Tricolor DAGs for Machine Translation 
Koichi Takeda 
Tokyo Research Laboratory, IBM Research 
1623-14 Shimotsuruma, Yamato, Kanagawa 242, Japan 
Phone: 81-462-73-4569, 81-462-73-7413 (FAX) 
t akeda@trl.vnet.ibm.com 
Abstract 
Machine translation (MT) has recently been for- 
mulated in terms of constraint-based knowledge 
representation and unification theories~ but it is 
becoming more and more evident that it is not 
possible to design a practical MT system without 
an adequate method of handling mismatches be- 
tween semantic representations in the source and 
target languages. In this paper, we introduce the 
idea of "information-based" MT, which is consid- 
erably more flexible than interlingual MT or the 
conventional transfer-based MT. 
Introduction 
With the intensive exploration of contemporary 
theories on unification grammars\[6, 15, 13\] and 
feature structures\[7, 19\] in the last decade, the 
old image of machine translation (MT) as a bru- 
tal form of natural language processing has given 
way to that of a process based on a uniform and 
reversible architecture\[16~ 1, 27\]. 
The developers of MT systems based on the 
constraint-based formalism found a serious prob- 
lem in "language mismatching," namely, the dif- 
ference between semantic representations in the 
source and target languages. 1 Attempts to de- 
sign a pure interlingual MT system were therefore 
abandoned, 2 and the notion of "semantic trans- 
fer"\[24, 22\] came into focus as a practical so- 
lution to the problem of handling the language 
mismatching. The constraint-based formalism\[2\] 
seemed promising as a formal definition of trans- 
fer, but pure constraints are too rigid to be pre- 
cisely imposed on target-language sentences. 
Some researchers(e.g., Russell\[14\]) introduced 
1For example, Yasuhara\[26\] reported there was an 
overlap of only 10% between his group's English and 
Japanese concept dictionaries, which covered 0.2 mil- 
lion concepts. 
2Even an MT system with a controlled input 
language\[12\] does not claim to be a pure interlingual 
system. 
the concept of defeasible reasoning in order to for- 
malize what is missing from a pure constraint- 
based approach, and control mechanisms for such 
reasoning have also been proposed\[5. 3\]. With 
this additional mechanism, we can formulate the 
"transfer" process as a mapping from a set of con- 
straints into another set of mandatory and defen- 
sible constraints. This idea leads us further to the 
concept of "information-based" MT, which means 
that, with an appropriate representation scheme, 
a source sentence can be represented by a set of 
constraints that it implies and that, given a target 
sentence, the set Co of constraints can be divided 
into three disjoint subsets: 
• The subset Co of constraints that is also implied 
by the target sentence 
• The subset C+ of constraints that is not im- 
plied by, but is consistent with, the translated 
sentence 
• The subset C- of constraints that is violated by 
the target sentence 
The target sentence may also imply another set 
C~eto of constraints, none of which is in Ca. That 
is~ the set Ct of constraints implied by the tar- 
get sentences is a union of C0 and C~e~o, while 
Cs = CoUC+UC_. When Ca = Co = Ct, we have 
a fully interlingual translation of the source sen- 
tence. If C+ ¢ ¢, C_ = ¢, and Chew = ¢, the tar- 
get sentence is said to be under-generated~ while it 
is said to be over-generated when C+ = ¢, C- = ¢, 
and Cacao y~ ¢.s In either case, C- must be empty 
if a consistent translation is required. Thus, the 
goal of machine translation is to find an optimal 
pair of source and target sentences that minimizes 
C+~C-, and C~w. Intuitively, Co corresponds 
to essential information, and C+ and Cneto can 
be viewed as language-dependent supportive in- 
formation. C_ might be the inconsistency be- 
ZThe notions of completeness and coherence in 
LFG\[6\] have been employed by Wedekind\[25\] to avoid 
over- and under-generation. 
226 
tween the assumptions of the source- and target- 
language speakers. 
In this paper~ we introduce tricolor DAGs 
to represent the above constraints, and discuss 
how tricolor DAGs are used for practical MT sys- 
tems. In particular, we give a generation algo- 
rithm that incorporates the notion of semantic 
transfer by gradually approaching the optimal tar- 
get sentence through the use of tricolor DAGs, 
when a fully interlingual translation fails. Tricolor 
DAGs give a graph-algorithmic interpretation of 
the constraints, and the distinctions between the 
types of constraint mentioned above allow us to 
adjust the margin between the current and opti- 
mal solution effectively. 
