A MODEL OF PLAN INFERENCE THAT DISTINGUISHES 
BETWEEN THE BELIEFS OF ACTORS AND OBSERVERS 
Martha E. Pollack 
Artificial Intelligence Center 
and 
Center for the Study of Language and Information 
SRI International 
333 Ravenswood Avenue 
Menlo Park, CA 94025 
ABSTRACT 
Existing models of plan inference (PI) in conversation have as- 
sumed that the agent whose plan is being inferred (the actor) 
and the agent drawing the inference (the observer) have iden- 
tical beliefs about actions in the domain. I argue that this as- 
sumption often results in failure of both the PI process and the 
communicative process that PI is meant to support. In par- 
ticular, it precludes the principled generation of appropriate 
responses to queries that arise from invalid plans. I describe 
a model of P1 that abandons this assumption. It rests on an 
analysis of plans as mental phenomena. Judgements that a 
plan is invalid are associated with particular discrepancies be- 
tween the beliefs that the observer ascribes to the actor when 
the former believes that the latter has some plan, and the be- 
liefs that the observer herself holds. I show that the content 
of an appropriate response to a query is affected by the types 
of any such discrepancies of belief judged to be present in the 
plan inferred to underlie that query. The PI model described 
here has been implemented in SPIRIT, a small demonstration 
system that answers questions about the domain of computer 
mail. 
INTRODUCTION 
The importance of plan inference (PI) in models of conversa- 
tion has been widely noted in the computational-linguistics lit- 
erature. Incorporating PI capabilities into systems that answer 
users' questions has enabled such systems to handle indirect 
speech acts \[13\], supply more information than is actually re- 
quested in a query \[2\], provide helpful information in response 
to a yes/no query answered in the negative \[2\], disambiguate 
requests \[17\], resolve certain forms of intersentential ellipsis 
\[6,11\], and handle such discourse phenomena as clarification 
subdialogues \[11\], and correction or "debugging ~ subdialogues 
The research reported in this paper has been made possible in part by 
an IBM Graduate Fellowship, in part by a gift from the Systems Develop- 
ment Foundation, and in part by support from the Defense Advanced Re- 
search Projects Agency under Contract N00039-84-K.0078 with the Space 
and Naval Warfare Command. The views and conclusions contained in 
this document are those of the author and should not be interpreted as 
representative of the official policies, either expressed or implied, of the 
Defense Advanced Research Projects Agency or the United States Gov- 
ernment. 
! am grateful to Barbara Grosz, James Allen, Phil Cohen, Amy Lansky, 
Candy Sidner and Bonnie Webber for their comments on an earlier draft. 
\[16,11\]. 
The PI process in each of these systems, however, has as- 
sumed that the agent whose plan is being inferred (to whom 
I shall refer as the actor), and the agent drawing the infer- 
ence (to whom I shall refer as the observer), have identical 
beliefs about the actions in the domain. Thus, Allen's model, 
which was one of the earliest accounts of PI in conversation 1 
and impired a great deal of the work done subsequently, in- 
cludes, as a typical PI rule, the following: "SBAW(P) ~i 
SBAW(ACT) if P is a precondition of ACT" \[2, page 120\]. 
This rule can be glossed as "if the system (observer) believes 
that an agent (actor) wants some proposition P to be true, 
then the system may draw the inference that the agent wants 
to perform some action ACT of which P is a precondition." 
Note that it is left unstated precisely who it is--the observer 
or the actor---that believes that P is a precondition of ACT. 
If we take this to be a belief of the observer, it is not clear 
that the latter will infer the actor's plan; on the other hand, if 
we consider it to he a belief of the actor, it is unclear how the 
observer comes to have direct access to it. In practice, there 
is only a single set of operators relating preconditions and ac- / 
tion* in Allen's system; the belief in question is regarded as 
being both the actor's and the observer's. 
In many situations, an assumption that the re~v~nt beliefs 
of the actor are identical with those of the observer results 
in failure not only of the PI process, but also of:~he commu- 
nicative process that PI is meant to suppgrt.-In particular, it 
precludes the principled generation of appropriate responses 
to queries that arise from invalid plans. In this paper, I report 
on a model of Pl in conversation that distinguishes between 
the beliefs of the actor and those of the observer. The model 
rests on an analysis of plans as mental phenomena: ~having a 
plan s is analyzed as having a particular configuration of k,c- 
lids and intentions. Judgements that a plan is invalid are 
associated with particular discrepancies between the beliefs 
that the observer ascribes to the actor when the former be- 
lieves that the latter has some plan, and the beliefs observer 
herself holds. I give an account of different types of plan in- 
validities, and show how this account provides an explanation 
for certain regularities that are observable in cooperative re- 
sponses to questions. The PI model described here has been 
implemented in SPIRIT, a small demonstration system that 
answers questions about the domain of computer mail. More 
'Allen's article Izl summarizes his dissertation r ..... ch Ill. 
207 
extensive discussion of both the PI model and SPIRIT can be 
found in my dissertation \[14\]. 
