A Uniform Treatment of Pragmatic Inferences in Simple and 
Complex Utterances and Sequences of Utterances 
Daniel Marcu and Graeme Hirst 
Department of Computer Science 
University of Toronto 
Toronto, Ontario 
Canada M5S 1A4 
{marcu, gh}©cs, toronto, edu 
Abstract 
Drawing appropriate defeasible infe- 
rences has been proven to be one of 
the most pervasive puzzles of natu- 
ral language processing and a recur- 
rent problem in pragmatics. This pa- 
per provides a theoretical framework, 
called stratified logic, that can ac- 
commodate defeasible pragmatic infe- 
rences. The framework yields an al- 
gorithm that computes the conversa- 
tional, conventional, scalar, clausal, 
and normal state implicatures; and 
the presuppositions that are associa- 
ted with utterances. The algorithm 
applies equally to simple and complex 
utterances and sequences of utteran- 
ces. 
1 Pragmatics and Defeasibility 
It is widely acknowledged that a full account of na- 
tural language utterances cannot be given in terms 
of only syntactic or semantic phenomena. For ex- 
ample, Hirschberg (1985) has shown that in order to 
understand a scalar implicature, one must analyze 
the conversants' beliefs and intentions. To recognize 
normal state implicatures one must consider mutual 
beliefs and plans (Green, 1990). To understand con- 
versationM implicatures associated with indirect re- 
plies one must consider discourse expectations, dis- 
course plans, and discourse relations (Green, 1992; 
Green and Carberry, 1994). Some presuppositions 
are inferrable when certain lexical constructs (fac- 
tives, aspectuals, etc) or syntactic constructs (cleft 
and pseudo-cleft sentences) are used. Despite all the 
complexities that individualize the recognition stage 
for each of these inferences, all of them can be de- 
feated by context, by knowledge, beliefs, or plans of 
the agents that constitute part of the context, or by 
other pragmatic rules. 
Defeasibili~y is a notion that is tricky to deal with, 
and scholars in logics and pragmatics have learned 
to circumvent it or live with it. The first observers of 
the phenomenon preferred to keep defeasibility out- 
side the mathematical world. For Frege (1892), Rus- 
sell (1905), and Quine (1949) "everything exists"; 
therefore, in their logical systems, it is impossible 
to formalize the cancellation of the presupposition 
that definite referents exist (Hirst, 1991; Marcu and 
Hirst, 1994). We can taxonomize previous approa- 
ches to defea~ible pragmatic inferences into three ca- 
tegories (we omit here work on defeasibility related 
to linguistic phenomena such as discourse, anaphora, 
or speech acts). 
1. Most linguistic approaches account for the de- 
feasibility of pragmatic inferences by analyzing them 
in a context that consists of all or some of the pre- 
vious utterances, including the current one. Con- 
text (Karttunen, 1974; Kay, 1992), procedural ru- 
les (Gazdar, 1979; Karttunen and Peters, 1979), 
lexical and syntactic structure (Weischedel, 1979), 
intentions (Hirschberg, 1985), or anaphoric cons- 
traints (Sandt, 1992; Zeevat, 1992) decide what pre- 
suppositions or implicatures are projected as prag- 
matic inferences for the utterance that is analyzed. 
The problem with these approaches is that they as- 
sign a dual life to pragmatic inferences: in the initial 
stage, as members of a simple or complex utterance, 
they are defeasible. However, after that utterance 
is analyzed, there is no possibility left of cancelling 
that inference. But it is natural to have implicatures 
and presuppositions that are inferred and cancelled 
as a sequence of utterances proceeds: research in 
conversation repairs (I-Iirst et M., 1994) abounds in 
such examples. We address this issue in more detail 
in section 3.3. 
2. One way of accounting for cancellations that 
occur later in the analyzed text is simply to extend 
the boundaries within which pragmatic inferences 
are evaluated, i.e., to look ahead a few utterances. 
Green (1992) assumes that implicatures are connec- 
ted to discourse entities and not to utterances, but 
her approach still does not allow cancellations across 
discourse units. 