Tricolor DAGs 
A tricolor DAG (TDAG, for short) is a rooted, 
directed, acyclic 4 graph with a set of three colors 
(red, yellow, and g'reen) for nodes and directed 
arcs. It is used to represent a feature structure of 
a source or target sentence. Each node represents 
either an atomic value or a root of a DAG, and 
each arc is labeled with a feature name. The only 
difference between the familiar usage of DAGs in 
unification grammars and that of TDAGs is that 
the color of a node or "arc represents its degree of 
importance: 
1. Red shows that a node (arc) is essential. 
2. Yellow shows that a node (arc) may be ignored, 
but must not be violated. 
3. Green shows that a node (arc) may be violated. 
For practical reasons, the above distinctions are 
interpreted as follows: 
1. Red shows that a node (arc) is derived from 
lexicons and grammatical constraints. 
2. Yellow shows that a node (arc) may be inferred 
from a source or a target sentence by using do- 
main knowledge, common sense, and so on. 
3. Green shows that a node (arc) is defeasibly in- 
ferred, specified as a default, or heuristically 
specified. 
When all the nodes and arcs of TDAGs are red, 
TDAGs are basically the same as the feature struc- 
tures 5 of grammar-based translation\[25, 17\]. A 
TDAG is well-formed iff the following conditions 
are satisfied: 
4Acyclicity is not crucial to the results in this pa- 
per, but it significantly simplifies the definition of the 
tricolor DAGs and semantic transfer. 
SWe will only consider the semantic portion of the 
feature structure although the theory of tricolor DAGS 
for representing entire feature structures is an interest- 
ing topic. 
1. The root is a red node. 
2. Each red arc connects two red nodes. 
3. Each red node is reachable from the root 
through the red arcs and red nodes. 
4. Each yellow node is reachable from the root 
through the arcs and nodes that are red and/or 
yellow. 
5. Each yellow arc connects red and/or yellow 
nodes. 
6. No two arcs start from the same node, and have 
the same feature name. 
Conditions 1 to 3 require that all the red nodes 
and red arcs between them make a single, con- 
nected DAG. Condition 4 and 5 state that a de- 
feasible constraint must not be used to derive an 
imposed constraint. In the rest of this paper, we 
will consider only well-formed TDAGs. Further- 
more, since only the semantic portions of TDAGs 
are used for machine translation, we will not dis- 
cuss syntactic features. 
The subsurnption relationship among the 
TDAGs is defined a~ the usual subsumption over 
DAGs, with the following extensions. 
• A red node (arc) subsumes only a red node (arc). 
• A yellow node (arc) subsumes a red node (arc) 
and a yellow node (arc). 
• A green node (arc) subsumes a node (arc) with 
any color. 
The unification of TDAGs is similarly defined. 
The colors of unified nodes and arcs are specified 
as follows: 
• Unification of a red node (arc) with another 
node (arc) makes a red node (arc). 
• Unification of a yellow node (arc) with a yellow 
or green node (arc) makes a yellow node (arc). 
• Unification of two green nodes (arcs) makes a 
green node (arc). 
Since the green nodes and arcs represent defensible 
constraints, unification of a green node (either a 
root of a TDAG or an atomic node) with a red 
or yellow node always succeeds~ and results in a 
red or yellow node. When two conflicting green 
nodes are to be unified, the result is indefinite, or 
a single non-atomic green node. 6 
Now, the problem is that a red node/arc in a 
source TDAG (the TDAG for a source sentence) 
6An alternative definition is that one green node 
has precedence over the other\[14\]. Practically, such 
a conflicting unification should be postponed until no 
other possibility is found. 
