{IBUTE TRANSI,'I~3R. Using these kinds of 
rules, the meaning types o1" complex sentences can 
I)e determined, and the reference of zero pr(m(mns 
c.an be deterufine.d. 
3.3 Algorithm 
In this sul)section, we t)ropose an algorithm for 
the deictic resolution of Japanese zero pronouns 
using the constraints proposed in this section. 
This algorithm was implemented in a Japanese- 
tod,3nglish machine translation system, so the only 
zero pron(mns that must be resolved are those tlu~t 
become mandatory elernents in li\]nglish. To real- 
ize the previously proposed conditions in an al- 
gorithm, we must consider eases when these tm- 
tece(lelll, s exist in the same selitellCe ;ts well as 
when these antecedents exist in another sent, ences 
in the text, and we must design the algorithm to 
increase the eve.rail accuracy of the resolution of 
zero pronouns. 
Anaphora resolution of zero pronouns is con- 
ducted as follows. In each step in the algorithm, 
when the referential element within or without the 
text is determined, the system checks not only the 
conditions that are written in the following algo- 
rithm, I)ut also the semantic conditions that verbs 
impose on zero pronouns in tile case elements in 
each pattern of the Japanese-to-English transfer 
dictionaries. 
l) \])etection of zero pronouns. 
If they exist, proceed to step 2. 
2) \[CXttlttilte whether there ~r(." ~ntecedents within 
the same sentelwes. (\]"or ex;mtple, a.n~tl)\[tora. 
rcsohttion is performed using Nakaiw~t's method 
(N,tkaiwtt and Ikehara, 1995)), 
If their antecedents can be found, finish the res- 
olution process. Else, proceed to step 3. 
3) Examine whether there are ,~ntecedents within 
other sentences in tit(." text. (For exam- 
ple, a.naphora resolutim, is performed using 
Nakaiwa's method (Nakaiw~t and Ikeharlt, 1992)) 
If their ~mtecedents can be found, linish the res- 
olution process. Else, proceed to step 4. 
4) l)eictie resolution of Japanese zero pronouns us- 
ing verb~tl semautic ~tttributes, modal expressions 
;ted the types of conjunctious are conducted. The 
conditions to (let(:rminc tile referents are summ~t- 
rized in Table 2. 
If their referents ca.n be found, finish the resoh> 
lion process. Else, proceed to step 5. 
5) \[f referentiM elements can not be tbnnd and the 
text can 1)e translated successfully in the passive 
voice, tr~tnsbtte in the passive voice. 
Else, ba.sed on the sm,mntic restrictions imposed 
on the zero pronoun by the verbs, deductively 
generMe itmtphor~t elements. 
Finish the resolution process. 
'\['able 2: Ih~solution conditions of deietic referents 
Ref~ 
tion of Condition ere- 
Zero Ills 
\[IFOll. 
.qa- modal:hope(-sita*) I 
(sul,j) (- sitehosii ) we 
(-simashou) 
~t m~STi~ 
+modal:polite 
(-sirnasu) 
i n o d al : p roll i bit 
(-siteha-ikenai) 
V~ A:ulad(!l" DxTt 1Oll 
q-modal:ol)ligation (-b~ki) 
VSA: 
bodily action 
thinking action 
emol, ive actioll 
emotive state 
bodily transfer 
~~C-- 
elleC alld th(, IliOn%n-- 
mE is abstvaeL 
VSA:attribute 
perceptual state 
~%Z- lllod\[tl ; 
case causal hope 
(ind. (-sitehoszi) _ 
obj.) .: .......... 