3. Another way of allowing pragmatic inferences 
to be cancelled is to assign them the status of de- 
feasible information. Mercer (1987) formalizes pre- 
144 
suppositions in a logical framework that handles de- 
faults (Reiter, 1980), but this approach is not tracta- 
ble and it treats natural disjunction as an exclusive- 
or and implication as logical equivalence. 
Computational approaches fail to account for the 
cancellation of pragmatic inferences: once presuppo- 
sitions (Weischedel, 1979) or implicatures (Hirsch- 
berg, 1985; Green, 1992) are generated, they can 
never be cancelled. We are not aware of any forma- 
lism or computational approach that offers a unified 
explanation for the cancellability of pragmatic infe- 
rences in general, and of no approach that handles 
cancellations that occur in sequences of utterances. 
It is our aim to provide such an approach here. In 
doing this, we assume the existence, for each type 
of pragmatic inference, of a set of necessary conditi- 
ons that must be true in order for that inference to 
be triggered. Once such a set of conditions is met, 
the corresponding inference is drawn, but it is as- 
signed a defeasible status. It is the role of context 
and knowledge of the conversants to "decide" whe- 
ther that inference will survive or not as a pragma- 
tic inference of the structure. We put no boundaries 
upon the time when such a cancellation can occur, 
and we offer a unified explanation for pragmatic in- 
ferences that are inferable when simple utterances, 
complex utterances, or sequences of utterances are 
considered. 
We propose a new formalism, called "stratified 
logic", that correctly handles the pragmatic infe- 
rences, and we start by giving a very brief intro- 
duction to the main ideas that underlie it. We give 
the main steps of the algorithm that is defined on 
the backbone of stratified logic. We then show how 
different classes of pragmatic inferences can be cap- 
tured using this formalism, and how our algorithm 
computes the expected results for a representative 
class of pragmatic inferences. The results we report 
here are obtained using an implementation written 
in Common Lisp that uses Screamer (Siskind and 
McAllester, 1993), a macro package that provides 
nondeterministic constructs. 
2 Stratified logic 
2.1 Theoretical foundations 
We can offer here only a brief overview of stratified 
logic. The reader is referred to Marcu (1994) for a 
comprehensive study. Stratified logic supports one 
type of indefeasible information and two types of 
defeasible information, namely, infelicitously defea- 
sible and felicitously defeasible. The notion of infe- 
licitously defeasible information is meant to capture 
inferences that are anomalous to cancel, as in: 
(1) * John regrets that Mary came to the party 
but she did not come. 
The notion of felicitously defeasible information is 
meant to capture the inferences that can be cancel- 
led without any abnormality, as in: 
T d ..L d 
T' _k' 
T" _L" 
Felicitously Defea.sible Layer 
Infelicitously Defeasible Layer 
Undefeasible Layer 
Figure 1: The lattice that underlies stratified logic 
(2) John does not regret that Mary came to the 
party because she did not come. 
The lattice in figure 1 underlies the semantics of 
stratified logic. The lattice depicts the three levels of 
strength that seem to account for the inferences that 
pertain to natural language semantics and pragma- 
tics: indefeasible information belongs to the u layer, 
infelicitously defeasible information belongs to the 
i layer, and felicitously defeasible information be- 
longs to the d layer. Each layer is partitioned accor- 
ding to its polarity in truth, T ~, T i, T a, and falsity, 
.L =, .l J, .1_ d. The lattice shows a partial order that is 
defined over the different levels of truth. For exam- 
ple, something that is indefeasibly false, .l_ u, is stron- 
ger (in a sense to be defined below) than something 
that is infelicitously defeasibly true, T i, or felici- 
tously defeasibly false, .L a. Formally, we say that the 
u level is stronger than the i level, which is stronger 
than the d level: u<i<d. At the syntactic level, we 
allow atomic formulas to be labelled according to the 
same underlying lattice. Compound formulas are 
obtained in the usual way. This will give us formu- 
las such as regrets u ( John, come(Mary, party)) ---, 
cornel(Mary, party)), or (Vx)('-,bachelorU(x) --~ 
(malea( ) ^ The satisfaction relation 