PLANS AS MENTAL PHENOMENA 
We can distinguish between two views of plans. As Bratman 
\[5, page 271\] has observed, there is an ambiguity in speaking 
of an agent's plan: "On the one hand, \[this\] could mean an 
appropriate abstract strncture--some sort of partial function 
from circumstances to actions, perhaps. On the other hand, 
\[it\] could mean an appropriate state of mind, one naturally 
describable in terms of such structures! We might call the 
former sense the data-structure view of plans, and the latter 
the mental phenomenon view of plans. Work in plan synthe- 
sis (e.g., Fikes and Nilsson \[8\], Sacerdoti \[15\], Wilkins \[18\], 
and Pednault \[12\]), has taken the data-structure view, con- 
sidering plans to be structures encoding aggregates of actions 
that, when performed in circumstances satisfying some speci- 
fied preconditions, achieve some specified results. For the pur- 
poses of PI, however, it is much more useful to adopt a mental 
phenomenon view and consider plans to be particular configu- 
rations of beliefs and intentions that some agent has. After all, 
inferring another agent's plan means figuring out what actions 
he "has in mind," and he may well be wrong about the effects 
of those intended actions. 
Consider, for example, the plan I have to find out how Kathy 
is feeling. Believing that Kathy is at the hospital, I plan to do 
this by finding out the phone number of the hospital, calling 
there, asking to be connected to Kathy's room, and finally 
saying "How are you doing?" If, unbeknownst to me, Kathy 
has already been discharged, then executing my plan will not 
lead to my goal of finding out how she is feeling. For me to 
have a plan to do fl that consists of doing some collection 
of actions I1, it is not necessary that the performance of II 
actually lead to the performance of ft. What is necessary is 
that I believe that its performance will do so. This insight is at 
the core of a view of plans as mental phenomena; in this view 
a plan "exists"--i.e., gains its status as a plan--by virtue of 
the beliefs, as well as the intentions, of the person whose plan 
it is. 
Further consideration of our common-sense conceptions of 
what it means to have a plan leads to the following analysis 
\[14, Chap. 312: 
(PO) An agent G has a plan to do fl, that consists in doing 
some set of acts II, provided that 
1. G believes that he can execute each act in I1. 
2. G believes that executing the acts in I1 will entail 
the performance of ft. 
3. G believes that each act in I/plays a role in his plan. 
(See discussion below.) 
4. C intends to execute each act in I1. 
5. G intends to execute II as a way of doing B. 
2Although this definition ignores some important issues of commitment 
over time, as discussed by Bratman \[4\] and Cohen and Levesque \[71, it is 
sufficient to support the PI process needed for many question-answering 
situations. This is because, in such situations, unexpected changes in 
the world that would force a reconsideration of the actor's intentions can 
usually be safely ignored. 
6. G intends each act in II to play a role in his plan. 
The notion of an act playing a role in a plan is defined in 
terms of two relationships over acts: generation, in the sense 
defined by Goldman \[9\], and enablement. Roughly, one act 
generates another if, by performing the first, the agent also 
does the second; thus, saying to Kathy "How are you doing?" 
may generate asking her how she is feeling. Or, to take an 
example from the computer-mail domain, typing DEL . at 
the prompt for a computer mail system may generate deleting 
the current message, which may in turn generate cleaning out 
one's mail file. In contrast, one act enables the generation of a 
second by a third if the first brings about circumstances that 
are necessary for the generation. Thus, typing HEADER 15 
may enable the generation of deleting the fifteenth message by 
typing DEL., because it makes message 15 be the current 
message, to which '.' refers, s The difference between gener- 
ation and enablement consists largely in the fact that, when 
an act a generates an act ~, the agent need only do a, and 
will automatically be done also. However, when a enables the 
generation of some "1 by fl, the agent needs to do something 
more than just a to have done either fl or "t. In this paper, 
I consider only the inference of a restricted subset of plans, 
which I shall call simple plans. An agent has a simple plan if 
and only if he believes that all the acts in that plan play a role 
in it by generating another act; i.e., if it includes no acts that 
he believes are related to one another by enablement. 
It is important to distinguish between types of actions (act- 
types), such as typing DEL., and actions themselves, such 
as my typing DE/.. right now. Actions or acts--I will use 
the two terms interchangeahly--can be thought of as triples 
of act.type, agent, and time. Generation is a relation over 
actions, not over act-types. Not every case of an agent typing 
DEL • will result in the agent deleting the current message; 
for example, my typing it just now did not, because I was not 
typing it to a computer mail system. Similarly, executability-- 
the relation expressed in Clause (1) of (P0) as "can execute"-- 
applies to actions, and the objects of an agent's intentions are, 
in this model, also actions. 