227 
sg 
WISH _ num~~ 
"JOHN 
Source T-DAG1 
sg ,a 
num• "WISH o ~ 
"JOHN 
• agent 
"WALK 
Target T-DAG2 
sg 
"WISH num .. .°...-" 
" "JOHN 
agent 
therne~ "WALK 
"WISH 
~ "JOHN 
"WALK 
Target T-DAG4 Source T-DAG3 
red node ~ red arc 
yellow node m m ~ yellow arc 
O green node ......... ,-- green arc 
Figure h Sample TDAGs 
may not always be a red node/arc in the target 
TDAG (the TDAG for a target sentence). For 
example, the functional control of the verb "wish" 
in the English sentence 
John ~ished to walk 
may produce the TDAGI in Figure 1, but the 
red arc corresponding to the agent of the *WALK 
predicate may not be preserved in a target 
TDAG2. 7 This means that the target sentence 
a\]one cannot convey the information that it is 
John who wished to walk, even if this information 
can be understood from the context. Hence the 
red arc is relaxed into a yellow one, and any tar- 
get TDAG must have an agent of *WALK that is 
consistent with *JOHN. This relaxation will help 
the sentence generator in two ways. First, it can 
prevent generation failure (or non-termination in 
the worst case). Second, it retains important in- 
formation for a choosing correct translation of the 
verb "walk". s 
rFor example, the Japanese counterpart "~" for 
the verb "wish" only takes a sentential complement, 
and no functional control is observed. 
SWhether or not the subject of the verb is human 
is often crucial information for making an appropriate 
choice between the verb's two Japanese counterparts 
"~ <" and "~?~7o". 
Another example is the problem of iden- 
tifying number and determiner in Japanese-to- 
English translation. This type of information is 
rarely available from a syntactic representation 
of a Japanese noun phrase, and a set of heuris- 
tic rules\[ll\] is the only known basis for making 
a reasonable guess. Even if such contextual pro- 
cessing could be integrated into a logical inference 
system, the obtained information should be defea- 
sible, and hence should be represented by green 
nodes and arcs in the TDAGs. Pronoun resolu- 
tion can be similarly represented by using green 
nodes and arcs. 
It is worth looking at the source and tar- 
get TDAGs in the opposite direction. From the 
Japanese sentence, 
John +subj walk +nom +obj wished 
we get the source TDAG3 in Figure I, where func- 
tional control and number information are miss- 
ing. With the help of contextual processing, we 
get the target TDAG4, which can be used to gen- 
erate the English sentence "John wished to walk.;" 
Semantic Transfer 
As illustrated in the previous section, it is often 
the case that we have to solve mismatches between 
source and target TDAGs in order to obtain suc- 
cessful translations. Syntactic/semantic transfer 
has been formulated by several researchers\[18, 27\] 
as a means of handling situations in which fully 
interlingual translation does not work. It is not 
enough, however, to capture only the equivalent 
relationship between source and target semantic 
representations: this is merely a mapping among 
red nodes and arcs in TDAGs. What is missing in 
the existing formulation is the provision of some 
margin between what is said and what is trans- 
lated. The semantic transfer in our framework is 
defined as a set of successive operations on TDAGs 
for creating a sequence of TDAGs to, tl, ..., tk 
such that to is a source TDAG and tk is a target 
TDAG that is a successful input to the sentence 
generator. 
A powerful contextual processing and a do- 
main knowledge base can be used to infer addi- 
tional facts and constraints, which correspond to 
the addition of yellow nodes and arcs. Default in- 
heritance, proposed by Russell et al.\[14\], provides 
an efficient way of obtaining further information 
necessary for translation, which corresponds to the 
addition of green nodes and arcs. A set of well- 
known heuristic rules, which we will describe later 
in the "Implementation" Section, can also be used 
to add green nodes and arcs. To complete the 
model of semantic transfer, we have to introduce 
228 
a "painter." A painter maps a red node to ei- 
ther a yellow or a green node, a yellow node to 
a green node, and so on. It is used to loosen the 
constraints imposed by the TDAGs. Every appli- 
cation of the painter monotonically loses some in- 
formation in a TDAG, and only a finite number of 
applications of the painter are possible before the 
TDAG consists entirely of green nodes and arcs 
except for a red root node. Note that the painter 
never removes a node or an arc from a TDAG, 
it simply weakens the constraints imposed by the 
nodes and arcs. 
Formally, semantic transfer is defined as a se- 
quence of the following operations on TDAGs: 
• Addition of a yellow node (and a yellow arc) to 
a given TDAG. The node must be connected to 
a node in the TDAG by a yellow arc. 
• Addition of a yellow arc to a given TDAG. The 
arc must connect two red or yellow nodes in the 
TDAG. 
• Addition of a green node (and a green arc) to a 
given TDAG. The node must be connected to a 
node in the TDAG by the green arc. 