is split according to the three levels of truth into 
u-satisfaction, i-satisfaction, and d-satisfaction: 
Definition 2.1 Assume ~r is an St. valuation such 
that t~ = di E   and assume that St. maps n-ary 
predicates p to relations R C 7~ × ... × 79. For any 
atomic formula p=(tl, t2,... ,t,), and any stratified 
valuation a, where z E {u, i, d} and ti are terms, the 
z-satisfiability relations are defined as follows: 
• a ~u p~(tl,...,tn) iff(dx,...,dnl E 1~ ~ 
• iff 
(dl,...,dn) E R u UR--ffUR i 
• o, ~u pa(tx,...,t,) iff 
(dz,..., d,) E R"U'R-¢URIU-~URa 
• tr ~ip~(tl,...,t, ) iff(dt,...,d,) E R i 
. cr ~ipi(tt,...,t,) iff(dl,...,d,) E R i 
• pd(tl,...,t,) ig 
(dl,...,d,) E R i U~TUR d 
• o" ~ap~(tz,...,tn) iff(dl,...,dn) E R a 
• ¢(tl,...,t,) iff (all,..., d,) e R d 
145 
• o" ~d pd(tl,...,tn ) iff (di,...,dr,) C= R d 
Definition 2.1 extends in a natural way to negated 
and compound formulas. Having a satisfaction de- 
finition associated with each level of strength provi- 
des a high degree of flexibility. The same theory can 
be interpreted from a perspective that allows more 
freedom (u-satisfaction), or from a perspective that 
is tighter and that signals when some defeasible in- 
formation has been cancelled (i- and d-satisfaction). 
Possible interpretations of a given set of utteran- 
ces with respect to a knowledge base are computed 
using an extension of the semantic tableau method. 
This extension has been proved to be both sound 
and complete (Marcu, 1994). A partial ordering, 
<, determines the set of optimistic interpretations 
for a theory. An interpretation m0 is preferred to, 
or is more optimistic than, an interpretation ml 
(m0 < ml) if it contains more information and that 
information can be more easily updated in the fu- 
ture. That means that if an interpretation m0 makes 
an utterance true by assigning to a relation R a 
defensible status, while another interpretation ml 
makes the same utterance true by assigning the same 
relation R a stronger status, m0 will be the preferred 
or optimistic one, because it is as informative as mi 
and it allows more options in the future (R can be 
defeated). 
Pragmatic inferences are triggered by utterances. 
To differentiate between them and semantic infe- 
rences, we introduce a new quantifier, V vt, whose 
semantics is defined such that a pragmatic inference 
of the form (VVtg)(al(,7) --* a2(g)) is instantiated 
only for those objects t' from the universe of dis- 
course that pertain to an utterance having the form 
al(~- Hence, only if the antecedent of a pragma- 
tic rule has been uttered can that rule be applied. 
A recta-logical construct uttered applies to the logi- 
cal translation of utterances. This theory yields the 
following definition: 
Definition 2.2 Let ~b be a theory described in terms 
of stratified first-order logic that appropriately for- 
malizes the semantics of lezical items and the ne- 
cessary conditions that trigger pragmatic inferences. 
The semantics of lezical terms is formalized using 
the quantifier V, while the necessary conditions that 
pertain to pragmatic inferences are captured using 
V trt. Let uttered(u) be the logical translation of a 
given utterance or set of utterances. We say that ut- 
terance u pragmatically implicates p if and only if p d 
or p i is derived using pragmatic inferences in at least 
one optimistic model of the theory ~ U uttered(u), 
and if p is not cancelled by any stronger informa- 
tion ('.p~,-.pi _.pd) in any optimistic model schema 
of the theory. Symmetrically, one can define what 
a negative pragmatic inference is. In both cases, 
W uttered(u) is u-consistent. 
2.2 The algorithm 
Our algorithm, described in detail by Marcu (1994), 
takes as input a set of first-order stratified formu- 
las • that represents an adequate knowledge base 
that expresses semantic knowledge and the necessary 
conditions for triggering pragmatic inferences, and 
the translation of an utterance or set of utterances 
uttered(u). The Mgorithm builds the set of all possi- 
ble interpretations for a given utterance, using a ge- 
neralization of the semantic tableau technique. The 
model-ordering relation filters the optimistic inter- 
pretations. Among them, the defeasible inferences 
that have been triggered on pragmatic grounds are 
checked to see whether or not they are cancelled in 
any optimistic interpretation. Those that are not 
cancelled are labelled as pragmatic inferences for the 
given utterance or set of utterances. 