Using the representation language specified in my thesis \[14\], 
which builds upon Allen's interval-based temporal logic \[3\], the 
conditions on G's having a simple plan to do fl can be encoded 
as follows: 
(P1) SIMPLE-PLAN(G ,a~,\[a~,..., a~-i 1,t2, tl )~ 
(i) BEL(G,EXEC(ai,G,t2),tl), for i = 1 ..... n A 
(ii) BEL(G,GEN(ai, cq+I,G,t2),tl), for i = 1 .... ,n-1 A 
(iii) INT(G,al, t2,tl), for i = 1 ..... n A 
(iv) INT(G,by(ai, ai+l), t2,tl), for i = 1 .... ,n-1 
The left-hand side of (P1) denotes that the agent G has, at 
time tl, a simple plan to do an, consisting of doing the set of 
acts {el,..., an-l} at t2. Note that all these are simultaneous 
acts; this is a consequence of the restriction to simple plans. 
The right-hand side of (P1) corresponds directly to (PO), ex- 
cept that, in keeping with the restriction to simple plans, spe- 
cific assertions about each act generating another replace the 
SEnablement here thus differs from the usual binary relation in which 
one action enables another. Since this paper does not further consider 
plans with enabling actions, the advantages of the alternative definition 
will not be discussed. 
208 
more general statement regarding the fact that each act plays 
a role in the plan. The relation BEL(G,P,t) should be taken 
to mean that agent G believes proposition P throughout time 
interval t; INT(G,a, tz,tl) means that at time tl G intends 
to do a at t2. The relation EXEC(a,G,t) is true if and only 
if the act of G doing a at t is ezecutable, and the relation 
GEN(a,//,G,t) is true if and only if the act of G doing a at 
t generates the act of G doing// at t. The function by maps 
two act-type terms into a third act-type term: if an agent G 
intends to do by(a,//), then G intends to do the complex act 
//-by-a, i.e., he intends to do a in order to do//. Further dis- 
cussion of these relations and functions can be found in Pollack 
\[14, Chap. 4\]. 
Clause (i) of (P1) captures clause (1) of (P0). 4 Clause (iS) of 
(P1) captures both clauses (2) and (3) of (P0): when i takes 
the value n-l, clause (iS) of (P1) captures the requirement, 
stated in clause (2) of (P01, that G believes his acts will entail 
his goal; when i takes values between 1 and n-2, it captures 
the requirement of clause (3) of (P0), that G believes each of 
his acts plays a role in his plan. Similarly, clause (iii) of (Pl) 
captures clause (4) of (P0), and clause (iv) of (P1) captures 
clauses (5) and (6) of (PO). 
(P1) can be used to state what it means for an actor to have 
an invalid simple plan: G has an invalid simple plan if and 
only if he has the configuration of beliefs and intentions listed 
in (P1), where one or more of those beliefs is incorrect, and, 
consequently, one or more of the intentions is unrealizable. The 
correctness of the actor's beliefs thus determines the validity 
of his plan: if all the beliefs that are part of his plan are 
correct, then all the intentions in it are realizable, and the 
plan is valid. Validity in this absolute sense, however, is not of 
primary concern in modeling plan inference in conversation. 
What is important here is rather the observer's judgement 
of whether the actor's plan is valid. It is to the analysis of 
such invalidity judgements, and their effect on the question- 
answering process, that we now turn. 
PLAN INFERENCE IN 
QUESTION-ANSWERING 
Models of the question-answering process often include a claim 
that the respondent (R) must infer the plans of the questioner 
(Q). So R is the observer, and Q the actor. Building on the 
analysis of plans as mental phenomena, we can say that, if R 
believes that she has inferred Q's plan, there is some set of be- 
liefs and intentions satisfying (P1) that R believes Q has (or is 
at least likely to have). Then there are particular discrepancies 
that may arise between the beliefs that R ascribes to Q when 
she believes he has some plan, and the beliefs that R herself 
holds. Specifically, R may not herself believe one or more of 
the beliefs, corresponding to Clauses (i) and (iS) of (P1), that 
she ascribes to Q. We can associate such discrepancies with 
41n fact, it captures more: to encode Clause (i) of (P0), the pacameter 
1 in Clause (i) of (PI) need only vary between I and n-l. However, given 
the relationship between EXEC and GEN specified in Pollack \[t4\], namely 
EX EC(a, G, t) A GEN (a, ~, G, t) ~ EXEC(~, G, t) 
the instance of Clause (i) of (P1) with i=n is a consequence of the instance 
of Clause (i) with i=n-1 and the instance of Clause (iS) with i=n-l. A 
similar argument can be made about Clause (iii). 
R's judgement that the plan she has inferred is invalid, s The 
type of any invalidities, defined in terms of the clauses of (PI) 
that contain the discrepant beliefs, can be shown to influence 
the content of a cooperative response. However, they do not 
fully determine it: the plan inferred to underlie a query, along 
with any invalidities it is judged to have, are but two factors 
affecting the response-generation process, the most significant 
others being factors of relevance and salience. 
