A HYBRID REASONING MODEL FOR INDIRECT ANSWERS 
Nancy Green 
Department of Computer Science 
University of Delaware 
Newark, DE 19716, USA 
Internet: green@udel.edu 
Sandra Carberry 
Department of Computer Science 
University of Delaware 
Visitor: Inst. for Research in Cognitive Science 
University of Pennsylvania 
Internet: carberry@udel.edu 
Abstract 
This paper presents our implemented computa- 
tional model for interpreting and generating in- 
direct answers to Yes-No questions. Its main fea- 
tures are 1) a discourse-plan-based approach to 
implicature, 2) a reversible architecture for gen- 
eration and interpretation, 3) a hybrid reasoning 
model that employs both plan inference and log- 
ical inference, and 4) use of stimulus conditions 
to model a speaker's motivation for providing ap- 
propriate, unrequested information. The model 
handles a wider range of types of indirect answers 
than previous computational models and has sev- 
eral significant advantages. 
1. INTRODUCTION 
Imagine a discourse context for (1) in which R's 
use of just (ld) is intended to convey a No, i.e., 
that R is not going shopping tonight. (By con- 
vention, square brackets indicate that the enclosed 
text was not explicitly stated.) The part of R's re- 
sponse consisting of (ld) - (le) is what we call an 
indirect answer to a Yes-No question, and if (lc) 
had been uttered, (lc) would have been called a 
direct answer. 
l.a. Q: I need a ride to the mall. 
b. Are you going shopping tonight? 
c. R: \[no\] 
d. My car's not running. 
e. The rear axle is broken. 
According to one study of spoken English 
\[Stenstrhm, 1984\], 13 percent of responses to Yes- 
No questions were indirect answers. Thus, the 
ability to interpret indirect answers is required for 
robust dialogue systems. Furthermore, there are 
good reasons for generating indirect answers in- 
stead of just yes, no, or I don't know. First, they 
may provide information which is needed to avoid 
misleading the questioner \[Hirschberg, 1985\]. Sec- 
ond, they contribute to an efficient dialogue by 
anticipating follow-up questions. Third, they may 
be used for social reasons, as in (1). 
This paper provides a computational model 
for the interpretation and generation of indirect 
answers to Yes-No questions in English. More pre- 
cisely, by a Yes-No question we mean one or more 
utterances used as a request by Q (the questioner) 
that R (the responder) convey R's evaluation of 
the truth of a proposition p. An indirect answer 
implicitly conveys via one or more utterances R's 
evaluation of the truth of the questioned proposi- 
tion p, i.e. that p is true, that p is false, that there 
is some truth to p, that p may be true, or that 
p may be false. Our model presupposes that Q's 
question has been understood by R as intended by 
Q, that Q's request was appropriate, and that Q 
and R are engaged in a cooperative goal-directed 
dialogue. The interpretation and generation com- 
ponents of the model have been implemented in 
Common Lisp on a Sun SPARCstation. 
The model employs an agent's pragmatic 
knowledge of how language typically is used to 
answer Yes-No questions in English to constrain 
the process of generating and interpreting indirect 
answers. This knowledge is encoded as a set of 
domain-independent discourse plan operators and 
a set of coherence rules, described in section 2.1 
Figure 1 shows the architecture of our system. It 
is reversible in that the same pragmatic knowl- 
edge is used by the interpretation and generation 
modules. The interpretation algorithm, described 
in section 3, is a hybrid approach employing both 
plan inference and logical inference to infer R's dis- 
course plan. The generation algorithm, described 
in section 4, constructs R's discourse plan in two 
phases. During the first phase, stimulus condi- 
tions are used to trigger goals to include appro- 
priate, extra information in the response plan. In 
the second phase, the response plan is pruned to 
eliminate parts which can be inferred by Q. 
hOur main sources of data were previous studies 
\[Hirschberg, 1985, Stenstrhm, 1984\], transcripts of 
naturally occurring two-person dialogue \[American 
Express transcripts, 1992\], and constructed examples. 