3 A set of examples 
We present a set of examples that covers a repre- 
sentative group of pragmatic inferences. In contrast 
with most other approaches, we provide a consistent 
methodology for computing these inferences and for 
determining whether they are cancelled or not for 
all possible configurations: simple and complex ut- 
terances and sequences of utterances. 
3.1 Simple pragmatic inferences 
3.1.1 Lexical pragmatic inferences 
A factive such as the verb regret presupposes its 
complement, but as we have seen, in positive envi- 
ronments, the presupposition is stronger: it is accep- 
table to defeat a presupposition triggered in a nega- 
tive environment (2), but is infelicitous to defeat one 
that belongs to a positive environment (1). There- 
fore, an appropriate formalization of utterance (3) 
and the req~fisite pragmatic knowledge will be as 
shown in (4). 
(3) John does not regret that Mary came to the 
party. 
(4) 
uttered(-,regrets u (john, come( ,,ry, 
party))) 
(VU'=, y, z)(regras (=, come(y, 
co e i (y, z) ) 
(Vu'=, y, z)( regret," (=, come(y, z)) -* corned(y, z) ) 
The stratified semantic tableau that corresponds to 
theory (4) is given in figure 2. The tableau yields 
two model schemata (see figure 3); in both of them, 
it is defeasibly inferred that Mary came to the party. 
The model-ordering relation < establishes m0 as the 
optimistic model for the theory because it contains 
as much information as ml and is easier to defeat. 
Model m0 explains why Mary came to the party is a 
presupposition for utterance (3). 
146 
"~regrets(john, come(mary, party)) 
(Vx, y, z)(-~regrets(x, come(y, z) ) ---* corned(y, z) ) 
(Vx, y, z)(regrets(x, come(y, z)) --* comei(y, z)) 
I 
-.regrets(john, come(mary, party)) -- corned(mary, party) 
regrets(john, come(mary,party)) --* comei(mary, party) 
regrets(john, come(mary, party)) corned(mary, party) 
u-closed 
-.regrets(john, come(mary, party)) come i(mary, party) 
m_0 mL1 
Figure 2: Stratified tableau for John does not regret that Mary came to the party. 
Schema # Indefeasible Infelicitously 
defeasible 
",regrets ~ (john, come(mary, party) 
-.regTets ~(joh., come(mary, party) 
mo 
ml 
come ~ ( mary, party) 
Felicitously 
defeasible 
corned(mary, party) 
cornea(mary, party) 
Figure 3: Model schemata for John does not regret that Mary came to the party. 
Schema # Indefeasible 
mo went"( some( boys ), theatre) 
-.went"( all( boys ), theatre) 
Infelicitously Felicitously 
defeasible de feasible 
-',wentd( most( boys ), theatre) 
-.wentd( many( boys ), theatre) 
-,wentd(all(boys), theatre) 
Figure 4: Model schema for John says that some of thc boys went to the theatre. 
Schema # Indefeasible In\]elicitously Felicitously 
de\]easible de feasible 
mo we,,t"( some(boy,), theatre) 
,oe,,t" ( most( boys ), theatre) 
went~(many(boys), theatre) 
went~(all(boys), theatre) 
d ".went (most(boys),theatre) 
d -.went (many(boys), theatre) 
-~wentd(all(boys), theatre) 
Figure 5: Model schema for John says that some of the boys went to the theatre. In fact all of them went to 
the theatre. 
147 
3.1.2 Scalar implicatures 
Consider utterance (5), and its implicatu- 
res (6). 
(5) John says that some of the boys went to the 
theatre. 
(6) Not {many/most/all} of the boys went to the 
theatre. 
An appropriate formalization is given in (7), where 
the second formula captures the defeasible scalar im- 
plicatures and the third formula reflects the relevant 
semantic information for all. 