I will illustrate the effect of invalidity judgements on re- 
sponse content with a query of the form "I want to perform 
an act of ~, so I need to find out how to perform an act of a," 
in which the goal is explicit, as in example (1) below°: 
(I) "I want to prevent Tom from reading my mail file. How 
can I set the permissions on it to faculty-read only? ~ 
In questions in which no goal is mentioned explicitly, analysis 
depends upon inferring a plan leading to a goal that is rea- 
sonable in the domain situation. Let us assume that, given 
query (1), R has inferred that Q has the simple plan that con- 
sists only in setting the permissions to faculty-read only, and 
thereby directly preventing Tom from reading the file, i.e.: 
(2)BEL(R,SIMPLE-PLAN(Q, prevent (mmfile,read,tom), 
\[set-permissions(mmfile,read,faeult y)\], 
t2, tl), 
tz) 
Later in this paper, I will describe the process by which R can 
come to have this belief. Bear in mind that, by (P1), (2) can 
be expanded into a set of beliefs that R has about Q's beliefs 
and intentions. 
The first potential discrepancy is that R may believe to be 
false some belief, corresponding to Clause (i) of (PI), that, 
by virtue of (2), she ascribes to Q. In such a case, I will say 
that she believes that some action in the inferred plan is un- 
e=~utable. Examples of responses in which R conveys this 
information are (3) (in which R believes that at least one in- 
tended act is unexecutable) and (4) (in which R believes that 
at least two intended acts are unexeeutable): 
(3) "There ia no way for you to set the permissions on a tile to 
faculty-read only. What you can do is move it into a password- 
protected subdirectory; that will prevent Tom from reading 
it." 
(4) "There is no way far you to set the permissions on a file 
to faculty.read only, nor is there any way for you to prevent 
Tom from reading it." 
SThle auumee that R always believes that her own beliefs are complete 
and correct. Such an usumption is not an unreasonable one for question- 
answering systems to make. More general conversational systems must 
abandon this usumption, sometimes updating their own beliefs upon de- 
tecting a discrepancy. 
eThe analysis below is related to that provided by 2oshi, Webber, and 
Weischedel \[10}. There are significant differences in my approach, how- 
ever, which involve (i) a different structural analysis, which applies ane=- 
scala6111lll to agtions rather than plans and introduces incoherence (this 
latter notion I dellne in the next section); (ii) a claim that the types of 
invtlldlties (e.g., formedness, executability of the queried action, and ex- 
ecutsbility of a goal action) are independent of one another; and (iii) a 
claim that recognition of any invalidities, while necessary for determining 
what information to include in an appropriate response, is not in itself 
sufficient for this purpose. Also, Joshi et el. do not consider the question 
of how invalid plans can be inferred. 
209 
The discrepancy resulting in (3) is represented in (5); the dis- 
crepancy in (4) is represented in (5) plus (6): 
(5) BEL(R,B EL(Q,EXEC(set-permissions(mmfile,read,facult y), 
Q,tz), 
tl), t~) 
A 
BEL(R,-,EXEC(set-permissions(mmfile,read,facult y), 
Q,t2), t~) 
(6) BEL(R,BEL(Q,EXEC(prevent(mmfile,read,tom), 
Q,t2), 
tl), 
ti) 
A 
BEL(R,--EXgC(prevent (ram file,read,tom), 
Q,t2), 
h) 
The second potential discrepancy is that R may believe false 
some belief corresponding to Clause (ii) of (P1) that, by virtue 
of (2), she ascribes to Q. I will then say that she believes the 
plan to be ill-formed. In this ease, her response may con~'ey 
that the intended acts in the plan will not fit together as ex- 
pected, as in (7), which might be uttered if R believes it to be 
mutually believed by R and Q that Tom is the system man- 
ager: 
(7) "Well, the command is SET PROTECTION ---- (Fac- 
ulty:Read), but that won't keep Tom out: file permissions 
don't apply to the system manager." 
The discrepancy resulting in (7) is (8): 
(8)BEL(R,BEL(Q,GEN(set-permissions(mmfile,read,facult y), 
prevent (ram file,read,tom), 
Q,t2), 
tl), 
h) 
A 
BEL(R,-~G EN (set-permissions(mmfile,read,facult y), 
prevent (mmfile,read,tom), 
Q,t2), 
h) 
Alternatively, there may be some combination of these dis- 
crepancies between R's own beliefs and those that R attributes 
to Q, as reflected in a response such as (9): 
(9) "There is no way for you to set the permissions to faculty- 
read only; and even if you could, it wouldn't keep Tom out: 
tile permissions don't apply to the system manager." 
The discrepancies encoded in (5) and (8) together might result 
in (9). 
Of course, it is also possible that no discrepancy exists at 
all, in which ease I will say that R believes that Q's plan is 
valid. A response such as (10) can be modeled as arising from 
an inferred plan that R believes valid: 
(10) "Type SET PROTECTION = (Faculty:Read)." 
Of the eight possible combinations of formedness, exe- 
curability of the queried act and executability of the goal act, 
seven are possible: the only logically incompatible combina- 
tion is a well-formed plan with an executable queried act, but 
unexecutable goal act. This range of invalidities accounts for a 
great deal of the information conveyed in naturally occurring 
dialogues. But there is an important regularity that the PI 
model does not yet explain. 
A PROBLEM FOR PLAN 
INFERENCE 
In all of the preceding cases, R has intuitively "made sense" of 
Q's query, by determining some underlying plan whose com- 
ponents she understands, though she may also believe that the 
plan is flawed. For instance in (7), R has determined that Q 
may mistakenly believe that, when one sets the permissions on 
a file to allow a particular access to a particular group, no one 
who is not a member of that group can gain access to the file. 
