A Practical Nonmonotonic Theory 
for Reasoning about Speech Acts 
Douglas Appelt, Kurt Konolige 
Artificial Intelligence Center and 
Center for the Study of Language and Information 
SRI International 
Menlo Park, California 
Abstract 
A prerequisite to a theory of the way agents un- 
derstand speech acts is a theory of how their be- 
liefs and intentions are revised as a consequence 
of events. This process of attitude revision is 
an interesting domain for the application of non- 
monotonic reasoning because speech acts have a 
conventional aspect that is readily represented by 
defaults, but that interacts with an agent's be- 
liefs and intentions in many complex ways that 
may override the defaults. Perrault has devel- 
oped a theory of speech acts, based on Rieter's 
default logic, that captures the conventional as- 
pect; it does not, however, adequately account for 
certain easily observed facts about attitude revi- 
sion resulting from speech acts. A natural the- 
ory of attitude revision seems to require a method 
of stating preferences among competing defaults. 
We present here a speech act theory, formalized 
in hierarchic autoepistemic logic (a refinement of 
Moore's autoepistemic logic), in which revision of 
both the speaker's and hearer's attitudes can be 
adequately described. As a collateral benefit, effi- 
cient automatic reasoning methods for the formal- 
ism exist. The theory has been implemented and 
is now being employed by an utterance-planning 
system. 
1 Introduction 
The general idea of utterance planning has been 
at the focus of much NL processing research for 
the last ten years. The central thesis of this 
170 
approach is that utterances are actions that are 
planned to satisfy particular speaker goals. This 
has led researchers to formalize speech acts in a 
way that would permit them to be used as op- 
erators in a planning system \[1,2\]. The central 
problem in formalizing speech acts is to correctly 
capture the pertinent facts about the revision of 
the speaker's and hearer's attitudes that ensues 
as a consequence of the act. This turns out to be 
quite difficult bemuse the results of the attitude 
revision are highly conditional upon the context of 
the utterance. 
To consider just a small number of the contin- 
gencies that may arise, consider a speaker S utter- 
ing a declarative sentence with propositional con- 
tent P to hearer H. One is inclined to say that, 
if H believes S is sincere, H will believe P. How- 
ever, if H believes -~P initially, he may not be 
convinced, even if he thinks S is sincere. On the 
other hand, he may change his beliefs, or he may 
suspend belief as to whether P is true. H may 
not believe --P, but simply believe that S is neiter 
competent nor sincere, and so may not come to 
believe P. The problem one is then faced with 
is this: How does one describe the effect of ut- 
tering the declarative sentence so that given the 
appropriate contextual elements, any one of these 
possibilities can follow from the description? 
One possible approach to this problem would be 
to find some fundamental, context-independent ef- 
fect of informing that is true every time a declara- 
tive sentence is uttered. If one's general theory of 
the world and of rational behavior were sufficiently 
strong and detailed, any of the consequences of 
attitude revision would be derivable from the ba- 
sic effect in combination with the elaborate theory 
of rationality. The initial efforts made along this 
path \[3,5\] entailed the axiomatization the effects 
of speech acts as producing in the hearer the be- 
lief that the speaker wants him to recognize the 
latter's intention to hold some other belief. The 
effects were characterized by nestings of Goal and 
Bel operators, as in 
Bel(H, Goal(S, Bel(H, P))). 
If the right conditions for attitude revision ob- 
tained, the conclusion BeI(H,P) would follow 
from the above assumption. 
This general approach proved inadequate be- 
cause there is in fact no such statement about b.e- 
liefs about goals about beliefs that is true in every 
performance of a speech act. It is possible to con- 
struct a counterexample contradicting any such ef- 
fect that might be postulated. In addition, long 
and complicated chains of reasoning are required 
to derive the simplest, most basic consequences of 
an utterance in situations in which all of the "nor- 
real" conditions obtain -- a consequence that runs 
counter to one's intuitive expectations. 
Cohen and Levesque \[4\] developed a speech act 
theory in a monotonic modal logic that incorpo- 
rates context-dependent preconditions in the ax- 
ioms that state the effects of a speech act. Their 
approach overcomes the theoretical difficulties of 
earlier context-independent attempts; however, if 
one desires to apply their theory in a practical 
computational system for reasoning about speech 
acts, one is faced with serious difficulties. Some 
of the context-dependent conditions that deter- 
mine the effects of a speech act, according to their 
theory, involve statements about what an agent 
does no~ believe, as well as what he does believe. 
