THE COMPUTATIONAL COMPLEXITY OF 
AVOIDING CONVERSATIONAL IMPLICATURES 
Ehud Reiterf 
Aiken Computation Lab 
Harvard University 
Cambridge, Mass 02138 
ABSTRACt 
Referring expressions and other object descriptions 
should be maximal under the Local Brevity, No 
Unnecessary Components, and Lexical Preference 
preference rules; otherwise, they may lead hearers to 
infer unwanted conversational implicatures. These 
preference rules can be incorporated into a polyno- 
mial time generation algorithm, while some alterna- 
tive formalizations of conversational impficature 
make the generation task NP-Hard. 
1. Introduction 
Natural language generation (NLG) systems 
should produce referring expressions and other object 
descriptions that are free of false implicatures, i.e., 
that do not cause the user of the system to infer 
incorrect and unwanted conversational implicatures 
(Grice 1975). The following utterances illustrate 
referring expressions that are and are not free of false 
implicatures: 
la) "Sit by the table" 
lb) "Sit by the brown wooden table" 
In a context where only one table was visible, and 
this table was brown and made of wood, utterances 
(la) and (lb) would both fulfill the referring goal: a 
hearer who heard either utterance would have no 
trouble picking out the object being referred to. 
However, a hearer who heard utterance (lb) would 
probably assume that it was somehow important that 
the table was brown and made of wood, i.e., that the 
speaker was trying to do more than just identify the 
table. If the speaker did not have this intention, and 
only wished to tell the hearer where to sit, then this 
would be an incorrect conversational implicature, and 
could lead to problems later in the discourse. 
Accordingly, a speaker who only wished to identify 
the table should use utterance (la) in this situation, 
f Currently at the Depamnem of Artificial Intelligence, 
University of Edinburgh, 80 South Bridge, Edinburgh EHI 
1HN, Scotland. 97 
and avoid utterance (lb). 
Incorrect conversational implicatures may also 
arise from inappropriate attributive (informational) 
descriptions. 1 This is illustrated by the following 
utterances, which might be used by a salesman who 
wished to inform a customer of the color, material, 
and sleeve-length of a shirt: 
2a) "I have a red T-shirt" 
2b) "I have a lightweight red cotton shirt with 
short sleeves" 
Utterances (2a) and (2b) both successfully inform the 
hearer of the relevant properties of the shirt, assum- 
ing the hearer has some domain knowledge about T- 
shirts. However, if the hearer has this domain 
knowledge, the use of utterance (2b) might 
incorrectly implicate that the object being described 
was not a T-shirt -- because if it was, the hearer 
would reason, then the speaker would have used 
utterance (Za). 
Therefore, in the above situations the speaker, 
whether a human or a computer NLG system, should 
use utterances (la) and (2a), and should avoid utter- 
ances (lb) and (2b); utterances (la) and (2a) are free 
of false implicatures, while the utterances (lb) and 
(2b) are not. This paper proposes a computational 
model for determining when an object description is 
free of false implicatures. Briefly, a description is 
considered free of false implicatures if it is maximal 
under the Local Brevity, No Unnecessary Com- 
ponents, and Lexical Preference preference rules. 
These preference rules were chosen on complexity- 
theoretic as well as linguistic criteria; descriptions 
that are maximal under these preference rules can be 
found in polynomial time, while some alternative for- 
malizations of the free-of-false-implicatures con- 
straint make the generation task NP-Hard. 
I The referring/attributive distinction follows Donnellan 
(1966): a referring expression is intended to identify an object 
in the current context, while an attributive description is in- 
tended to communicate information about an object. 
This paper only addresses the problem of gen- 
erating free-of-false-implicatures referring expres- 
sions, such as utterance (la). Reiter (1990a,b) uses 
the same preference rules to formalize the task of 
generating free-of- false-implicatures attributive 
descriptions, such as utterance (2a). 