• Addition of a green arc to a given TDAG. The 
arc can connect two nodes of any color in the 
TDAG. 
• Replacement of a red node (arc) with a yellow 
one, as long as the well-formedness is preserved. 
• Replacement of a yellow node (arc) with a green 
one, as long as the well-formedness is preserved. 
The first two operations define the logical impli- 
cations (possibly with common sense or domain 
knowledge) of a given TDAG. The next two op- 
erations define the defensible (or heuristic) infer- 
ence from a given TDAG. The last two operations 
define the painter. The definition of the painter 
specifies that it can only gradually relax the con- 
straints. That is, when a red or yellow node (or 
arc) X has other red or yellow nodes that are only 
connected through X, X cannot be "painted" un- 
til each of the connected red and yellow nodes is 
painted yellow or green to maintain the reachabil- 
ity through X. 
In the sentence analysis phase, the first four 
operations can be applied for obtaining a source 
TDAG as a reasonable semantic interpretation of 
a sentence. The application of these operations 
can be controlled by "weighted abduction"\[5\], de- 
fault inheritance, and so on. These operations can 
also be applied at semantic transfer for augment- 
ing the TDAG with a common sense knowledge of 
the target language. On the other hand, these op- 
erations are not applied to a TDAG in the gener- 
ation phase, as we will explain in the next section. 
This is because the lexicon and grammatical con- 
straints are only applied to determine whether red 
nodes and arcs are exactly derived. If they are not 
exactly derived, we will end up with either over- or 
under-generation beyond the permissible margin. 
Semantic transfer is applied to a source TDAG as 
many times 9 as necessary until a successful gen- 
eration is made. Recall the sample sentence in 
Figure 1~ where two painter calls were made to 
change two red arcs in TDAG1 into yellow ones 
in TDAG2. These are examples of the first sub- 
stitution operation shown above. An addition of 
a green node and a green arc, followed by an ad- 
dition of a green arc, was applied to TDAG3 to 
obtain TDAG4. These additions are examples of 
the third and fourth addition operations. 
Sentence Generation Algorithm 
Before describing the generation algorithm, let us 
look at the representation of lexicons and gram- 
mars for machine translation. A lexical rule is 
represented by a set of equations, which intro- 
duce red nodes and arcs into a source TDAG. l° A 
phrasal rule is similarly defined by a set of equa- 
tions, which also introduce red nodes and arcs for 
describing a syntactic head and its complements. 
For example, if we use Shieber's PATR-II\[15\] 
notation~ the lexical rule for "wished" can be rep- 
resented as follows: 
V "-~ wished 
(V cat) ---- v 
(V form) - past 
(V subj cat} = np 
(V obj cat) = v 
(V obj form) = infinitival 
(V wed) -- *WISH 
(V pred agent) = (V subj pred) 
(V pred theme) = (V obj pred) 
(V pred theme agent) = (V subj pred) 
The last four equations are semantic equa- 
tions. Its TDAG representation is shown in Fig- 
ure 2. It would be more practical to further as- 
sume that such a lexicai rule is obtained from 
a type inference system, 11 which makes use of a 
syntactic class hierarchy so that each lexical class 
can inherit general properties of its superclasses. 
Similarly, semantic concepts such as *WISH and 
*WALK should be separately defined in an onto- 
logical hierarchy together with necessary domain 
knowledge (e.g., selectional constraints on case 
9The iteration is bounded by the number of nodes 
and arcs in the TDAG, although the number of possi- 
ble sequences of operations could be exponential. 
1°For simplicity, we will only consider semantic equations 
to form the TDAGs. 
11as in Shieber\[15\], Pollard and Sag\[13\], and Russell 
et al.\[14\] 
229 
*WISH 
predJ~ Qnp 
cat~ o~ ~prme: ~agent 
v c., v 
Figure 2: TDAG representation of the verb 
"wished" (embedded in the entire feature struc- 
ture) 
caller • -.. work-for 
• "-. *OFF!CF~BoSTON *CAL'~ 
definite singular 
Figure 3: Source TDAG for the sentence "The 
Boston Office called." 
fillers and part-of relationships. See KBMT-8918\].) 
A unification grammar is used for both analysis 
and generation. Let us assume that we have two 
unification grammars for English and Japanese. 