This means that for conclusions about the effect of 
speech acts to follow from the theory, it must in- 
clude an explicit representation of an agent's igno- 
rance as well as of his knowledge, which in practice 
is difficult or even impossible to achieve. 
A further complication arises from the type of 
reasoning necessary for adequate characterization 
of the attitude revision process. A theory based on 
monotonic reasoning can only distinguish between 
belief and lack thereof, whereas one based on non- 
monotonic reasoning can distinguish between be- 
171 
lief (or its absence) as a consequence of known 
facts, and belief that follows as a default because 
more specific information is absent. To the extent 
that such a distinction plays a role in the attitude 
revision process, it argues for a formalization with 
a nonmonotonic character. 
Our research is therefore motivated by the fol- 
lowing observations: (1) earlier work demonstrates 
convincingly that any adequate speech-act theory 
must relate the effects of a speech act to context- 
dependent preconditions; (2) these preconditions 
must depend on the ignorance as well as on the 
knowledge of the relevant agents; (3)any prac- 
tical system for reasoning about ignorance must 
be based on nonmonotonic reasoning; (4) existing 
speech act theories based on nonmonotonic rea- 
soning cannot account for the facts of attitude re- 
vision resulting from the performance of speech 
acts. 
2 Perrault's Default Theory 
of Speech Acts 
As an alternative to monotonic theories, Perrault 
has proposed a theory of speech acts, based on an 
extension of Reiter's default logic \[11\] extended 
to include-defanlt-rule schemata. We shall sum- 
marize Perrault's theory briefly as it relates to in- 
forming and belief. The notation p =~ q is intended 
as an abbreviation of the default rule of inference, 
p:Mq 
q 
Default theories of this form are called normal. 
Every normal default theory has at least one ex- 
tension, i.e., a mutually consistent set of sentences 
sanctioned by the theory. 
The operator Bz,t represents Agent z's beliefs at 
time t and is assumed to posess all the properties 
of the modal system weak $5 (that is, $5 without 
the schema Bz,t~ D ~b), plus the following axioms: 
Persistence: 
B~,t+IB~,~P D B~,~+IP 
Memory: 
(1) 
B~,~P D B~,t+IB~,~P (2) 
Observability: 
Do~,,a ^ D%,,(Obs(Do~,,(a))) 
B.,,+lDo.,,(a) 
Belief Transfer: 
(3) 
B~,tBy,~P =~ B,,tP (4) 
Declarative: 
Do~,t(Utter(P)) =~ Bz,,P (5) 
In addition, there is a default-rule schema stat- 
ing that, if p =~ q is a default rule, then so is 
B~,~p =~ Bx,tq for any agent z and time t. 
Perrault could demonstrate that, given his the- 
ory, there is an extension containing all of the 
desired conclusions regarding the beliefs of the 
speaker and hearer, starting from the fact that 
a speaker utters a declarative sentence and the 
hearer observes him uttering it. Furthermore, the 
theory can make correct predictions in cases in 
which the usual preconditions of the speech act 
do not obtain. For example, if the speaker is ly- 
ing, but the hearer does not recognize the lie, then 
the heater's beliefs are exactly the same as when 
the speaker tells the truth; moreover the speaker's 
beliefs about mutual belief are the same, but he 
still does not believe the proposition he uttered m 
that is, he fails to be convinced by his own lie. 
3 Problems with Perrault's 
Theory 
A serious problem arises with Perrault's theory 
concerning reasoning about an agent's ignorance. 
His theory predicts that a speaker can convince 
himself of any unsupported proposition simply by 
asserting it, which is clearly at odds with our in- 
tuitions. Suppose that it is true of speaker s that 
~Bs,tP. Suppose furthermore that, for whatever 
reason, s utters P. In the absence of any further 
information about the speaker's and hearer's be- 
liefs, it is a consequence of axioms (1)-(5) that 
Bs,~+IBh,~+IP. From this consequence and the 
belief transfer rule (4) it is possible to conclude 
B,,~+IP. The strongest conclusion that can be 
derived about s's beliefs at t + 1 without using 
172 
this default rule is B,,t+I"~B,,~P, which is not suf- 
ficient to override the default. 
This problem does not admit of any simple fixes. 