58 
discourse plan operators 
discourse expectation 
response --I INTERPRETATION I I G:NERATION I 
coherence rules 
discourse expectation 
R's beliefs 
Figure 1: Architecture of system 
2. PRAGMATIC KNOWLEDGE 
Linguists (e.g. see discussion in \[Levinson, 1983\]) 
have claimed that use of an utterance in a dia- 
logue may create shared expectations about sub- 
sequent utterances. In particular, a Yes-No ques- 
tion creates the discourse expectation that R will 
provide R's evaluation of the truth of the ques- 
tioned proposition p. Furthermore, Q's assump- 
tion that R's response is relevant triggers Q's at- 
tempt to interpret R's response as providing the 
requested information. We have observed that 
coherence relations similar to the subject-matter 
relations of Rhetorical Structure Theory (RST) 
\[Mann and Thompson, 1987\] can be used in defin- 
ing constraints on the relevance of.an indirect an- 
swer. For example, the relation between the (im- 
plicit) direct answer in (2b) and each of the indi- 
rect answers in (2c) - (2e) is similar to RST's rela- 
tions of Condition, Elaboration, and (Volitional) 
Cause, respectively. 
2.a. Q: Are you going shopping tonight? 
b. R: \[yes\] 
c. if I finish my homework 
d. I'm going to Macy's 
e. Winter clothes are on sale 
Furthermore, for Q to interpret any of (2c) - (2e) 
as conveying an affirmative answer, Q must be- 
lieve that R intended Q to recognize the relational 
proposition holding between the indirect answer 
and (2b), e.g. that (2d) is an elaboration of (25). 
Also, coherence relations hold between parts of an 
indirect answer consisting of multiple utterances. 
For example, (le) describes the cause of the fail- 
ure reported in (ld). Finally, we have observed 
that different relations are usually associated with 
different types of answers. Thus, a speaker who 
has inferred a plausible coherence relation holding 
between an indirect answer and a possible (im- 
plicit) direct answer may be able to infer the di- 
rect answer. (If more than one coherence relation 
( (Plausible (cr-obstacle 
((not (in-state ?stateq ?tq)) 
(not (occur ?eventp ?tp))))) <- 
(state ?stateq) 
(event ?eventp) 
(timeperiod ?tq) 
(timeperiod ?tp) 
(before ?tq ?tp) 
(app-cond ?stateq ?eventp) 
(unless (in-state ?stateq ?tq)) 
(unless (occur ?eventp ?tp))) 
Figure 2: A coherence rule for cr-obstacle 
is plausible, or if the same coherence relation is 
used with more than one type of answer, then the 
indirect answer may be ambiguous.) 
In our model we formally represent the co- 
herence relations which constrain indirect answers 
by means of coherence rules. Each rule consists 
of a consequent of the form (Plausible (CR q 
p)) and an antecedent which is a conjunction of 
conditions, where CR is the name of a coherence 
relation and q and p are formulae, symbols pre- 
fixed with "?" are variables, and all variables are 
implicitly universally quantified. Each antecedent 
condition represents a condition which is true iff 
it is believed by R to be mutually believed with 
Q.2 Each rule represents sufficient conditions for 
the plausibility of (CR q p) for some CR, q, p. An 
example of one of the rules describing the Obsta- 
2Our model of R's beliefs (and similarly for Q's), 
represented as a set of Horn clauses, includes 1) general 
world knowledge presumably shared with Q, 2) knowl- 
edge about the preceding discourse, and 3) R's beliefs 
(including "weak beliefs"} about Q's beliefs. Much of 
the shared world knowledge needed to evaluate the co- 
herence rules consists of knowledge from domain plan 
operators. 
59 
(Answer-yes s h ?p): 
Applicability conditions: 
(discourse-expectation 
(informif s h ?p)) 
(believe s ?p) 
Nucleus: 
(inform s h ?p) 
Satellites: 
(Use-condition s h ?p) 
(Use-cause s h ?p) 
(Use-elaboration s h ?p) 
Primary goals: 
(BMB h s ?p) 
Figure 3: Discourse plan 
(Answer-no s h ?p): 
Applicability conditions: 
(discourse-expectation 
(informif s h ?p)) 
(believe s (not ?p)) 
Nucleus: 
(inform s h (not ?p)) 
Satellites: 
(Use-otherwise s h (not ?p)) 
(Use-obstacle s h (not ?p)) 
(Use-contrast s h (not ?p)) 
Primary goals: 
(BMB h s (not ?p)) 
operators for Yes and No answers 
cle relation 3 is shown in Figure 2. The predicates 
used in the rule are defined as follows: (in-state p 
/) denotes that p holds during t, (occur p t) de- 
notes that p happens during t, (state z) denotes 
that the type of x is state, (event x) denotes that 
the type of x is event, (timeperiod t) denotes that 
t is a time interval, (before tl t2) denotes that tl 
begins before or at the same time as t2, (app-cond 
q p} denotes that q is a plausible enabling con- 
dition for doing p, and (unless p) denotes that p 
is not provable from the beliefs of the reasoner. 