2. Referring Expression Model 
The referring-expression model used in this 
paper is a variant of Dale's (1989) model for full 
definite noun phrase referring expressions. Dale's 
model is applicable in situations in which the speaker 
intends to refer to an object that the speaker and 
hearer are mutually aware of, and the speaker has no 
other communicative goal besides identifying the 
referred-to object. 2 The model assumes that objects 
belong to a taxonomy class (e.g., Chair) and possess 
values for various attributes (e.g., Color:Brown). 3 
Referring expressions are represented as a 
classification and a set of attribute-value pairs: the 
classification is syntactically realized as the head 
noun, while the attribute-value pairs are syntactically 
realized as NP modifiers. Successful referring 
expressions are required to be distinguishing descrip- 
t/ons, i.e., descriptions that contain a classification 
and a set of attributes that are true of the object being 
referred to, but not of any other object in the current 
discourse context. 4 
More formally, and using a somewhat different 
terminology from Dale, let a component be either a 
classification or an attribute-value pair. A 
classification component will be written class:Class; 
an attribute-value pair component will be written 
Attribute:Value. Then, given a target object, denoted 
Target, and a set of contrasting objects in the current 
discourse context, denoted Excluded, a set of com- 
ponents will represent a successful referring expres- 
sion (a distinguishing description, in Dale's terminol- 
2 Appelt (1985) presented a more complex rderring- 
expression model that covered situations where the hearer 
was not already aware of the referred-to object, and that al- 
lowed the speaker to have more complex communicative 
goals. A similar laalysis to the one presented in this paper 
could in principle be done for Appelt's model, but it would 
be substantially more difficult, in part because the model is 
more complex, and in pa~t because Appeh did not separate 
his 'content detcrminatiou' subsystem frona his planner and 
his sudaee-form generator. 
3 All auributes are assumed to be predicative (Karnp 
1975). 
4 Dale also suggested that NLG systems should choose 
distinguishing descril0dons of minimal cardinality; this is dis- 
cussed in footnote 7. 
ogy) if the set, denoted RE, satisfies the following 
constraints: 
1) Every component in RE applies to Target: that 
is, every component in RE is either a 
classification that subsumes Target, or an 
attribute-value pair that Target possesses. 
2) For every member E of Excluded, there is at 
least one component in RE that does not apply 
toE. 
Example: the current discourse context con- 
tains objects A, B, and C (and no other objects), and 
these objects have the following classifications and 
attributes (of which both the speaker and the hearer 
are aware): 
A) Table with Material:Wood and Color:Brown. 
B) Chair with Material:Wood and Color:Brown 
C) Chair with Material:Wood and Color:Black 
In this context, the referring expressions 
{class:Table} ("the table") and {class:Table, 
Material:Wood, Color:Brown} ("the brown wooden 
table") both successfully refer to object A, because 
they match object A but no other object. Similarly, 
the referring expressions {class:Chair, 
Color:Brown} ("the brown chair") and {class:Chair, 
Material:Wood, Color:Brown} ("the brown wooden 
chair") both successfully refer to object B, because 
they match object B, but no other object. The refer- 
ring expression {class:Chair} (~the chair"), how- 
ever, does not successfully refer to object B, because 
it also matches object C. 
98 
3. Conversational Implicature 
3.1. Grice's Maxims and Their Interpretation 
Grice (1975) proposed four maxims of conver- 
sation that speakers needed to obey: Quality, Quan- 
tity, Relevance, and Manner. For the task of generat- 
ing referring expressions as formalized in Section 2, 
these maxims can be interpreted as follows: 
Quality: The Quality maxim requires utter- 
anees to be truthful. In this context, it requires refer- 
ring expressions to be factual descriptions of the 
referred-to object. This condition is already part of 
the definition of a successful referring expression, 
and does not need to be restated as a conversational 
implicature constraint. 
Quantity: The Quality maxim requires utter- 
antes to contain enough information to fulfill the 
speaker's communicative goal, but not more informa- 
tion. In this context, it requires referring expressions 
to contain enough information to enable the hearer to 
identify the referred-to object, but not more informa- 
tion. Therefore, referring expressions should be suc- 
cessful (as defined in Section 2), but should not con- 
rain additional elements that are unnecessary for 
fulfilling the referring goal. 