Analyzing a sentence yields a source TDAG with 
red nodes and arcs. Semantic interpretation re- 
solves possible ambiguity and the resulting TDAG 
may include all kinds of nodes and arcs. For ex- 
ample, the sentence 12 
The Boston office called 
would give the source TDAG in Figure 3. By 
utilizing the domain knowledge, the node labeled 
*PERSON is introduced into the TDAG as a real 
caller of the action *CALL, and two arcs repre- 
senting *PERSON work-for *OFFICE and *OF- 
FICE in *BOSTON are abductively inferred. 
Our generation algorithm is based on 
Wedekind's DAG traversal algorithm\[25\] for 
LFG. la The algorithm runs with an input TDAG 
by traversing the nodes and arcs that were derived 
from the lexicon mand grammar rules. The termi- 
nation conditions are as follows: 
12in Hobbs et al.\[5\] 
13It would be identical to Wedekind's algorithm if 
an input TDAG consisted of only red nodes and arcs. 
. *PERSON 
caller • ".. work-for 
• ",,. *OFFICE *BOSTON _ (~ *CALL= "~ A m 
..... / 
(~ --npm~~r~~ (~ 
definite singular 
Figure 4: Target TDAG for the sentence "The 
Boston Office called." 
• Every red node and arc in the TDAG was de- 
rived. 
• No new red node (arc) is to be introduced into 
the TDAG if there is no corresponding node 
(arc) of any color in the TDAG. That is, the 
generator can change the color of a node (arc) 
to red, but cannot add a new node (arc). 
• For each set of red paths (i.e., the sequence of 
red arcs) that connects the same pair of nodes, 
the reentrancy was also derived. 
These conditions are identical to those of 
Wedekind except that yellow (or green) nodes and 
arcs may or may not be derived. For example, the 
sentence "The Boston Office called" in Figure 3 
can be translated into Japanese by the following 
sequence of semantic transfer and sentence gener- 
ation. 
1. Apply the painter to change the yellow of the 
definite node and the def arc to green. 
2. Apply the painter to change the yellow of the 
singular node and the hum arc to green. The 
resulting TDAG is shown in Figure 4. 
3. Run the sentence generator with an input fea- 
ture structure, which has a root and an arc pred 
connecting to the given TDAG. (See the node 
marked "1" in Figure 4.) 
4. The generator applies a phrasal rule, say S ---* 
NP VP, which derives the subj arc connecting 
to the subject NP (marked "2"), and the agent 
arc. 
5. The generator applies a phrasal rule, say NP ---+ 
MOD NP, TM which derives the npmod arc to the 
14There are several phrasal rules for deriving this 
LHS NP in Japanese: (1) A noun-noun compound, (2) 
a noun, copula, and a noun, and (3) a noun, postposi- 
tional particle, and a noun. These three rules roughly 
correspond to the forms (1) Boston Office, (2) office 
of Boston, and (3) office in Boston. Inference of the "*OFFICE in *BOSTON" 
relation is easiest if rule (3) 
230 
modifier of the NP (marked "3") and the rood 
arc. 
6. Lexical rules are applied and all the semantic 
nodes, *CALL, *OFFICE, and *BOSTON are 
derived. 
The annotated sample run of the sentence gen- 
erator is shown in Figure 5. The input TDAG in 
the sample run is embedded in the input feature 
structure as a set of PRED values, but the seman- 
tic arcs are not shown in the figure. The input 
feature structure has syntactic features that were 
specified in the lexical rules. The feature value 
*UNDEFINED* is used to show that the node has 
been traversed by the generator. 
The basic property of the generation algo- 
rithm is as follows: 
Let t be a given TDAG, tmi~ be the connected 
subgraph including all the red nodes and arcs 
in t, and t,~, be the connected subgraph of 
t obtained by changing all the colors of the 
nodes and arcs to red. Then, any successful 
generation with the derived TDAG tg satisfies 
the condition that t,,i~ subsumes ta, and t a 
subsumes trnaz. 
The proof is immediately obtained from the defini- 
tion of successful generation and the fact that the 
generator never introduces a new node or a new 
arc into an input TDAG. The TDAGs can also 
be employed by the semantic head-driven genera- 
tion algorithm\[17\] while retaining the above prop- 
erty. Semantic monotonicity always holds for a 
TDAG, since red nodes must be connected. It has 
been shown by Takeda\[21\] that semantically non- 
monotonic representations can also be handled by 
introducing a functional semantic class. 