For example, this rule describes the relation be- 
tween (ld) and (lc), where (ld) is interpreted as 
(not (in-state (running R-car) Present)) and (lc) 
as (not (occur (go-shopping R) Future)). That is, 
this relation would be plausible if Q and R share 
the belief that a plausible enabling condition of a 
subaction of a plan for R to go shopping at the 
mall is that R's car be in running condition. 
In her study of responses to questions, Sten- 
strSm \[Stenstrfm, 1984\] found that direct an- 
swers are often accompanied by extra, relevant 
information, 4 and noted that often this extra in- 
formation is similar in content to an indirect an- 
swer. Thus, the above constraints on the relevance 
of an indirect answer can serve also as constraints 
on information accompanying a direct answer. For 
maximum generality, therefore, we went beyond 
our original goal of handling indirect answers to 
the goal of handling what we call full answers. A 
full answer consists of an implicit or explicit direct 
answer (which we call the nucleus) and, possibly, 
extra, relevant information (satellites). s In our 
awhile Obstacle is not one of the original relations 
of RST, it is similar to the causal relations of RST. 
461 percent of direct No answers and 24 percent of 
direct Yes answers 
5The terms nucleus and satellite have been bor- 
rowed from RST to reflect the informational con- 
straints within a full answer. Note that according to 
RST, a property of the nucleus is that its removal re- 
model, we represent each type of full answer as a 
(top-level) discourse plan operator. By represent- 
ing answer types as plan operators, generation can 
be modeled as plan construction, and interpreta- 
tion as plan recognition. 
Examples of (top-level) operators describing a 
full Yes answer and a full No answer are shown 
in Figure 3. 6 To explain our notation, s and 
h are constants denoting speaker (R) and hearer 
(Q), respectively. Symbols prefixed with "?" de- 
note propositional variables. The variables in the 
header of each top-level operator will be instan- 
tiated with the questioned proposition. In inter- 
preting example (1), ?p would be instantiated with 
the proposition that R is going shopping tonight. 
Thus, instantiating the Answer-No operator in 
Figure 3 with this proposition would produce a 
plan for answering that P~ is not going shopping 
tonight. Applicability conditions are necessary 
conditions for appropriate use of a plan operator. 
For example, it is inappropriate for R to give an 
affirmative answer that p if R believes p is false. 
Also, an answer to a Yes-No question is not ap- 
propriate unless s and h share the discourse ex- 
pectation that s will provide s's evaluation of the 
truth of the questioned proposition p, which we 
denote as (discourse-ezpectation (informif s h p)). 
Primary goals describe the intended effects of the 
plan operator. We use (BMB h s p) to denote 
that h believes it mutually believed with s that p 
\[Clark and Marshall, 1981\]. 
In general, the nucleus and satellites of a dis- 
course plan operator describe primitive or non- 
primitive communicative acts. Our formalism el- 
suits in incoherence. However, in our model, a di- 
rect answer may be removed without causing incoher- 
ence, provided that it is inferable from the rest of the 
response. 
6The other top-level operators in our model, Answer-hedged, Answer-maybe, 
and Answer-maybe- not, 
represent the other answer types handled. 
60 
(Use-obstacle s h ?p): 
;; s tells h of an obstacle explaining 
;; the failure ?p 
Existential variable: ?q 
Applicability conditions: 
(believe s (cr-obstacle ?q ?p)) 
(Plausible (cr-obstacle ?q ?p)) 
Stimulus conditions: 
(explanation-indicated s h ?p ?q) 
(excuse-indicated s h ?p ?q) 
Nucleus: 
(inform s h ?q) 
Satellites: 
(Use-elaboration s h ?q) 
(Use-obstacle s h ?q) 
(Use-cause s h ?q) 
Primary goals: 
(BMB h s (cr-obstacle ?q ?p)) 
Figure 4: Discourse plan operator for Obstacle 
lows zero, one, or more occurrences of a satellite 
in a full answer, and the expected (but not re- 
quired) order of nucleus and satellites is the order 
they are listed in the operator. (inform s h p) de- 
notes the primitive act of s informing h that p. 