This (incorrect) belief explains why Q believes that setting the 
permissions will prevent Tom from reading the file. 
There are also cases in which R may not even be able to 
"make sense" of Q's query. As a somewhat whimsical example, 
imagine Q saying: 
(11) ~I want to talk to Kathy, so I need to Fred out how to 
stand on my head. ~ 
In many contexts, a perfectly reasonable response to this query 
is ~Huh? ~. Q's query is incoherent: R cannot understand why 
Q believes that finding out how to stand on his head (or stand- 
ing on his head) will lead to talking with Kathy. One can, of 
course, construct scenarios in which Q's query makes perfect 
sense: Kathy might, for example, be currently hanging by her 
feet in gravity boots. The point here is not to imagine such 
circumstances in which Q's query would be coherent, but in- 
stead to realize that there are many circumstances in which it 
would not. 
The judgement that a query is incoherent is not the same as 
a judgement that the plan inferred to underlie it is ill-formed. 
To see this, contrast example (11) with the following: 
(12) al want to talk to Kathy. Do you know the phone number 
at the hospital?" 
Here, if R believes that Kathy has already been discharged 
from the hospital, she may judge the plan she infers to underlie 
Q's query to be ill-formed, and may inform him that calling 
the hospital will not lead to talking to Kathy. She can even 
inform him why the plan is ill-formed, namely, because Kathy 
is no longer at the hospital. This differs from (11), in which R 
cannot inform Q of the reason his plan is invalid, because she 
cannot, on an intuitive level, even determine what his plan is. 
Unfortunately, the model as developed so far does not dis- 
tinguish between incoherence and ill-formedness. The reason 
is that, given a reasonable account of semantic interpretation, 
it is transparent from the query in (11) that Q intends to 
talk to Kathy, intends to find out how to stand on his head, 
and intends his doing the latter to play a role in his plan to 
do the former and that he also believes that he can talk to 
Kathy, believes that he can find out how to stand on his head, 
and believes that his doing the latter will play a role in his 
210 
plan to do the former. ~ But these beliefs and intentions are 
precisely what are required to have a plan according to (P0). 
Consequently, after hearing (11), R can, in fact, infer a plan 
underlying Q's query, namely the obvious one: to find out how 
to stand on his head (or to stand on his head) in order to talk 
to Kathy. Then, since R does not herself believe that the for- 
mer act will lead to the latter, on the analysis so far given, we 
would regard R as judging Q's plan to be ill-formed. But this 
is not the desired analysis: the model should instead capture 
the fact that R cannot make sense of Q's query here--that it 
is incoherent. 
Let us return to the set of examples about setting the per- 
missions on a file, discussed in the previous section. In her se- 
mantic interpretation of the query in (1), R may come to have 
a number of beliefs about Q's beliefs and intentions. Specifi- 
cally, all of the following may be tr~e: 
(13) BEL(R,BgL(Q,gXEC(set-permissions(mmfile,read,facult y), 
q,tz), 
tl), 
t~) 
(14) BEL(R,BEL(Q,gXEC(prevent(mmfile,read,tom), 
Q,t2), 
tl), 
t~) 
(15) BEL(R,BEL(Q,G EN(set-permissions(mmfile,read,facult y), 
prevent (mmfile,read,tom), 
Q,tz), 
tl), 
t~) 
(16) BEL( R,I NT(Q,set-permissions(mm file,read,facult y), 
t2,~l), 
tt) 
(17) BEL(R,INT(Q,prevent (mmfile,read,tom), 
t2,tl), 
t~) 
(18) BEL(R,I iT(Q,by(set-permissions(mmfile,read,facult y), 
prevent (mmfile,read,tom)), 
t2,tl), 
tl) 
Together, (13)-(18) are sumcient for R's believing that Q has 
the simple plan as expressed in (2). This much is not surpris- 
ing. In effect Q has stated in his query what his plan is--to 
prevent Tom from reading the file by setting the permission on 
it to faculty-read only--so, of course, R should be able to infer 
just that. And if R further believes that the system manager 
can override file permissions and that Tom is the system man- 
ager, but also that Q does not know the former fact, R will 
judge that Q's plan is ill-formed, and may provide a response 
such as that in (7). There is a discrepancy here between the 
belief R ascribes to Q in satisfaction of Clause (ii) of (Pl)-- 
namely, that expressed in (15)--and R's own beliefs about the 
domain. 
But what if R, instead of believing that it is mutually be- 
lieved by Q and R that Tom is the system manager, believes 
that they mutually believe that he is a faculty member? In 
this case, (13)-(18) may still be true. However we do not want 
to say that this case is indistinguishable from the previous one. 
7Actually, the requirement that Q have these beliefs may be slightly 
too strong; see Pollack \[14, Chap. 3\] for discussion. 
In the previous case, R understood the source of Q's erroneous 
belief: she realized that Q did not know that the system man- 
ager could override file protections, and therefore thought that, 
by setting permissions to restrict access to a group that Tom is 
not a member of, he could prevent Tom from reading the file. 