Relevance: The Relevance maxim requires 
utterances to be relevant to the discourse. In this 
context, where the speaker is assumed just to have 
the communicative goal of identifying an object to 
the hearer, the maxim prohibits referring expressions 
from containing elements that do not help distinguish 
the target object from other objects in the discourse 
context. Irrelevant elements are also unnecessary 
elements, so the Relevance maxim may be con- 
sidered to be a special case of the Quantity maxim, at 
least for the referring-expression generation task as 
formalized in Section 2. 
Manner: The Brevity submaxim of the Manner 
maxim requires a speaker to use short utterances if 
possible. In this context it requires the speaker to use 
a short referring expression if such a referring 
expression exists. The analysis of the other Manner 
submaxims is left for future work. 
An additional source of conversational impli- 
catm'e was proposed by Cruse (1977) and Hirschberg 
(1985), who hypothesized that. implicatures might 
arise from the failure to use basic-level classes 
(Rosch 1978) in an utterance. In this paper, such 
implicatures are generalized by assuming that there is 
a lexical-preference hierarchy among the lexical 
classes (classes that can be realized with single lexi- 
cal units) known to the hearer, and that the use of a 
lexical class in an utterance implicates that no pre- 
ferred lexical class could have been used in its place. 
In summary, conversational implicature con- 
siderations require referring expressions to be brief, 
to not contain unnecessary elements, and to use 
lexically-preferred classes whenever possible. The 
following requests illustrate how violations of these 
principles in referring expressions may lead to 
unwanted conversational implicatares: 
3a) "Wait for me by the pine." 
({class:Pine}) 
99 
3b) "Wait for me by the tree that has pinecones." 
({class:Tree, Seed-type :Pinecone } ) 
3c) "Wait for me by the 50-foot-high pine." 
({class:Pine, Height:50-feet } ) 
3d) ~Wait for me by the sugar pine." 
({ class:Sugar-pine }) 
If there were only two trees in the hearer's immediate 
surroundings, a pine and an oak, then all of the above 
utterances would be successful referring expressions 
that enabled the hearer to pick out the object being 
referred to (assuming the hearer could recognize 
pines and oaks). In such a situation, however, utter- 
ance (3b) would violate the brevity principle, and 
thus would implicate that the tree could not be 
described as a "pine" (which might lead the hearer to 
infer that the tree was not a real pine, but some other 
tree that happened to have pinecones). Utterance 
(3c) would violate the no-unnecessary-elements prin- 
ciple, and thus would implicate that it was important 
that the tree was 50 feet tall (which might lead the 
hearer to infer that there was another pine tree in the 
area that had a different height). Utterance (3d) 
would violate the lexical-preference principle, and 
thus would implicate that the speaker wished to 
emphasize that the tree was a sugar pine and not 
some other kind of pine (which might lead the hearer 
to infer that the speaker was trying to impress her 
with his botanical knowledge). A speaker who only 
wished to tell the hearer where to wait, and did not 
want the hearer to make any of these implicatures, 
would need to use utterance (3a), and to avoid utter- 
ances (3b), (3c), and (30). 
3.2. Formalizing Conversational Implicature 
Through Preference Rules 
The brevity, no-unnecessary-elements, and 
lexical-preference principles may be formalized by 
requiring a description to be a maximal element 
under a preference function of the set of successful 
referring expressions. More formally, let D be the set 
of successful referring expressions, and let >> be a 
preference function that prefers descriptions that are 
short, that do not contain unnecessary elements, and 
that use lexically preferred classes. Then, a referring 
expression is considered free of false implicatures if 
it is a maximal element of D with respect to >>. In 
other words, a description B in D is free of false 
implicatures if there is no description A in D, such 
that A >> B. This formalization is similar to the par- 
tially ordered sets that Hirschberg (1985) used to for- 
malize scalar implicatures: D and >> together form a 
partially ordered set, and the assumption is that the 
use of an element in D carries the conversational 
implicature that no higher-ranked element in D could 
have been used. 