The satellites in Figure 3 refer to non-primitive 
acts, described by discourse plan operators which 
we have defined (one for each coherence relation 
used in a full answer). For example, Use-obstacle, 
a satellite of Answer-no in Figure 3, is defined in 
Figure 4. 
To explain the additional notation in Figure 4, 
(cr-obstacle q p) denotes that the coherence rela- 
tion named obstacle holds between q and p. Thus, 
the first applicability condition can be glossed as 
requiring that s believe that the coherence rela- 
tion holds. In the second applicability condition, 
(Plausible (cr-obstacle q p)) denotes that, given 
what s believes to be mutually believed with h, 
the coherence relation (cr-obstacle q p) is plausi- 
ble. This sort of applicability condition is evalu- 
ated using the coherence rules described above. 
Stimulus conditions describe conditions moti- 
vating a speaker to include a satellite during plan 
construction. They can be thought of as trig- 
gers which give rise to new speaker goals. In 
order for a satellite to be selected during gen- 
eration, all of its applicability conditions and at 
least one of its stimulus conditions must hold. 
While stimulus conditions may be derivative of 
principles of cooperativity \[Grice, 1975\] or po- 
liteness \[Brown and Levinson, 1978\], they provide 
a level of precompiled knowledge which reduces 
the amount of reasoning required for content- 
planning. For example, Figure 5 depicts the dis- 
course plan which would be constructed by R (and 
Answer-no /\ 
\[Ic\] Use-obstacle /\ 
Id Use-obstacle 
J 
le 
Figure 5: Discourse plan underlying (ld) - (le) 
must be inferred by Q) for (1). The first stimu- 
lus condition of Use-obstacle, which is defined as 
holding whenever s suspects that h would be sur- 
prised that p holds, describes R's reason for includ- 
ing (le). The second stimulus condition, which is 
defined as holding whenever s suspects that the 
Yes-No question is a prerequest \[Levinson, 1983\], 
describes R's reason for including (ld). 7 
3. INTERPRETATION 
We assume that interpretation of dialogue is 
controlled by a Discourse Model Processor 
(DMP), which maintains a Discourse Model 
\[Carberry, 1990\] representing what Q believes R 
has inferred so far concerning Q's plans. The dis- 
course expectation generated by a Yes-No question 
leads the DMP to invoke the answer recognition 
process to be described in this section. If answer 
recognition is unsuccessful, the DMP would invoke 
other types of recognizers for handling less pre- 
ferred types of responses, such as I don't know or 
a clarification subdialogue. To give an example of 
where our recognition algorithm fits into the above 
framework, consider (4). 
4a. Q: Is Dr. Smith teaching CSI next fall? 
b. R: Do you mean Dr. Smithson? 
c. Q: Yes. 
d. R: \[no\] 
e. He will be on sabbatical next fall. 
f. Why do you ask? 
Note that a request for clarification and its answer 
are given in (4b) - (4c). Our recognition algorithm, 
when invoked with (4e) - (4f) as input, would infer 
an Answer-no plan accounting for (4e) and satis- 
fying the discourse expectation generated by (4a). 
When invoked by the DMP, our interpretation 
module plays the role of the questioner Q. The 
inputs to interpretation in our model consist of 
7Stimulus conditions are formally defined by rules 
encoded in the same formalism as used for our co- 
herence rules. A full description of the stimu- 
lus conditions used in our model can be found in 
\[Green, in preparation\]. 
61 
1) the set of discourse plan operators and the set 
of coherence rules described in section 2, 2) Q's 
beliefs, 3) the discourse expectation (discourse- 
expectation (informif s h p)), and 4) the semantic 
representation of the sequence of utterances per- 
formed by R during R's turn. The output is a 
partially ordered set (possibly empty) of answer 
discourse plans which it is plausible to ascribe to R 
as underlying It's response. The set is ordered by 
plausibility using preference criteria. Note that we 
assume that the final choice of a discourse plan to 
ascribe to R is made by the DMP, since the DMP 
must select an interpretation consistent with the 
interpretation of any remaining parts of R's turn 
not accounted fo~ by the answer discourse plan, 
e.g. (4f). 