In contrast, in the current ease, R cannot really understand 
Q's plan: she cannot determine why Q believes that he will 
prevent Tom from reading the file by setting the permissions 
on it to faculty-read only, given that Q believes that Tom is a 
faculty member. This current case is like the case in (11): Q's 
query is incoherent to R. 
To capture the difference between iil-formedness and inco- 
herence, I will claim that, when an agent R is asked a question 
by an actor Q, R needs to attempt to ascribe to Q more than 
just a set of beliefs and intentions satisfying (Pl). Specifi- 
cally, for each belief satisfying Clause (ii) of (Pl), R must also 
ascribe to Q another belief that explains the former in a cer- 
tain specifiable way. The beliefs that satisfy Clause (ii) are 
beliefs about the relation between two particular actions: for 
instance, the plan underlying query (12) includes Q's belief 
that his action of calling the hospital at tz will generate his 
action of establishing a communication channel to Kathy at 
t2. This belief can be explained by a belief Q has about the 
relation between the act-types ~calling a location" and ~estab- 
lishing a communication channel to an agent." Q may believe 
that sets of the former type generate acts of the latter type 
provided that the agent to whom the communication channel 
is to be established is at the location to be called. Such a belief 
can be encoded using the predicate CGEN, which can be read 
"conditionally generates," as follows: 
(19)BEL(Q, CGEN(call(X),establish-channel(Y),at(X,Y)), tl) 
The relation CGEN(a, B, C) is true if and only if acts of type a 
performed when condition C holds will generate acts of type #. 
Thus, the sentence CGEN(a, B, C) can be seen as one possible 
interpretation of a hieran=hical planning operator with header 
B, preconditions C, and body a. Conditional generation is a 
relation between two act-types and a set of conditions; gener- 
ation, which is a relation between two actions, can be defined 
in terms of conditional generation. 
In reasoning about (12), R can attribute to Q the belief ex- 
pressed in (19), combined with a belief that Kathy will be at 
the hospital at time t2. Together, these beliefs explain Q's be- 
lief that, by calling the hospital at t2, he will establish a com- 
mtmieation channel to Kathy. Similarly, in reasoning about 
query (1) in the case in which R does not believe that Q knows 
that Tom is a faculty member, R can ascribe to Q the beliefs 
that, by setting the permissions on a file to restrict access to a 
partieulac group, one denies access to everyone who is neither 
s member of that group nor the system manager, as expressed 
in (20): 
(20)BEL(R,BEL(Q,CGEN(set-permissions(X,P,Y), 
prevent(X,P,Z), 
-,member(g,Y)), 
h), 
tt) 
She can also ascribe to Q the belief that Tom is not a mem- 
ber of the faculty, (or more precisely, that Tom will not be a 
member of the faculty at the intended performance time tz), 
i.e., 
211 
• I 
(21)BEL(R,BEL(Q, HOLDS(-~member(tom,facuity),t2),tl),tl} 
The conjunction of these two beliefs explains Q's further belief, 
expressed in (15), that, by setting the permissions to faculty- 
read only at t2, he can prevent Tom from reading the file. 
In contrast, in example (11), R has no basis for ascribing to 
Q beliefs that will explain why he thinks that standing on his 
head will lead to talking with Kathy. And, in the version of 
example (1) in which R believes that Q believes that Tom is a 
faculty member, R has no basis for ascribing to Q a belief that 
explains Q's belief that setting the permissions to faculty-read 
only will prevent Tom from reading the file. 
Explanatory beliefs are incorporated in the PI model by the 
introduction of ezplanatory plans, or eplans. Saying that an 
agent R believes that another agent Q has some eplan is short- 
hand for describing a set of beliefs possessed by R, specifically: 
(P2) (R,EPLAN(Q,~n,\[al ..... an-l\],\[pl ..... Pn-l\], 
t2, tl),tl ) 
(i) BEL(R,BEL(Q,EXEC(cq,Q,t2),tl),tl), 
for i = 1,...,n A 
(ii) BEL(R,BEL(Q,G EN(~, ai+t,Q,t2),tt),tl ), 
for i = 1,...,n-I A 
(iii) BEL(R,INT(Q,~I, tz, tl),tl), 
for i = 1,..., n A 
(iv) BEL(R,INT(Q,by~al, ai+l), t2, tl),tl), 
for i = 1,... ,n-1 A 
(v) BEL(R,BEL(Q,pi, tl),tl), 
where each Pi is 
CGEN(ai, cq+l, Ci) A HOLDS(Ci, t2) 
I claim that the PI process underlying cooperative question- 
answering can be modeled as an attempt to infer an eplan, 
i.e., to form a set of beliefs about the questioner's beliefs and 
intentions that satisfies (P2). Thus the next question to ask 
is: how can R come to have such a set of beliefs? 