The overall preference function >> will be 
decomposed into separate preference rules that cover 
each type of implicature: >>B for brevity, >>u for 
unnecessary elements, and >>t. for lexical prefer- 
euce. >> is then defined as the disjunction of these 
preference rules, i.e., A >> B if A >>s B, A >>v B, 
or A >>L B. The assumption will be made in this 
paper that there are no conflicts between preference 
rules, i.e., that it is never the case that A is preferred 
over B by one preference rule, but B is preferred over 
A by another preference rule. 5 Therefore, >> will be 
a partial order if >>B, >>v, and >>n are partial ord- 
ers. 
3.3. Computational Tractability 
Computational complexity considerations are 
used in this paper to determine exactly how the no- 
unnecessary-elements, brevity, and lexical- 
preference principles should be formalized as prefer- 
enee rules. Sections 4, 5, and 6 examine various 
preference rules that might plausibly be used to for- 
malize these implicatures, and reject preference rules 
that make the generation task NP-Hard. This is 
justified on the grounds that computer NLG systems 
should not be asked to solve NP-Hard problems. 6 
Human speakers and hearers are also probably not 
very proficient at solving NP-Hard problems, which 
suggests that it is unlikely that NP-Hard preference 
rules have been incorporated into language. 
4. Brevity 
Grice's submaxim of brevity states that utter- 
auces should be kept brief. Many NLG researchers 
(e.g., Dale 1989; Appelt 1985: pages 117-118) have 
suggested that this means generation systems need to 
produce the shortest possible utterance. This will be 
called the Full Brevity preference rule. Unfor- 
tunately, it is NP-Hard to find the shortest successful 
referring expression (Section 4.1). Local Brevity 
(Section 4.2) is a weaker version of the brevity sub- 
maxim that can be incorporated into a polynomial- 
time algorithm for generating successful referring 
expressions. 
5 Section 7.2 discusses this assumption. 
6 Section 7.1 discusses the computational impact of NP- 
Hard preference rules. 
i00 
4.1. Full Brevity 
The Full Brevity preference rule requires the 
generation system to generate the shortest successful 
referring expression. Formally, A >>FB B if 
length(A) < length(B). The task of finding a maximal 
element of >>FB, i.e., of finding the shortest success- 
ful referring expression, is NP-Hard. This result 
holds for all definitions of length the author has 
examined (number of open-class words, number of 
words, number of characters, number of com- 
ponents). 
To prove this, let Target-Components denote 
those components (classifications and attribute-value 
pairs) of Target that are mutually known by the 
speaker and the hearer. For each Tj in Target- 
Components, let Rules-Out(Tj) be the members of 
Excluded that do not possess Tj (so, the presence of 
Tj in a referring expression 'rules out' these 
members). Then, consider a potential referring 
expression, RE = {Ct ..... C,}. RE will be a suc- 
cessful referring expression if and only if 
a) Every Ci is in Target-Components 
b) The union of Rules-Out(Ci), for all Ci in RE, is 
equal to Excluded. 
For example, if the task was referring to object 
B in the example context of Section 2, then Target- 
Components would be {class:Chair, Material:Wood, 
Color:Brown}, Excluded would be {A, C}, and 
Rules-Out(class:Chair) = { A } 
Rules-Out(Material:Wood) = empty set 
Rules-Out(Color:Brown) = {C} 
Therefore, {class:Chair, Color:Brown} (i.e., "the 
brown chair") would be a successful referring 
expression for object B in this context. 
If description length is measured by number of 
components, 7 finding the minimal length referring 
expression is equivalent to solving a minimum set 
cover problem, where Excluded is the set being 
covered, and the Rules-Out(Tj) are the covering sets. 
Unfortunately, finding a minimal set cover is an NP- 
7 Dale's (1989) minimal distinguishing descriptions are, 
in the terminology of this paper, successful referring expres- 
sions that are maximal under Full Brevity when number of 
components is used as the measure of description length. 
Therefore, finding a minimal distinguishing description is an 
NP-Hard problem. The algorithm Dale used was essentially 
equivalent to the greedy heuristic for minimal set cover 
(Johnson 1974); as such it ran quickly, but did not always 
find a tree minimal distinguishing description. 
Hard problem (Garey and Johnson 1979), and thus 
solving it is in general computationally intractable 
(assuming that P ~ NP). 