L you 
hkl- 
Illall 
(1, 
We, 
y()llj 
.H) 
Comment 
..... i 
sl)eakcr/writm' hopes 
~~ es 
to hearec/l'eadec 
invites 
social vela£ionship 
\])(:tweell 
speaker/writer and 
hearer/reader 
speaker/writer 
prohibits h( arcr/ 
l't)lt(le Iris actioll 
speaker/writer 
ln{ike h e 0A'e i'/rt! 0~d ( ,I,~s 
action obligation 
When the verb that 
show the action or 
emotion that only 
hilHlall Call do 
apl>ears in the sent- 
elite ~tI\]d when theFte 
a,l'e tlool;heP l'e\['el'ent 
candidates, I:hc roll 
el'Oll~S of Zel'O pl'Oll- 
o/illS is hlllp,~ldl 
~F-, - Pronoun of abs~ 
noun should be it 
v~:rbs l:hat h~(~- 
weatheI, Sl.lCh as (l~,S'lt~ 
'hot', -samui 'cold' 
to hearcl'/l'c~lder 
4 Evaluation 
4.1 Evaluation Method 
In this section, w('. show the results of evaluation 
of the method that was proposed above. The 
method to resolve zero pronouns with deictic ref- 
erence was tested using the Japanese-to-l'hlglish 
machine translation system AI/\['-J/F, (lkehara et 
al., 1991). The criteria for tile evaluation and pro- 
eedures used were as folh)ws. 
815 
4.1.1 Resolution Target 
The target was to resolve successfully the five 
types of zero pronouns (ga-case ~-- 'T' or "we", ga- 
case e- "you" , ga-case +-- HUMAN, ga-case ~-- "it" 
, hi-case ~- "you"; 175 instances). These are the 
zero pronouns with deictic reference found within 
the 512 zero pronouns in the a718 sentence set 
for the evaluation of Japanese-to-English machine 
translation systems. 
4.1.2 Rules to Resolve Zero Pronouns 
The rules to resolve 175 zero pronouns were cre- 
ated by examining these zero pronouns using the 
constraints discussed in section 3 (46 rule@. 
4.1.3 Tests for the Evaluation 
'l'o examine the relationship between conditions 
of resolution and accuracy of resolution, we con- 
ducted the following two tests. 
(1) Resolution aeeuraey for eonditions of 
resolution 
We examined the accuracy of resolution depend- 
ing on the types of conditions in a.naphora reso- 
lutiou such as semantic constraints to the cases, 
modal expression, verbal semantic attributes and 
conjunctive expressions. We evaluated the accu- 
racy depending on the types of constraints used. 
(2) Resolution accuracy for rule complexity 
We examined the accuracy of the resohttions to 
see how they were affected by the complexities of 
the rules that were used in the resolution. In this 
test we evaluated the accuracy using simple, easily 
created and universal rules. 
4.2 Resolution Accuracy for Conditions 
of Resolution 
To examine the resolution accuracy under differ- 
ent conditions, we examined the accuracy of the 
method proposed in this paper with the tbllowing 
4 kinds of conditions: 
• using conditions of semantic constraints on cases 
only 
• using conditions of semantic constraints on cases 
and modal expression 
• using conditions of semantic constraints on cases, 
modal expression and verbal semantic attributes 
• using conditions of semantic constraints on cases, 
modal expression, verbal semantic attributes and 
conjunctions 
Table 3 shows the results of the resolution de- 
pending on the types of the rules. As shown in 
tAt the moment, it is difficult to use sentences 
which were not successfully syntactically and semanti- 
cally a.nalyzed for the evaluation of our method. So, to 
evaluate the technical limitation of proposed method, 
we evaluated the resolution accuracy in the sentences 
which were examined to make the 46 rules (window 
test). We will conduct blind tests after we have fin- 
ished debugging the whole system. 
this table, all 175 zero pronouns can be resolved 
using the rules that were proposed in section 3. 
The. introduction of verbal semantic attributes has 
achieved the same accuracy of resolution as the in-- 
troduction of modM expressions (41 entries, 24%). 
From this result, we can say that the verbal se- 
mantic attributes are comparatively as effective 
as modal expressions. The results also show that 
, without using the constraints of conjunctions, 
the accuracy achieved is as high as 85%. 