To give a high-level description of our answer 
interpretation algorithm, first, each (top-level) an- 
swer discourse plan operator is instantiated with 
the questioned proposition from the discourse ex- 
pectation. For example (1), each answer operator 
would be instantiated with the proposition that 
R is going shopping tonight. Next, the answer 
interpreter must verify that the applicability con- 
ditions and primary goals which would be held by 
R if R were pursuing the plan are consistent with 
Q's beliefs about It's beliefs and goals. Consis- 
tency checking is implemented using a Horn clause 
theorem-prover. For all candidate answer plans 
which have not been eliminated during consistency 
checking, recognition continues by attempting to 
match the utterances in R's turn to the actions 
specified in the candidates. However, no candi- 
date plan may be constructed which violates the 
following structural constraint. Viewing a candi- 
date plan's structure as a tree whose leaves are 
primitive acts from which the plan was inferred, 
no subtree Ti may contain an act whose sequential 
position in the response is included in the range 
of sequential positions in the response of acts in a 
subtree Tj having the same parent node as 7~. For 
example, (5e) cannot be interpreted as related to 
(5c) by cr-obstaele, due to the occurrence of (5d) 
between (5c) and (5e). Note that a more coherent 
response would consist of the sequence, (5c), (5e), (Sd). 
5.a. O: Are you going shopping tonight? 
b. R: \[no\] 
c. My car's not running. 
d, Besides, I'm too tired. 
e. The timing belt is broken. 
To recognize a subplan for a non-primitive ac- 
tion, e.g. Use-obstacle in Figure 4, a similar proce- 
dure is used. Note that any applicability condition 
of the form (Plausible (CR q p)) is defined to be 
consistent with Q's beliefs if it is provable, i.e., 
if the antecedents of a coherence rule for CR are 
true with respect to what Q believes to be mutu- 
ally believed with R. The recognition process for 
non-primitive actions differs in that these opera- 
tors contain existential variables which must be 
instantiated. In our model, the answer interpreter 
first attempts to instantiate an existential variable 
with a proposition from R's response. For exam- 
ple (1), the existential variable ?q of Use-obstacle 
would be instantiated with the proposition that 
R's car is not running. However, if (ld) was not 
explicitly stated by R, i.e., if R's response had just 
consisted of (le), it would be necessary for ?q to 
be instantiated with a hypothesized proposition, 
corresponding to (ld), to understand how (le) re- 
lates to R's answer. The answer interpreter finds 
the hypothesized proposition by a subprocedure 
we refer to as hypothesis generation. 
Hypothesis generation is constrained by the 
assumption that R's response is coherent, i.e., that 
(le) may play the role of a satellite in a subplan of 
some Answer plan. Thus, the coherence rules are 
used as a source of knowledge for generating hy- 
potheses. Hypothesis generation begins with ini- 
tializing the root of a tree of hypotheses with a 
proposition p0 to be related to a plan, e.g. the 
proposition conveyed by (le). A tree of hypothe- 
ses is constructed by expanding each of its nodes 
in breadth-first order until all goal nodes (as de- 
fined below) have been reached, subject to a limit 
on the depth of the breadth-first search, s A node 
containing a proposition Pi is expanded by search- 
ing for all propositions Pi+l such that for some 
coherence relation CR which may be used in the 
type of answer being recognized, (Plausible ( CR pi 
pi+l)) holds from Q's point of view. (The search is 
implemented using a Horn clause theorem prover.) 
The plan operator invoking hypothesis gener- 
ation has a partially instantiated applicability con- 
dition of the form, (Plausible (CR ?q p)), where 
CR is a coherence relation, p is the proposition 
that was used to instantiate the header variable of 
the operator, and ?q is the operator's existential 
variable. Since the purpose of the search is to find 
a proposition q with which to instantiate ?q, a goal 
node is defined as a node containing a proposition 
q satisfying the above condition. (E.g. in Figure 6 
P0 is the proposition conveyed by (le), Px is the 
proposition conveyed by (ld), P0 and Pl are plau- 
sibly related by er-obstaele, P2 is the proposition 
conveyed by a No answer to (la), Pl and P2 are 
plausibly related by cr-obstacle, P2 is a goal node, 
and therefore, Pl will be used to instantiate the 
existential variable ?q in Use-obstacle.) 