(r) 
uttered(went(some(boys), theatre)) 
went" (some(boys), theatre) ---* 
(-~wentd(many(boys), theatre)A 
",wentd(most(boys), theatre)^ 
-~wentd(aii(boys), theatre)) 
went" (all(boys), theatre) 
(went" (most(boys), theatre)A 
went" (many(boys), theatre)^ 
went"( some(boys), theatre) ) 
The theory provides one optimistic model schema 
(figure 4) that reflects the expected pragmatic in- 
ferences, i.e., (Not most/Not many/Not all) of the 
boys went to the theatre. 
3.1.3 Simple cancellation 
Assume now, that after a moment of thought, the 
same person utters: 
(8) John says that some of the boys went to the 
theatre. In fact all of them went to the thea- 
tre. 
By adding the extra utterance to the initial 
theory (7), uttered(went(ail(boys),theatre)), one 
would obtain one optimistic model schema in which 
the conventional implicatures have been cancelled 
(see figure 5). 
3.2 Complex utterances 
The Achilles heel for most theories of presupposition 
has been their vulnerability to the projection pro- 
blem. Our solution for the projection problem does 
not differ from a solution for individual utterances. 
Consider the following utterances and some of their 
associated presuppositions (11) (the symbol t> pre- 
cedes an inference drawn on pragmatic grounds): 
(9) Either Chris is not a bachelor or he regrets 
that Mary came to the party. 
(10) Chris is a bachelor or a spinster. 
(11) 1> Chris is a (male) adult. 
Chris is not a bachelor presupposes that Chris is a 
male adult; Chris regrets that Mary came to the party 
presupposes that Mary came to the party. There is 
no contradiction between these two presuppositions, 
so one would expect a conversant to infer both of 
them if she hears an utterance such as (9). Howe- 
ver, when one examines utterance (10), one observes 
immediately that there is a contradiction between 
the presuppositions carried by the individual com- 
ponents. Being a bachelor presupposes that Chris 
is a male, while being a spinster presupposes that 
Chris is a female. Normally, we would expect a con- 
versant to notice this contradiction and to drop each 
of these elementary presuppositions when she inter- 
prets (10). 
We now study how stratified logic and the model- 
ordering relation capture one's intuitions. 
3.2.1 Or-- non-cancellation 
An appropriate formalization for utterance (9) 
and the necessary semantic and pragmatic know- 
ledge is given in (12). 
(12) 
l uttered(-~bachelor(Chris)V 
regret(Chris, come(Mary, party))) 
(- bachelor" (Chris)V 
regret" (Chris, come(Mary, party))) 
-~(-~bachelord( Chris)A 
regret d( chris, come(Mary, party))) 
--,male(Mary) (Vx )( bachelor" ( x ) .--+ 
I male"(x) A adultU(z) A "-,married"(x)) (VUtx)(-4bachelorU(=) --~ marriedi(x)) 
(vUt x )(-~bachelor"( x ) --~ adulta( x ) ) (vu'x)(--,bachelorU(x) .-, maled(=)) 
y, z)(- regret"(=, come(y, z) ) 
cored(y, ,)) 
(vv'=, y, z )( regret" ( =,  ome(y, ) ) - 
come i (y, z ) ) 
Besides the translation of the utterance, the initial 
theory contains a formalization of the defeasible im- 
plicature that natural disjunction is used as an exclu- 
sive or, the knowledge that Mary is not a name for 
males, the lexical semantics for the word bachelor, 
and the lexical pragmatics for bachelor and regret. 
The stratified semantic tableau generates 12 model 
schemata. Only four of them are kept as optimistic 
models for the utterance. The models yield Mary 
came to the party; Chris is a male; and Chris is an 
adult as pragmatic inferences of utterance (9). 
3.2.2 Or- cancellation 
Consider now utterance (10). The stratified se- 
mantic tableau that corresponds to its logical theory 
yields 16 models, but only Chris is an adult satisfies 
definition 2.2 and is projected as presupposition for 
the utterance. 
3.3 Pragmatic inferences in sequences of 
utterances 
We have already mentioned that speech repairs con- 
stitute a good benchmark for studying the genera- 
148 
tion and cancellation of pragmatic inferences along 
sequences of utterances (McRoy and Hirst, 1993). 