Similar proofs will work for the other 
definitions of length mentioned above. On an intui- 
tive level, the basic problem is that finding the shor- 
test description requires searching for the global 
minimum of the length function, and this global 
minimum (like many global minima) may be very 
expensive to locate. 
4.2. Local Brevity 
The Local Brevity preference rule is a weaker 
interpretation of Grice's brevity submaxim. It states 
that it should not be possible to generate a shorter 
successful referring expression by replacing a set of 
components by a single new componenL Formally, 
>>us is the transitive closure of >>us', where A >>us, 
B if size(components(A)-components(B)) = 1, s and 
length(A) < length(B). The best definition of 
length(A) is probably the number of open-class 
words in the surface realization of A. 
Local brevity can be checked by selecting a 
potential new component, finding all minimal sets of 
old components whose combined length is greater 
than the length of the new component, performing 
the substitution, and checking if the result is a sue- 
cessful referring expression. This can be done in 
polynomial time if the number of minimal sets is 
polynomial in the length of the description, which 
will happen if (non-zero) upper and lower bounds are 
placed on the length of any individual component 
(e.g., the surface realization of every component 
must use at least one open-class word, but no more 
than some fixed number of open-class words). 
element is defined: detecting unnecessary words in 
referring expressions is NP-Hard (Section 5.1), but 
unnecessary components can always be found in 
polynomial time (Section 5.2). 
5.1. No Unnecessary Words 
The No Unnecessary Words preference rule 
forbids referring expressions from containing 
unnecessary words. Formally, A >>ow B if A's sur- 
face form uses a subset of the words used by B's sur- 
face form. There are several variants, such as only 
considering open-class words, or requiring the words 
in B to be in the same order as the corresponding 
words in A. All of these variants make the genera- 
tion problem NP-Hard. 
The formal proofs are in Reiter (1990b). Intui- 
tively, the basic problem is that any preference that is 
stated solely in terms of surface forms must deal with 
the possibility that new parses and semantic interpre- 
tations may arise when the surface form is modified. 
This means that the only way a generation system 
can guarantee that an utterance satisfies the No 
Unnecessary Words rule is to generate all possible 
subsets of the surface form, and then run each subset 
through a parser and semantic interpreter to check if 
it happens to be a successful referring expression. 
The number of subsets of the surface form is 
exponential in the size of the surface form, so this 
process will take exponential time. 
To illustrate the 'new parse' problem, consider 
two possible referring expressions: 
4a) "the child holding a pumpkin" 
4b) "the child holding a slice of pumpkin pie" 
5. No Unnecessary Elements 
The Gricean maxims of Quantity and 
Relevance prohibit utterances from containing ele- 
ments that are unnecessary for fulfilling the speaker's 
communicative goals. The undesirability of unneces- 
sary elements is further supported by the observation 
that humans find pleonasms (Cruse 1986) such as "a 
female mother" and "an unmarried bachelor" to be 
anomalous. The computational tractability of the 
no-unnecessary-elements principle depends on how 
8 This is a set formula, where "-* means set-difference 
and "size" means nmnher of members. The formula requires 
A to have exactly one COmlx~ent that is not present in B; B 
can have an ~oitra W number of components that are not 
present in A. 
i01 
If utterances (4a) and (4b) were both successful 
referring expressions (i.e., the child had a pumpkin in 
one hand, and a slice of pumpkin pie in the other), 
then (4a) >>ow (4b) under any of the variants men- 
tioned above. However, because utterance (4a) has a 
different syntactic structure than utterance (4b), the 
only way the generation system could discover that 
(4a) >>vw (4b) would be by constructing utterance 
(4b)'s surface form, removing the words "slice," 
"of," and "pie" from it, and analyzing the reduced 
surface form. 
This problem, of new parses and semantic 
interpretations being uncovered by modifications to 
the surface form, causes difficulties whenever a 
preference rule is stated solely in terms of the surface 
form. Accordingly, such preference rules should be 
avoided. 
5.2. No Unnecessary Components 
The No Unnecessary Components preference 
rule forbids referring expressions from containing 
unnecessary components. Formally, A >>uc B if A 
uses a a subset of the components used by B. 