One clearly does not want an axiom or default rule 
of the form that asserts what amounts to "igno- 
rance persists" to defeat conclusions drawn from 
speech acts. In that case, one could never con- 
clude that anyone ever learns anything as a result 
of a speech act. The alternative is to weaken the 
conditions under which the default rules can be 
defeated. However, by adopting this strategy we 
are giving up the advantage of using normal de- 
faults. In general, nonnormal default theories do 
not necessarily have extensions, nor is there any 
proof procedure for such logics. 
Perrault has intentionally left open the question 
of how a speech act theory should be integrated 
with a general theory of action and belief revision. 
He finesses this problem by introducing the per- 
sistence axiom, which states that beliefs always 
persist across changes in state. Clearly this is not 
true in general, because actions typically change 
our beliefs about what is true of the world. Even 
if one considers only speech acts, in some cases • 
one can get an agent to change his beliefs by say- 
ing something, and in other cases not. Whether 
one can or not, however, depends on what be- 
lief revision strategy is adopted by the respective 
agents in a given situation. The problem cannot 
be solved by simply adding a few more axioms 
and default rules to the theory. Any theory that 
allows for the possibility of describing belief revi- 
sion must of necessity confront the problem of in- 
consistent extensions. This means that, if a hearer 
initially believes -~p, the default theory will have 
(at least) one extension for the case in which his 
belief that -~p persists, and one extension in which 
he changes his mind and believes p. Perhaps it 
will even have an extension in which he suspends 
belief as to whether p. 
The source of the difficulties surrounding Per- 
ranlt's theory is that the default logic h e adopts 
is unable to describe the attitude revision that oc- 
curs in consequence of a speech act. It is not our 
purpose here to state what an agent's belief re- 
vision strategy should be. Rather we introduce a 
framework within which a variety of belief revision 
strategies can be accomodated efficiently, and we 
demonstrate that this framework can be applied in 
a way that eliminates the problems with Perranlt's 
theory. 
Finally, there is a serious practical problem 
faced by anyone who wishes to implement Per- 
fault's theory in a system that reasons about 
speech acts. There is no way the belief transfer 
rule can be used efficiently by a reasoning sys- 
tem; even if it is assumed that its application is 
restricted to the speaker and hearer, with no other 
agents in the domain involved. If it is used in a 
backward direction, it applies to its own result. In- 
voking the rule in a forward direction is also prob- 
lematic, because in general one agent will have a 
very large number of beliefs (even an infinite num- 
ber, if introspection is taken into account) about 
another agent's beliefs, most of which will be ir- 
relevant to the problem at hand. 
4 Hierarchic Autoepistemic 
Logic 
Autoepistemic (AE) logic was developed by Moore 
\[I0\] as a reconstruction of McDermott's nonmono- 
tonic logic \[9\]. An autoepistemic logic is based on 
a first-order language augmented by a modal op- 
erator L, which is interpreted intuitively as self 
belief. A stable ezpansio, (analogous to an exten- 
sion of a default theory) of an autoepistemic base 
set A is a set of formulas T satisfying the following 
conditions: 
1. T contains all the sentences of the base the- 
ory A 
2. T is closed under first-order consequence 
3. If ~b E T, then L~b E T 
4. If ¢ ~ T, then --L~b 6 T 
Hierarchic autoepistemic logic (HAEL) was de- 
veloped in response to two deficiences of autoepis- 
temic logic, when the latter is viewed as a logic 
for automated nonmonotonic reasoning. The first 
is a representational problem: how to incorporate 
preferences among default inferences in a natural 
way within the logic. Such preferences arise in 
many disparate settings in nonmonotonic reason- 
ing -- for example, in taxonomic hierarchies \[6\] 
or in reasoning about events over time \[12\]. To 
some extent, preferences among defaults can be 
173 
encoded in AE logic by introducing auxiliary in- 
formation into the statements of the defaults, but 
this method does not always accord satisfactorily 
with our intuitions. The most natural statement 
of preferences is with respect to the multiple ex- 
pansions of a particular base set, that is, we pre- 
fer certain expansions because the defaults used in 
them have a higher priority than the ones used in 
alternative expansions. 
The second problem is computational: how to 
tell whether a proposition is contained within the 
desired expansion of a base set. As can be seen 
from the above definition, a stable expansion of 
an autoepistemic theory is defined as a fixedpoint; 
the question of whether a formula belongs to this 
fixedpoint is not even semidecidable. This prob- 
lem is shared by all of the most popular nonmono- 
tonic logics. The usual recourse is to restrict the 
expressive power of the language, e.g., normal de- 
fault theories \[11\] and separable circumscriptive 
theories \[8\]. However, as exemplified by the diffi- 
culties of Perrault's approach, it may not be easy 
or even possible to express the relevant facts with 
a restricted language. 