THE INFERENCE PROCESS 
In the complete PI model, the inference of an eplan is a two- 
stage process. First, R infers beliefs and intentions that Q 
plausibly has. Then when she has found some set of theme 
that is large enough to account for Q's query, their epistemie 
status can be upgraded, from beliefs and intentions that R be- 
lieves Q plausibly has, to beliefs and intentions that R will, for 
the purposes of forming her response, consider Q actually to 
have. Within this paper, however, I will blur the distinction 
between attitudes that R believes Q plausibly has and atti- 
tudes that R believes Q indeed has; in consequence I will also 
omit discussion of the second stage of the PI process. 
A set of plan inference rules encodes the principles by which 
an inferring agent R can reason from some set of beliefs and 
intentions--call this the antecedent eplan--that she thinks Q 
has, to some further set of beliefs and intentions--call this the 
consequent eplan--that she also thinks he has. The beliefs and 
intentions that the antecedent eplan comprises are a proper 
subset of those that the consequent eplan comprises. To reason 
from antecedent eplan to consequent eplan, R must attribute 
some explanatory belief to Q on the basis of something other 
than just Q's query. In more detail, if part of R's belief that 
Q has the antecedent eplan is a belief that Q intends to do 
some act a, and R has reason to believe that Q believes that 
act-type a conditionally generates act-type 3' under condition 
C, then R can infer that Q intends to do a in order to do % 
believing as well that C will hold at performance time. R can 
also reason in the other direction: if part of her belief that Q 
has some plausible eplan is a belief that Q intends to do some 
act a and R has reason to believe that Q believes that act-type 
conditionally generates act-type a under condition C, then 
R can infer that Q intends to do "~ in order to do a, believing 
that C will hold st performance time. 
The plan inference rules encode the pattern of reasoning ex- 
pressed in the last two sentences. Different plan inference rules 
encode the different bases upon which R may decide that Q 
may believe that a conditional generation relation holds be- 
tween some a, an act of which is intended as part of the an- 
tecedent eplan, and some % This ascription of beliefs, as well 
as the ascription of intentions, is a nonmonotonic process. For 
arbitrary proposition P, R will only decide that Q may believe 
that P if R has no reason to believe Q believes that -~P. 
In the most straightforward case, R will ascribe to Q a be- 
lief about s conditional generation relation that she herself 
believes true. This reasoning can be encoded in the represen- 
tation language in rule (PI1): 
(PII) BEL(R,EPLAN(Q,an,\[al ..... an-a\],\[pl ..... On-t\], 
t2,h),h) 
A 
BEL(R,CGEN(an, % C),q) 
BEL( R,EPLAN(Q,%\[al ..... a,\],\[pl ..... p, \],t2, tl ),tl ) 
where p, ~. CGEN(ar,,"I, C) ^ HOLDS(C, t2) 
This rule says that, if R's belief that Q has some eplan includes 
a belief that Q intends to do an act an, and R also believes that 
act-type a~ conditionally generates some "~ under condition C, 
then R can (nonmonotonically) infer that Q has the additional 
intention of doing a, in order to do ~--i.e., that he intends to 
do by(an, "~). Q's having this intention depends upon his also 
having the supporting belief that a n conditionally generates ~' 
under some condition C, and the further belief that this C will 
hold at performance time. A rule symmetric to (PI1) is also 
needed since R can not only reason about what acts might be 
generated by an act that she already believes Q intends, but 
also about what acts might generate such an act. 
Consider R's use of (PI1) in attempting to infer the plan 
underlying query (1)) R herself has a particular belief about 
the relation between the act-types "setting the permissions on 
• file" and "preventing someone access to the file," a belief we 
can encode as follows: 
(22) BEL{ R,CG EN (met-permissions(X,P,Y), 
prevent(X,P,Z), 
-~member(Z,Y) A--system-mgr(Z)), q) 
From query (1}, R can directly attribute to Q two trivial 
eplans: 
sI have simplified somewhat in the following account for presentational 
purposes. A step-by-step account of this inference process is given in 
Poll~ck \[14, Chap. 6\]. 
212 
( 23 ) B E L( R, E P b A N ( Q,set-p ermissions( mmfile,read,facult y ), 
\[ \],t2, t,), 
tl) 
(24)BEL(R,EPLAN(Q,prevent(mmfile,read,tom),\[ \],t2, tl ), 
tl) 
The belief in (23) is justified by the fact that (13) satisfies 
Clause (i) of (P2), (16) satisfies Clause (iv) of (P2), and 
Clauses (ii), (iii), and (v) are vacuously satisfied. An anal- 
ogous argument applies to (24). 
Now, if R applies (PII), she will attribute to Q exactly the 
same belief as she herself has, as expressed in (22), along with 
a belief that the condition C specified there will hold at t2. 
That is, as part of her belief that a particular eplan underlies 
(1), R will have the following belief: 
(25) BEL(R,BEL(Q,CG EN(set-permissions(X,P,Y), 
prevent(X,P,Z), 
-,member(Z,Y) A -~system-mrg(Z)) 
A 
HOLDS(-,member(tom,faeulty) 
A --system-mgr(tom), tz), 
tl), 
q) 
The belief that R attributes to Q, as expressed in (25), is 
an explanatory belief supporting (15). Note that it is not the 
same explanatory belief that was expressed in (20) and (21). In 
(25), the discrepancy between R's beliefs and R's beliefs about 
Q's beliefs is about whether Tom is the system manager. This 
discrepancy may result in a response like (26), which conveys 
different information than does (7} about the source of the 
judged ill-formedness. 