Unnecessary components can be found in poly- 
nomial time by using a simple incremental algorithm 
that just removes each component in turn, and checks 
if what is left constitutes a successful referring 
expression. 
The key algorithmic difference between No 
Unnecessary Components and No Unnecessary 
Words is that this simple incremental algorithm will 
not work for the No Unnecessary Words preference 
rule. This is because there are cases where removing 
any single word from an utterance's surface form 
wifl leave an unsuccessful (or incoherent) referring 
expression (e.g., imagine removing just "slice" from 
utterance (4b)), but removing several words will 
uncover a new parse that corresponds to a successful 
referring expression. In contrast, if B is a successful 
referring expression, and there exists another sue- 
cessful referring expression A that satisfies 
components(A) c components(B) (and hence A is 
preferred over B under the No Unnecessary Com- 
ponents preference rule), then it will be the case that 
any referring expression C that satisfies 
components(A) c components(C) c components(B) 
will also be successful. This means that the simple 
algorithm can always produce A from B by incre- 
mental steps that remove a single component at a 
time, because the intermediate descriptions formed in 
this process will always be successful referring 
expressions. Therefore, the simple incremental algo- 
rithm will always find unnecessary components, but 
may not always find unnecessary words. 
6. Lexlcal Preference 
If the attribute values and classifications used 
in the description are members of a taxonomy, then 
they can be realized at different levels of specificity. 
For example, the object in the parking lot outside the 
author's window might be called "a vehicle," "a 
motor vehicle," "a car," "a sports car," or "a 
Porsche." 
The Lexical Preference rule assumes there is a 
lexical-preference hierarchy among the taxonomy's 
lexical classes (classes that can be realized with sin- 
gle lexical units). The rule states that utterances 
should use preferred lexical classes whenever possi- 
ble. Formally, A >>t. B if for every component in A, 
that is a component in B that has the same structure, 
102 
and the lexieal class used by the A component is 
equal to or lexically preferred over the lexical class 
used by the B component. 
The lexical-preference hierarchy should, at 
minimum, incorporate the following preferences: 
i) Lexical class A is preferred over lexical class 
B if A's realization uses a subset of the open- 
class words used in B's realization. For exam- 
ple, the class with realization ``vehicle" is pre- 
ferred over the class with realization "motor 
vehicle." 
ii) Lexical class A is preferred over lexical class 
B if A is a basic-level class, and B is not. For 
example, if car was a basic-level class, then "a 
car" would be preferred over ``a vehicle" or ``a 
porsche. "9 
In some cases these two preferences may conflict; 
this is discussed in Section 7.2. 
Utterances that violate either preference (i) or 
preference (ii) may implicate unwanted implicatures. 
Preference rule (ii) has been discussed by Cruse 
(1977) and Hirschberg (1985). Preference rule (i) 
may be considered to be another application of the 
Gricean maxim of quantity, and is illustrated by the 
following utterances: 
5a) "Wait for me by my car" 
5b) "Walt for me by my sports car" 
If utterances (5a) and (5b) were both successful 
referring expressions (e.g., if the speaker possessed 
only one ear), then the use of utterance (5b) would 
implicate that the speaker wished to emphasize that 
his vehicle was a sports car, and not some other kind 
of car. 
From an algorithmic point of view, referring 
expressions that are maximal under the lexical- 
preference criteria can be found in polynomial time if 
the following restriction is imposed on the lexical- 
preference hierarchy: 
Restriction: 
If lexical class A is preferred over lexical class 
B, then A must either subsume B or be sub- 
sumed by B in the class taxonomy. 
For example, it is acceptable for car to be preferred 
over vehicle or Porsche, but it is not acceptable for 
car to be preferred over gift (because car neither sub- 
sumes nor is subsumed by g~ft). 
If the above reslriction holds, a variant of the 
simple incremental algorithm of Section 5.2 may be 
used to implement lexical preference: the algorithm 
simply attempts each replacement that lexical prefer- 
ence suggests, and checks if this results in a success- 
ful referring expression. If the restriction does not 
hold, then the simple incremental algorithm may fall, 
and obeying the Lexical Preference rule is in fact 
N-P-Hard (the formal proof is in Reiter (1990b)). 