Hierarchical autoepistemic logic is a modifica- 
tion of autoepistemic logic that addresses these 
two considerations. In HAEL, the primary struc- 
ture is not a single uniform theory, but a collection 
of subtheories linked in a hierarchy. Snbtheories 
represent different sources of information available 
to an agent, while the hierarchy expresses the way 
in which this information is combined. For ex- 
ample, in representing taxonomic defaults, more 
specific information would take precedence over 
general attributes. HAEL thus permits a natural 
expression of preferences among defaults. Further- 
more, given the hierarchical nature of the subthe- 
ory relation, it is possible to give a constructive 
semantics for the autoepistemic operator, in con- 
trast to the usual self-referential fixedpoints. We 
can then arrive easily at computational realiza- 
tions of the logic. 
The language of HAEL consists of a standard 
first-order language, augmented by a indexed set 
of unary modal operators Li. If ~b is any sentence 
(containing no free variables) of the first-order lan- 
guage, then L~ is also a sentence. Note that nei- 
ther nesting of modal operators nor quantifying 
into a modal context is allowed. Sentences with- 
out modal operators are called ordinary. 
An HAEL structure r consists of an indexed 
set of subtheories rl, together with a partial order 
on the set. We write r~ -< rj if r~ precedes rj in 
the order. Associated with every subtheory rl is a 
base set Ai, the initial sentences of the structure. 
Within A~, the occurrence of Lj is restricted by 
the following condition: 
If Lj occurs positively (negatively) in (6) 
Ai, then rj _ r~ (rj -< ri). 
This restriction prevents the modal operator from 
referring to subtheories that succeed it in the hier- 
archy, since Lj~b is intended to mean that ~b is an 
element of the subtheory rj. The distinction be- 
tween positive and negative occurrences is simply 
that a subtheory may represent (using L) which 
sentences it contains, but is forbidden from repre- 
senting what it does not contain. 
A complez stable e~pansion of an HAEL struc- 
ture r is a set of sets of sentences 2~ corresponding 
to the subtheories of r. It obeys the following con- 
ditions (~b is an ordinary sentence): 
1. Each T~ contains Ai 
2. Each Ti is closed under first-order conse- 
quence 
3. If eEl, and ~'j ~ rl, then Lj~b E~ 
4. If ¢ ~ ~, and rj -< rl, then -,Lj ~b E 
5. If ~ E Tj, and rj -< vi, then ~bE~. 
These conditions are similar to those for AE sta- 
ble expansions. Note that, in (3) and (4), 2~ con- 
tains modal atoms describing the contents of sub- 
theories beneath it in the hierarchy. In addition, 
according to (5) it also inherits all the ordinary 
sentences of preceeding subtheories. 
Unlike AE base sets, which may have more 
than one stable expansion, HAEL structures have 
a unique minimal complex stable expansion (see 
Konolige \[7\]). So we are justified in speaking of 
"the" theory of an HAEL structure and, from this 
point on, we shall identify the subtheory r~ of a 
structure with the set of sentences in the complex 
stable expansion for that subtheory. 
Here is a simple example, which can be inter- 
preted as the standard "typically birds fly" default 
i74 
scenario by letting F(z) be "z flies," B(z) be "z 
is a bird," and P(z) be "z is a penguin." 
Ao -- {P(a), B(a)} 
AI - {LIP(a) A",LoF(a) D -,F(a)} 
A2 -" {L2B(a) A ",LI-,F(a) D F(a)} 
(7) 
Theory r0 contains all of the first-order con- 
sequences of P(a), B(a), LoP(a), and LoB(a). 
-~LoF(a) is not in r0, hut it is in rl, as is LoP(a), 
-LooP(a), etc. Note that P(a) is inherited by 
rl; hence L1P(a) is in rl. Given this, by first- 
order closure ",F(a) is in rl and, by inheritance, 
LI",F(a) is in r2, so that F(a) cannot be derived 
there. On the other hand, r2 inherits ",F(a) from 
rl. 