After the existential variable is instantiated, 
plan recognition proceeds as described above at 
SPlacing a limit on the maximum depth of the tree 
is reasonable, given human processing constraints. 
62 
~ goal (conveyed if lc were uttered) 
hypothesized (conveyed if ld were uttered) 
proposition from utterance (conveyed in le) 
Figure 6: Hypothesis generation tree relating (le) 
to (lc) 
the point where the remaining conditions are 
checked for consistency. 9 For example, as recog- 
nition of the Use-obstacle subplan proceeds, (le) 
would be recognized as the realization of a Use- 
obstacle satellite of this Use-obstacle subplan. Ul- 
timately, the inferred plan would be the same as 
that shown in Figure 5, except that (ld) would be 
marked as hypothesized. 
The set of candidate plans inferred from a re- 
sponse are ranked using two preference criteria. 1° 
First, as the number of hypothesized propositions 
in a candidate increases, its plausibility decreases. 
Second, as the number of non-hypothesized propo- 
sitions accounted for by the plan increases, its 
plausibility increases. 
To summarize the interpretation algorithm, it 
is primarily expectation-driven in the sense that 
the answer interpreter attempts to interpret R's 
response as an answer generated by some answer 
discourse plan operator. Whenever the answer in- 
terpreter is unable to relate an utterance to the 
plan which it is currently attempting to recognize, 
the answer interpreter attempts to find a connec- 
tion by hypothesis generation. Logical inference 
plays a supplementary role, namely, in consistency 
checking (including inferring the plausibility of co- 
herence relations) and in hypothesis generation. 
4. GENERATION 
The inputs to generation consist of 1) the same 
sets of discourse plan operators and coherence 
rules used in interpretation, 2) R's beliefs, and 3) 
the same discourse expectation. The output is a 
9Note that, in general, any nodes on the path be- 
tween p0 and Ph, where Ph is the hypothesis returned, 
will be used as additional hypotheses (later) to connect 
what was said to ph. 
1°Another possible criterion is whether the actual 
ordering reflects the default ordering specified in the 
discourse plan operators. We plan to test the useful- 
ness of this criterion. 
discourse plan for an answer (indirect, if possible). 
Generation of an indirect reply has two phases: 1) 
content planning, in which the generator creates a 
discourse plan for a full answer, and 2) plan prun- 
ing, in which the generator determines which parts 
of the planned full answer do not need to be ex- 
plicitly stated. For example, given an appropriate 
set of R's beliefs, our system generates a plan for 
asserting only the proposition conveyed in (le) as 
an answer to (lb). 11 
Content-planning is performed by top-down 
expansion of an answer discourse plan operator. 
Note that applicability conditions prevent inap- 
propriate use of an operator, but they do not 
model a speaker's motivation for providing extra 
information. Further, a full answer might provide 
too much information if every satellite whose oper- 
ator's applicability conditions held were included 
in a full answer. On the other hand, at the time R 
is asked the question, R may not yet have the pri- 
mary goals of a potential satellite. To overcome 
these limitations, we have incorporated stimulus 
conditions into the discourse plan operators in our 
model. As mentioned in section 2, stimulus condi- 
tions can be thought of as triggers or motivating 
conditions which give rise to new speaker goals. 
By analyzing the speaker's possible motivation for 
providing extra information in the examples in our 
corpus, we have identified a small set of stimu- 
lus conditions which reflect general concerns of 
accuracy, efficiency, and politeness. In order for 
a satellite to be included in a full answer, all of 
its applicability conditions and at least one of its 
stimulus conditions must hold. (A theorem prover 
is used to search for an instantiation of the exis- 
tential variable satisfying the above conditions.) 
The output of the content-planning phase, a 
discourse plan representing a full answer, is the 
input to the plan-pruning phase. The goal of this 
phase is to make the response more concise, i.e. to 
determine which of the planned acts can be omit- 
ted while still allowing Q to infer the full plan. To 
do this, the generator considers each of the acts 
in the frontier of the full plan tree from right to 
left (thus ensuring that a satellite is considered be- 
fore its nucleus). The generator creates trial plans 
consisting of the original plan minus the nodes 
pruned so far and minus the current node. Then, 
the generator simulates Q's interpretation of the 
trial plan. If Q could infer the full plan (as the 
most preferred plan), then the current node can 
be pruned. Note that, even when it is not possi- 
ble to prune the direct answer, a benefit of this 
approach is that it generates appropriate extra in- 
formation with direct answers. 