(26) "Well, the command is SET PROTECTION = (Fac- 
ulty:Read), but that won't keep Tom out: he's the system 
manager." 
(PI1) (and its symmetric partner) are not sufficient to model 
the inference of the eplan that results in (7). This is because, in 
using (PI1), R is restricted to ascribing to Q the same beliefs 
about the relation between domain act-types as she herself 
has. ~ The eplan that results in (7) includes a belief that R 
attributes to Q involving a relation between act-types that R 
believes false, specifically, the CGEN relation in (20). What 
is needed to derive this is a rule such as (PI2): 
(PI2) BEL(R,EPLAN(Q,on,\[al ..... an-l\],\[pl ..... Pn-l\], 
t2, t,),q ) 
A 
BEL(R,CGEN(an, 7, C~ A... A Cm),tl) 
--4 
BEL(R,EPLAN(Q,7,\[al,..., a,\],\[pl ..... p,\],tz, q ),q ) 
where p, = CGEN(an, % CIA...ACi-IACi+IA...ACm)A 
HOLDS(C, A... A Ci-1 A Ci+l h ...A Cm,t2) 
~Hence, existing PI systems that equate R's and Q's beliefs about 
actions could, in principle, have handled examples such as (26) which 
r,: ~:Sre only the use of (PI1), although they have not done so. Further, 
whi\]~ they could have handled the particular type of invalidity that can be 
inferred using (PII), without an analysis of the general problem of invalid 
plans and their effects on cooperative responses, these systems would need 
to treat this as a special case in which a variant response is required. 
What (PI2) expresses is that R may ascribe to Q a belief about 
a relation between act-types that is a slight variation of one 
she herself has. What (PI2) asserts is that, if there is some 
CGEN relation that R believes true, she may attribute to Q 
a belief in a similar CGEN relation that is stronger, in that it 
is missing one of the required conditions. If R uses (PI2) in 
attempting to infer the plan that underlies query (1), she may 
decide that Q's belief about the conditions under which setting 
the permissions on a file prevents someone from accessing the 
file do not include the person's not being the system manager. 
This can result in R attributing to Q the explanatory belief in 
(20) and (21), which, in turn, may result in a response such as 
that in (7). 
Of course, both the kind of discrepancy that may be in- 
troduced by (PI1) and the kind that is always introduced by 
(PI2) may be present simultaneously, resulting in a response 
like (27): 
(27) "Well, the command is SET PROTECTION = (Fac- 
ulty:Read), but that won't keep Tom out: he's the system 
manager, and file permissions don't apply to the system man- 
ager." 
(PI2) represents just one kind of variation of her own beliefs 
that R may consider attributing to Q. Additional PI rules 
encode other variations and can also be used to encode any 
typical misconceptions that R may attribute to Q. 
IMPLEMENTATION 
The inference process described in this paper has been imple- 
mented in SPIRIT, a System for Plan Inference that Reasons 
about Invalidities Too. SPIRIT infers and evaluates the plans 
underlying questions asked by users about the domain of com- 
puter mail. It also uses the result of its inference and eval- 
uation to generate simulated cooperative responses. SPIRIT 
is implemented in C-Prolog, and has run on several differ- 
ent machines, ineludinga Sun Workstation, a Vax 11-750, 
and a DEC-20. SPIRIT is a demonstration system, imple- 
mented to demonstrate the PI model developed in this work; 
consequently only a few key examples, which are sufficient to 
demonstrate SPIRIT's capabilities, have been implemented. 
Of course, SPIRIT's knowledge base could be expanded in a 
straightforward manner. SPIRIT has no mechanisms for com- 
puting relevance or salience and, consequently, always pro- 
duces as complete an answer as possible. 
CONCLUSION 
In this paper I demonstrated that modeling cooperative con- 
versation, in particular cooperative question-answcring, re- 
quires a model of plan inference that distinguishes between 
the beliefs of actors and those of observers. I reported on such 
a model, which rests on an analysis of plans as mental phenom- 
ena. Under this analysis there can be discrepancies between an 
agent's own beliefs and the beliefs that she ascribes to an actor 
when she thinks he has some plan. Such discrepancies were as- 
sociated with the observer's judgement that the actor's plan is 
invalid. Then the types of any invalidities judged to be present 
in a plan inferred to underlie a query were shown to affect the 
content of a cooperative response. 1 further suggested that, to 
213 
guarantee a cooperative response, the observer must attempt 
to ascribe to the questioner more than just a set of beliefs and 
intentions sufficient to believe that he has some plan: she must 
also attempt to ascribe to him beliefs that explain those beliefs 
and intentions. The eplan construct was introduced to capture 
this requirement. Finally, I described the process of inferring 
eplans--that is, of ascribing to another agent beliefs and in- 
tentions that explain his query and can influence a response 
to it. 
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214 