Note from this example that information 
present in the lowest subtheories of the hierarchy 
percolates to its top. More specific evidence, or 
preferred defaults, should be placed lower in the 
hierarchy, so that their effects will block the action 
of higher-placed evidence or defaults. 
HAEL can be given a constructive semantics 
that is in accord with the closure conditions. 
W'hen the inference procedure of each subtheory 
is decidable, an obvious decidable proof method 
for the logic exists. The details of this develop- 
ment are too complicated to be included here, but 
are described by Konolige \[7\]. For the rest of this 
paper, we shall use a propositional base language; 
the derivations can be readily checked. 
5 A HAEL Theory of Speech 
Acts 
We demonstrate here how to construct a hierarchic 
autoepistemic theory of speech acts. We assume 
that there is a hierarchy of autoepisternic subthe- 
ories as illustrated in Figure i. The lowest subthe- 
ory, ~'0, contains the strongest evidence about the 
speaker's and hearer's mental states. For exam- 
ple, if it is known to the hearer that the speaker 
is lying, this information goes into r0. 
In subtheory vl, defaults are collected about the 
effects of the speech act on the beliefs of both 
hearer and speaker. These defaults can be over- 
ridden by the particular evidence of r0. Together 
r0 and rl constitute the first level of reasoning 
about the speech act. At Level 2, the beliefs of 
the speaker and hearer that can be deduced in 
rl are used as evidence to guide defaults about 
nested beliefs, that is, the speaker's beliefs about 
the heater's beliefs, and vice versa. These results 
are collected in r2. In a similar manner, successive 
levels contain the result of one agent's reflection 
upon his and his interlocutor's beliefs and inten- 
tions at the next lower level. We shall discuss here 
how Levels r0 and rl of the HAEL theory are ax- 
iomatized, and shall extend the axiomatization to 
the higher theories by means of axiom schemata. 
An agent's belief revision strategy is represented 
by two features of the model. The position of 
the speech act theory in the general hierarchy of 
theories determines the way in which conclusions 
drawn in those theories can defeat conclusions that 
follow from speech acts. In our model, the speech 
act defaults will go into the subtheory rl, while 
evidence that will be used to defeat these defaults 
will go in r0. In addition, the axioms that relate 
rl to r0 determine precisely what each agent is 
willing to accept from 1"0 as evidence against the 
default conclusions of the speech act theory. 
It is easy to duplicate the details of Perrault's 
analysis within this framework. Theory r0 would 
contain all the agents' beliefs prior to the speech 
act, while the defaults of rl would state that an 
agent believed the utterance P if he did not be- 
lieve its negation in r0. As we have noted, this 
analysis does not allow for the situation in which 
the speaker utters P without believing either it 
or its opposite, and then becomes convinced of its 
truth by the very fact of having uttered it m nor 
does it allow the hearer to change his belief in -~P 
as a result of the utterance. 
We choose a more complicated and realistic ex- 
pression of belief revision. Specifically, we allow 
an agent to believe P (in rl) by virtue of the ut- 
terance of P only if he does not have any evidence 
(in r0) against believing it. Using this scheme, 
we can accommodate the hearer's change of be- 
lief, and show that the speaker is not convinced 
by his own efforts. 
We now present the axioms of the HAEL theory 
for the declarative utterance of the proposition P. 
The language we use is a propositional modal one 
175 
for the beliefs of the speaker and hearer. Agents s 
and h represent the speaker and hearer; the sub- 
scripts i and f represent the initial situation and 
the situation resulting from the utterance, respec- 
tively. There are two operators: \[a\] for a's belief 
and {a} for a's goals. The formula \[hI\]c~, for exam- 
ple, means that the hearer believes ~b in the final 
situation, while {si}¢ means that the speaker in- 
tended ~b in the initial situation. In addition, we 
use a phantom agent u to represent the content of 
the utterance and certain assumptions about the 
speaker's intentions. We do not argue here as to 
what constitutes the correct logic of these opera- 
tors; a convenient one is weak $5. 
The following axioms are assumed to hold in all 
subtheories. 
\[u\]P, P the propositional content of ut- (8) 
terance 
\[~\]¢ D \[~\]{s~}\[hA¢ (9) 
\[a\]{a}¢ ~. {a}¢, where a is any (10) 
agent in any sit- 
uation. 