11The tactical component must choose an appropri- 
ate expression to refer to R's car's timing belt, de- 
pending on whether (ld) is omitted. 
63 
5. RELATED RESEARCH 
It has been noted \[Diller, 1989, Hirsehberg, 1985, 
Lakoff, 1973\] that indirect answers conversa- 
tionally implicale \[Grice, 1975\] direct answers. 
Recently, philosophers \[Thomason, 1990, MeCaf- 
ferty, 1987\] have argued for a plan-based ap- 
proach to conversational implicature. Plan-based 
computational models have been proposed for 
similar discourse interpretation problems, e.g. 
indirect speech acts \[Perrault and Allen, 1980, 
Hinkelman, 1989\], but none of these models ad- 
dress the interpretation of indirect answers. Also, 
our use of coherence relations, both 1) as con- 
straints on the relevance of indirect answers, and 
2) in our hypothesis generation algorithm, is 
unique in plan-based interpretation models. 
In addition to RST, a number of theories of 
text coherence have been proposed \[Grimes, 1975, 
Halliday, 1976, Hobbs, 1979, Polanyi, 1986, 
Reiehman, 1984\]. Coherence relations have 
been used in interpretation \[Dahlgren, 1989, 
Wu and Lytinen, 1990\]. However, inference of co- 
herence relations alone is insufficient for inter- 
preting indirect answers, since additional prag- 
matic knowledge (what we represent as discourse 
plan operators) and discourse expectations are 
necessary also. Coherence relations have been 
used in generation \[MeKeown, 1985, Hovy, 1988, 
Moore and Paris, 1988, Horacek, 1992\] but none 
of these models generate indirect answers. Also, 
our use of stimulus conditions is unique in gener- 
ation models. 
Most previous formal and computational 
models of conversational implicature \[Gazdar, 
1979, Green, 1990, Hirschberg, 1985, Lasearides 
and Asher, 1991\] derive implieatures by classi- 
cal or nonclassical logical inference with one or 
more licensing rules defining a class of implica- 
tures. Our coherence rules are similar conceptu- 
ally to the licensing rules in Lascarides et al.'s 
model of temporal implicature. (However, dif- 
ferent coherence relations play a role in indirect 
answers.) While Lascarides et al. model tem- 
poral implicatures as defeasible inferences, such 
an approach to indirect answers would fail to 
distinguish what R intends to convey by his re- 
sponse from other default inferences. We claim 
that R's response in (1), for example, does not 
warrant the attribution to R of the intention to 
convey that the rear axle of R's car is made of 
metal. Hirsehberg's model for deriving scalar im- 
plicatures addresses only a few of the types of 
indirect answers that our model does. Further- 
more, our discourse-plan-based approach avoids 
problems faced by licensing-rule-based approaches 
in handling backward cancellation and multiple- 
utterance responses \[Green and Carberry, 1992\]. 
Also, a potential problem faced by those ap- 
proaches is scalability, i.e., as licensing rules for 
handling more types of implieature are added, rule 
conflicts may arise and tractability may decrease. 
In contrast, our approach avoids such problems by 
restricting the use of logical inference. 
6. CONCLUSION 
We have described our implemented computa- 
tional model for interpreting and generating in- 
direct answers to Yes-No questions. Its main fea- 
tures are 1) a discourse-plan-based approach to 
implicature, 2) a reversible architecture, 3) a hy- 
brid reasoning model, and 4) use of stimulus condi- 
tions for modeling a speaker's motivation for pro- 
viding appropriate extra information. The model 
handles a wider range of types of indirect answers 
than previous computational models. Further- 
more, since Yes-No questions and their answers 
have features in common with other types of adja- 
cency pairs \[Levinson, 1983\], we expect that this 
approach can be extended to them as well. Fi- 
nally, a discourse-plan-based approach to implica- 
ture has significant advantages over a licensing- 
rule-based approach. In the future, we would 
like to integrate our interpretation and generation 
components with a dialogue system and investi- 
gate other factors in generating indirect answers 
(e.g. multiple goals, stylistic concerns). 

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