Suppose, for example, that Jane has two friends -- 
John Smith and John Pevler -- and that her room- 
mate Mary has met only John Smith, a married fel- 
low. Assume now that Jane has a conversation with 
Mary in which Jane mentions only the name John 
because she is not aware that Mary does not know 
about the other John, who is a five-year-old boy. In 
this context, it is natural for Mary to become confu- 
sed and to come to wrong conclusions. For example, 
Mary may reply that John is not a bachelor. Alt- 
hough this is true for both Johns, it is more appro- 
priate for the married fellow than for the five-year- 
old boy. Mary knows that John Smith is a married 
male, so the utterance makes sense for her. At this 
point Jane realizes that Mary misunderstands her: 
all the time Jane was talking about John Pevler, the 
five-year-old boy. The utterances in (13) constitute 
a possible answer that Jane may give to Mary in 
order to clarify the problem. 
(13) a. No, John is not a bachelor. 
b. I regret that you have misunderstood me. 
c. He is only five years old. 
The first utterance in the sequence presuppo- 
ses (14). 
(14) I> John is a male adult. 
Utterance (13)b warns Mary that is very likely she 
misunderstood a previous utterance (15). The war- 
ning is conveyed by implicature. 
(15) !> The hearer misunderstood the speaker. 
At this point, the hearer, Mary, starts to believe 
that one of her previous utterances has been elabo- 
rated on a false assumption, but she does not know 
which one. The third utterance (13)c comes to cla- 
rify the issue. It explicitly expresses that John is not 
an adult. Therefore, it cancels the early presupposi- 
tion (14): 
(16) ~ John is an adult. 
Note that there is a gap of one statement between 
the generation and the cancellation of this presup- 
position. The behavior described is mirrored both 
by our theory and our program. 
3.4 Conversational implicatures in indirect 
replies 
The same methodology can be applied to mode- 
ling conversational impIicatures in indirect replies 
(Green, 1992). Green's algorithm makes use of dis- 
course expectations, discourse plans, and discourse 
relations. The following dialog is considered (Green, 
1992, p. 68): 
(17) Q: Did you go shopping? 
A: a. My car's not running. 
b. The timing belt broke. 
c. (So) I had to take the bus. 
Answer (17) conveys a "yes", but a reply consisting 
only of (17)a would implicate a "no". As Green no- 
tices, in previous models of implicatures (Gazdar, 
1979; Hirschberg, 1985), processing (17)a will block 
the implicature generated by (17)c. Green solves the 
problem by extending the boundaries of the analysis 
to discourse units. Our approach does not exhibit 
these constraints. As in the previous example, the 
one dealing with a sequence of utterances, we obtain 
a different interpretation after each step. When the 
question is asked, there is no conversational impli- 
cature. Answer (17)a makes the necessary conditi- 
ons for implicating "no" true, and the implication is 
computed. Answer (17)b reinforces a previous con- 
dition. Answer (17)c makes the preconditions for 
implicating a "no" false, and the preconditions for 
implicating a "yes" true. Therefore, the implicature 
at the end of the dialogue is that the conversant who 
answered went shopping. 
4 Conclusions 
Unlike most research in pragmatics that focuses on 
certain types of presuppositions or implicatures, we 
provide a global framework in which one can ex- 
press all these types of pragmatic inferences. Each 
pragmatic inference is associated with a set of ne- 
cessary conditions that may trigger that inference. 
When such a set of conditions is met, that infe- 
rence is drawn, but it is assigned a defeasible status. 
An extended definition of satisfaction and a notion 
of "optimism" with respect to different interpreta- 
tions yield the preferred interpretations for an ut- 
terance or sequences of utterances. These interpre- 
tations contain the pragmatic inferences that have 
not been cancelled by context or conversant's know- 
ledge, plans, or intentions. The formalism yields an 
algorithm that has been implemented in Common 
Lisp with Screamer. This algorithm computes uni- 
formly pragmatic inferences that are associated with 
simple and complex utterances and sequences of ut- 
terances, and allows cancellations of pragmatic infe- 
rences to occur at any time in the discourse. 
Acknowledgements 
This research was supported in part by a grant 
from the Natural Sciences and Engineering Research 
Council of Canada. 
149 

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