The contents of the u theory are essentially the 
same for all types of speech acts. The precise ef- 
fects upon the speaker's and heater's mental states 
is determined by the propositional content of the 
utterance and its mood. We assume here that the 
speaker utters, a simple declarative sentence, (Ax- 
iom 8), although a similar analysis could be done 
for other types of sentences, given a suitable repre- 
sentation of their propositional content. Proposi- 
tions that are true in u generally become believed 
by the speaker and hearer in rl, provided that 
these propositions bear the proper relationship to 
their beliefs in r0. Finally, the speaker in$ends to 
bring about each of the beliefs the hearer acquires 
in rl, also subject to the caveat that it is consistent 
with his beliefs in to. 
Relation between subtheories: 
ro -~ n (11) 
Speaker's beliefs as a consequence of the speech 
act: 
in AI: \[u\]¢ A -~L0-~\[sl\]¢ D \[s/\]¢ (12) 
Level 1 
SSSS~S~SS~SSS~S SSSS~SSSSSSS~ 
SSS~S~ SS~ SSS 
SSS SSS SS~ SS~ 
SS~ S~ ~S S~S 
SSS SS~ 
s~SSSSSSS~SSS~S 
Level 3 
1 S,S ~'~'~" ~'s" S SS Ss" S S SSSSe'~'SS~'SSSS SSO' SS 
SSSSSSSSSfSSSS, SSSSSSSss/ssss, 
SSSSSSS S/S//S, SSS~SS, 
SSS SS, SsS SS, 
SSS SS, /SS 
S/. SSS 
SS, ~ SSJ 
......... -iS, SSSSSSs~SSSSSS, 
SSSSSSSSSSSSSS, ¢sssss¢¢¢sssss, 
Figure 1: A Hierarchic Autoepistemic Theory 
Hearer's beliefs as a consequence of the speech act: 
in AI: 
^ (13) 
-~L0--\[h/\]~b ^ ~Zo\[hy\]',\[Sl\]¢~ ^ 
"~Lo\[hy\]"{si}\[hy\]~) D \[h/l~b 
The asymmetry between Axioms 12 and 13 is a 
consequence of the fact that a speech act has dif- 
ferent effects on the speaker's and hearer's mental 
states. The intuition behind these axioms is that 
a speech act should never change the speaker's 
mental attitudes with regard to the proposition 
he utters. If he utters a sentence, regardless of 
whether he is lying, or in any other way insincere, 
he should believe P after the utterance if and only 
if he believed it before. However, in the bearer's 
case, whether he believes P depends not only on 
his prior mental state with respect to P, but also 
on whether he believes that the speaker is being 
sincere. ~iom 13 states that a hearer is willing to 
believe what a speaker says if it does not conflict 
with his own beliefs in ~, and if the utterance does 
not conflict with what the hearer believes about 
the speaker's mental state, (i.e., that the speaker 
is not lying), and if he believes that believing P 
is consistent with his beliefs about the speaker's 
prior intentions (i.e., that the speaker is using the 
utterance with communicative intent, as distinct 
from, say, testing a microphone). 
As a first example of the use of the theory, con- 
sider the normal case in which A0 contains no evi- 
dence about the speaker's and bearer's beliefs after 
the speech act. In this event, A0 is empty and A1 
contains Axioms 8-1b. By the inheritance condi- 
tions, 1"1 contains -~L0-,\[sl\]P , and so must contain 
\[s/\]P by axiom 12. Similarly, from Axiom 13 it fol- 
lows that \[h/\]P is in rl. Further derivations lead 
to {sl}\[hl\]P , {si}\[hl\]{si}\[hy\]P , and so on. 
As a second example, consider the case in which 
the speaker utters P, perhaps to convince the 
hearer of it, but does not himself believe either 
P or its negation. In this case, 1"0 contains -~\[sf\]P 
and -~\[sl\]-~P , and ~'1 must contain Louis tiP by 
the inheritance condition. Hence, the application 
of Axiom 12 will be blocked, and so we cannot 
conclude in ~'1 that the speaker believes P. On 
the other hand, since none of the antecedents of 
Axiom 13 are affected, the hearer does come to 
believe it. 
Finally, consider belief revision on the part of 
the hearer. The precise path belief revision takes 
depends on the contents of r0. If we consider the 
hearer's belief to be stronger evidence than that of 
the utterance, we would transfer the heater's ini- 
tial belief \[hl\]~P to \[h/\]'-,P in ~'0, and block the de- 
fault Axiom 13. But suppose the hearer does not 
believe --P strongly in the initial situation. Then 
176 
we would transfer (by default) the belief \[h\]\]~P 
to a subtheory higher than rl, since the evidence 
furnished by the utterance is meant to override the 
initial beliefi Thus, by making the proper choices 
regarding the transfer of initial beliefs in various 
subtheories, it becomes possible to represent, the 
revision of the hearer's beliefs. 