Implementation 
We have been developing a prototype English- 
to-Japanese MT system, called Shalt2122\], with 
a lexicon for a computer-manual domain includ- 
ing about 24,000 lexemes each for English and 
Japanese, and a general lexicon including about 
50,000 English words and their translations. A 
sample set of 736 sentences was collected from 
the "IBM AS/400 Getting Started" manual, and 
was tested with the above semantic transfer and 
generation algorithmJ s The result of the syntac- 
tic analysis by the English parser is mapped to 
a TDAG using a set of semantic equations 16 oh- 
is used, but the noun-noun compound is probably the 
best translation. ! 
15We used McCord's English parser based on his 
English Slot Grammar\[10\], which covered more than 
93% of the sentences. 
l~We call such a set of semantic equations mapping 
rules (see Shalt2\[20\] or KBMT-8918\]). 
;; run the generator with input f-structure 
O> *J-GG-START called with 
((PRED "~") (CAT V) (VTYPE V-bDAN-B) 
(SUBCAT TRANS) (ASP-TYPE SHUNKAN) 
(:MOOD ((PKED "@dec"))) 
(AUX ((PRED "@aux") (:TIME ((PRED "@past"))) 
(:PASSIVE ((PRED "@minus"))))) 
(SUBJ ((CAT N) (PRED "~i~;~") 
(XADJL1BCT ((XCOP ,,'C'Cr),,) (CAT N) 
(PRED ",~°5~ ~ ~")))))) 
°.. 
3> *J-GG-S called ;;<start> ->...-> <S> 
4> *J-GG-XP called with ;;subj-filler 
((CASE (.0,'I* "~ .... %¢")) (CAT N) 
(NEG *UNDEFINED*) (PRED "~P~") 
(\](ADJUNCT ((COP -) (CAT N) 
(PRED "~, }" >'")))) 
5> *J-GG-NP called ;;head NP of subj 
10< *GG-N-ROOT returns ;;np mod 
",~°~ ~ M" ; ;"Boston" 
9> *J-GG-N called ; ;head np 
10< *GG-N-ROOT returns 
"~" ;;"office" 
7< *9 (<SS> <NP>) returns ;;mod+NP 
5< .i (<NP> <P>) returns ;;NP+case-marker 
'~A I- >z~$~I$, 
4< *J-GG-XP returns "~°A b >'7~69~&~" 
4> *J-GG-S called with ;;VP part 
5> *J-GG-VP called ;;stem + 
6> *J-GG-V called ; ;function word chains 
( (SUBJ *UNDEFINED*) 
(ADVADJUBCT *UNDEFINED*) 
(PPAD JUNCT *UNDEFINED*) 
( :MOOD *UNDEFINED*) 
(AUX ((:TIME ((PRED "@past"))) 
(:PASSIVE 
((PRED (*OR* *UNDEFINED* "@minus"))) ) 
(PRED "@aux") )) 
(CAT V) (TYPE FINAL) (ASP-TYPE SHUNKAN) 
(VTYPE V-bDAN-B) (SUBCAT TRIIlIS) 
(PKED "l~2g" ) ) 
7> *J-GG-RENTAI-PAST called ; ;past-form 
14< *GG-V-ROOT returns "~" ; ;stem 
• .. 
6< *J-GG-V returns "~\[~ b~C" 
5< *J-GG-VP returns "~\[~ ~fC" 
4< *J-GG-S returns "~\[~ ~" 
3< *J-GG-S returns 
O< *J-GG-START returns 
Figure 5: Sentence generation from the TDAG for 
"The Boston Office called." 
231 
tained from the lexicons. We have a very shal- 
low knowledge base for the computer domain, 
and no logical inference system was used to de- 
rive further constraints from the given source sen- 
tences. The Japanese grammar is similar to the 
one used in KBMT-89, which is written inpseudo- 
unification\[23\] equations, but we have added sev- 
eral new types of equation for handling coordi- 
nated structures. The Japanese grammar can gen- 
erate sentences from all the successful TDAGs for 
the sample English sentences. 
It turned out that there were a few collections 
of semantic transfer sequences which contributed 
very strongly to the successful generation. These 
sequences include 
• Painting the functional control arcs in yellow. 
• Painting the gaps of relative clauses in yellow. 
• Painting the number and definiteness features 
in yellow. 