4.3 Resolution Accuracy against Rule 
Complexity 
To examine how the resolution accuracy varied 
according to the complexity of' rules, we tested the 
accuracy of the method proposed in this paper at 
different levels of complexity. The complexities C 
were evaluated using the following formula, and 
depended on the number of constraints used. 
C = # of modal const.* 1 + # of VSA coast.* 1 
+ # of conjunctions coast.* 2 
In this formula, 1 in the modal and VSA and 
2 in the conjunction indicate the weights. Be- 
cause conjunction constraints affect both sides of 
the unit sentence, we gave the conjunctions con- 
straints a weight of 2. According to this formula, 
the complexity of a rule that has a constraint fbr 
conjunctions and for VSA in the main clause and 
for modM and VSA in the sub clause, becoines 5(-- 
l(modal)*l + I(VSA)*2 + 2(conjunction)*l). 
Table 4 shows the accuracy of the resolution de- 
pending on the complexities of the rules. 46 kinds 
of rules were used in the deictic resolution of 175 
zero pronouns as shown in |;able 4. The accuracy 
of resolution using rules with complexities of 3 or 
less, is 90%, and the accuracy of resolution us- 
ing rules with complexities of 4 or less, is 95%. 
This result shows that the use of the constraints 
based on modM expressions, VSA and conjunc- 
tions can achieve high accuracy using relatively 
simple rules. 
5 Conclusion 
This paper proposes a powerful method for the 
resolution of Japanese zero pronouns with deic- 
tic reference. It was found possible to resolve all 
of the sentences in the window test where the 
referential elements were not in the sentence re- 
solved. This was achieved by the introduction of 
rules based on four kinds of constraints: seman- 
tic constraints on cases, modal expressions, verbal 
semantic attributes and conjunctions. In the fu- 
ture, we will examine the universality of the rules 
that have been discussed in this paper by applying 
them to other texts and examine a method tbr au- 
tomatically acquiring the rules needed to resolve 
zero pronouns with deictic references. 
Acknowledgments: We would like to thank 
Professor Satoru lkehara of 'lbttori University for 
providing valuable comments and suggestions. 
816 
'l'able 3: l{esolution accuracy for conditions of resolution 
\] ,OC~ttiOll 
of Zero 
PPOIIOMn8 
ga-caso (~.bj) 
Ili-(:as{ 
(ind.obj.) 
-} ttesolution Condition 
lI,efiwents AI SS~\[i(~22,'o~T£t~\]l,S~on Cases \] -I-Modal \]Bxprossi .... \[ + VSA \] l-Co,~¢:fiSi~ 
1 or We 23%/7~ 16 o --~8-~o- 6,t ~T{) ~ 17 ---- (iq -- 
-- \]-- --~i% ..... ~\] o% -- ~\]?,ZT+-gg%T~T- -~o ~ a3 - - ~) 
\[TG~IT°,,Z~--C6T---I-T-~_TgC+>/_,,2 -- -(q;f)\[-iT}~-T:iT Z--we .... ~o~,,~, -- m0--T- ~,~ -~7 V-_ ~£- 7 T~I--7 ~° ~- " <~ 
'Fabh~' 4: l{,eso\[ution accuracy for complexities oI" rules 
ltesoludon Condition 
Modal F x I-) i~\] ~~- C~Sgi\]j~u~TR'gl o~-n s 
1- ~T-- 
?5 T--- 
6 
1 l ! \] \] 
L_ ~ J 3- ..... 
_J_Y_L__ A_ _ 
{ \]Oml)lexities ~l~ccv I Accuracy 
or m~lo.~ _ L °r_\[!.'l~'"~ 
0 F0~Only sen,anti ..... ,,st- --O ..... ~ 6~)- 
raints Li ......... ) . -(1~-Ft1~) ~%(-t72a%)--07JT(q~q41~)Y 0 
0 ..... ~ ~\]~&Z ~5~l,,~- 
\] ..... 3o +Ak!L - 8.~%(+1%) (14'.}(-H)) 
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