This theory of speech acts has been presented 
with respect to declarative sentences and repre- 
sentative speech acts. To analyze imperative sen- 
tences and directive speech acts, it is clear in 
what direction one should proceed, although the 
required augmentation to the theory is quite com- 
plex. The change in the utterance theory that is 
brought about by an imperative sentence is the 
addition of the belief that the speaker intends the 
hearer to bring about the propositional content of 
the utterance. That would entail substituting the 
following effect for that stated by Axiom 8: 
\[u\]{s/}P, P the propositional con- (14) 
tent of utterance 
One then needs to axiomatize a theory of intention 
revision as well as belief revision, which entails de- 
scribing how agents adopt and abandon intentions, 
and how these intentions are related to their be- 
liefs about one another. Cohen and Levesque have 
advanced an excellent proposal for such a theory 
\[4\], but any discussion of it is far beyond the scope 
of this article. 
6 Reflecting on the Theory 
When agents perform speech acts, not only are 
their beliefs about the uttered proposition af- 
fected, but also their beliefs about one another, 
to arbitrayr levels of reflection. 
If a speaker reflects on what a hearer believes 
about the speaker's own beliefs, he takes into ac- 
count not only the beliefs themselves, but also 
what he believes to be the hearer's belief revi- 
sion strategy, which, according to our theory, is 
reflected in the hierarchical relationship among the 
theories. Therefore, reflection on the speech-act- 
understanding process takes place at higher levels 
of the hierarchy illustrated in Figure 1. For exam- 
ple, if Level 1 represents the speaker's reasoning 
about what the hearer believes, then Level 2 rep- 
177 
resents the speaker's reasoning about the heater's 
beliefs about what the speaker' believes. 
In general, agents may have quite complicated 
theories about how other agents apply defaults. 
The simplest assumption we can make is that they 
reason in a uniform manner, exactly the same as 
the way we axiomatized Level 1. Therefore, we ex- 
tend the analysis just presented to arbitrary reflec- 
tion of agents on one another's belief by proposing 
axiom schemata for the speaker's and heater's be- 
liefs at each level, of which Axioms 12 and 13 are 
the Level 1 instances. We introduce a schematic 
operator \[(s, h)n\] which can be thought of as n lev- 
els of alternation of s's and h's beliefs about each 
other. This is stated more precisely as 
\[(8, h),,\]¢ (is) 
n times 
Then, for example, Axiom 12 can be restated as 
the general schema 
in An+l : 
(\[,\]~ ^ (16) 
"L.\[(hl, 8I).\]'\[8j\]~) 
\[(hi, 81),\] \[81\]~. 
7 Conclusion 
A theory of speech acts based on default reasoning 
is elegant and desirable. Unfortunately, the only 
existing proposal that explains how this should be 
done suffers from three serious pioblems: (1) the 
theory makes some incorrect predictions; (2) the 
theory cannot be integrated easily with a theory 
of action; (3) there seems to be no efficient imple- 
mentation strategy. The problems are stem from 
the theory's formulation in normal default logic. 
We have demonstrated how these difficulties can 
be overcome by formulating the theory instead in 
a version of autoepistemic logic that is designed to 
combine reasoning about belief with autoepistemic 
reasoning. Such a logic makes it possible to for- 
realize a description of the agents' belief revision 
processes that can capture observed facts about 
attitude revision correctly in response to speech 
acts. This theory has been tested and imple- 
mented as a central component of the GENESYS 
utterance-planning system. 
Acknowledgements 
This research was supported in part by a contract 
with the Nippon Telegraph and Telephone Cor- 
poration, in part by the Office of Naval Research 
under Contract N00014-85-C-0251, and in part 
under subcontract with Stanford University un- 
der Contract N00039-84-C-0211 with the Defense 
Advanced Research Projects Agency. The original 
draft of this paper has been substanti .ally improved 
by comments from Phil Cohen, Shozo Naito, and 
Ray Perrault. The authors are also grateful to the 
participants in the Artificial Intelligence Principia 
seminar at Stanford for providing their stimulat- 
ing discussion of these and related issues. 
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