• Painting the passivization feature in green. ~7 
Other kinds of semantic transfer are rather id- 
iosyncratic, and are usually triggered by a par- 
ticular lexical rule. Some of the sample sentences 
used for the translations are as follows: ~s 
Make sure you are using the proper edition 
for the level of the product. ~-+f- ~ ~ © p~<m ~ ~t~ 
user +subj product +pos level +for proper 
edition +obj use +prog +nom +obj 
confirm +imp 
Publications are not stocked at the address 
publication +subj following +loc provide 
address +loc stock +passive +neg 
This publication could contain technical 
inaccuracies or typographical errors. 
this publication +subj technical inaccuracy 
or typographical error +obj 
contain +ability +past 
17We decided to include the passivization feature in 
the semantic representation in order to determine the 
proper word ordering in Japanese. 
1s Japanese translation reflects the errors made in 
English analysis. For example, the auxiliary verb 
"could" is misinterpreted in the last sample sentence. 
The overall accuracy of the translated sen- 
tences was about 63%. The main reason for trans- 
lation errors was the occurrence of errors in lexi- 
cal and structural disambiguation by the syntac- 
tic/semantic analyzer. We found that the accu- 
racy of semantic transfer and sentence generation 
was practically acceptable. 
Though there were few serious errors, some 
occurred when a source TDAG had to be com- 
pletely "paraphrased" into a different TDAG. For 
example, the sentence 
Let's get started. 
was very hard to translate into a natural Japanese 
sentence. Therefore, a TDAG had to be para- 
phrased into a totally different TDAG, which is an- 
other important role of semantic transfer. Other 
serious errors were related to the ordering of con- 
stituents in the TDAG. It might be generally ac- 
ceptable to assume that the ordering of nodes in a 
DAG is immaterial. However, the different order- 
ing of adjuncts sometimes resulted in a misleading 
translation, as did the ordering of members in a 
coordinated structure. These subtle issues have to 
be taken into account in the framework of seman- 
tic transfer and sentence generation. 
Conclusions 
In this paper, we have introduced tricolor DAGs 
to represent various degrees of constraint, and de- 
fined the notions of semantic transfer and sen- 
tence generation as operations on TDAGs. This 
approach proved to be so practical that nearly 
all of the source sentences that were correctly 
parsed were translated into readily acceptable sen- 
tences. Without semantic transfer, the translated 
sentences would include greater numbers of incor- 
rectly selected words, or in some cases the gener- 
ator would simply fail 19 
Extension of TDAGs for disjunctive informa- 
tion and a set of feature structures must be fully 
incorporated into the framework. Currently only 
a limited range of the cases are implemented. Op- 
timal control of semantic transfer is still unknown. 
Integration of the constraint-based formalism, de- 
feasible reasoning, and practical heuristic rules are 
also important for achieving high-quality transla- 
tion. The ability to process and represent various 
levels of knowledge in TDAGs by using a uniform 
architecture is desirable, but there appears to be 
some efficient procedural knowledge that is very 
hard to represent declaratively. For example, the 
negative determiner "no" modifying a noun phrase 
in English has to be procedurally transferred into 
~gThe Essential Arguments Algorithm\[9\] might be 
an alternative method for finding a successful genera- 
tion path. 
232 
the negation of the verb governing the noun phrase 
in 3 apanese. Translation of "any", "yet", "only", 
and so on involves similar problems. 
While TDAGs reflect three discrete types of 
constraints, it is possible to generalize the types 
into continuous, numeric values such as potential energy\[4\]. 
This approach will provide a consider- 
ably more flexible margin that defines a set of per- 
missible translations, but it is not clear whether 
we can successfully define a numeric value for each 
lexical rule in order to obtain acceptable transla- 
tions. 
Acknowledgments 
The idea of the tricolor DAGs grew from discus- 
sions with Shiho 0gino on the design and im- 
plementation of the sentence generator. I would 
also like to thank the members of the NL group 
- Naohiko Uramoto, Tetsuya Nasukawa, Hiroshi 
Maruyama, Hiroshi Nomiyama, Hideo Watanabe, 
Masayuki Morohashi, and Taijiro Tsutsumi -for 
stimulating comments and discussions that di- 
rectly and indirectly contributed to shaping the 
paper. Michael McDonald, who has always been 
the person I turn to for proofreading, helped me 
write the final version. 

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