7. ISSUES 
7.1. The Impact of NP-Hard Preference Rules 
It is difficult to precisely determine the compu- 
tational expense of generating referring expressions 
that are maximal under the Full Brevity or No 
Unnecessary Words preference rules. The most 
straightforward algorithm that obeys Full Brevity (a 
similar analysis can be done for No Unnecessary 
Words) simply does an exhaustive search: it first 
checks if any one-component referring expression is 
successful, then checks if any two-component refer- 
ring expression is successful, and so forth. Let L be 
the number of components in the shortest referring 
expression, and let N be the number of components 
that are potentially useful in a description, i.e., the 
number of members of Target-Components that rule 
out at least one member of Excluded. The straight- 
forward full-brevity algorithm will then need to 
examine the following number of descriptions before 
it finds a successful referring expression: 
For the problem of generating a referring expression 
that identifies object B in the example context 
presented in Section 2, N is 3 and L is 2, so the 
straightforward brevity algorithm will take only 6 
steps to find the shortest description. This problem is 
artificially simple, however, because N, the number 
of potential description components, is so small. In a 
more realistic problem, one would expect Target- 
Components to include size, shape, orientation, posi- 
tion, and probably many other attribute-value pairs as 
well, which would mean that N would probably be at 
least 10 or 20. L, the number of attributes in the 
shortest possible referring expression, is probably 
fairly small in most realistic situations, but there are 
cases where it might be at least 3 or 4 (e.g., consider 
Uthe upside-down blue cup on the second shelf"). 203 
For some example values of L and N in this range, 
the straightforward brevity algorithm will need to 
examine the following number of descriptions: 
L = 3, N = 10; 175 descriptions 
L = 4, N = 20; over 6000 descriptions 
L = 5, N = 50; over 2,000,000 descriptions 
The straightfo~vard full-brevity algorithm, 
then, seems prohibitively expensive in at least some 
circumstances. Because finding the shortest descrip- 
tion is N-P-Hard, it seems likely (existing 
complexity-theoretic techniques are too weak to 
prove such statements) that all algorithms for finding 
the shortest description will have similarly bad per- 
formance in the worst case. It is possible, however, 
that there exist algorithms that have acceptable per- 
formance in almost all 'realistic' cases. Any such 
proposed algorithm, however, should be carefully 
analyzed to determine in what circumstances it will 
fail to find the shortest description or will take 
exponential time to run. 
7.2. Conflicts Between Preference Rules 
The assumption has been made in this paper 
that the preference rules do not conflict, i.e., that it is 
never the case that description A is preferred over 
description B by one preference rule, while descrip- 
tion B is preferred over description A by another 
preference rule. This means, in particular, that if lex- 
ical class LC1 is preferred over lexical class LC2, 
then LC,'s realization must not contain more open- 
class words than LC2's realization; otherwise, the 
Lexical Preference and Local Brevity preference 
rules may conflict. 1° This can be supported by 
psychological and linguistic findings that basic-level 
classes are almost always realized with single words 
(Rosch 1978; Berlin, Breedlove, and Raven 1973). 
However, there are a few exceptions to this rule, i.e., 
there do exist a small number of basic-level 
categories that have realizations that require more 
than one open-class word. For example, Washing- 
Machine is a basic-level class for some people, and it 
has a realization that uses two open-class words. 
This leads to a conflict of the type mentioned above: 
basic-level Washing-Machine is preferred over non- 
10 This assmnes that the Local Brevity pTcfenmcc rule 
uses number of open-class words as its measure of descrip- 
tic~ length. If number of comp~cnts or number of lcxical 
units is used as the measure of description length, then Local 
Brevity will never conflict with Lcxical Prcfc~-ncc. 
No other conflicts can occur between the No Unneces- 
saw Components, Local Brevity, and Lexical Preference 
preference rules. 
basic-level Appliance, but Washing-Machine's reali- 
zation contains more open-class words than 
Appliance's. 
The presence of a basic-level class with a 
multi-word realization can also cause a conflict to 
occur between the two lexical-preference principles 
given in Section 6 (such conflicts are otherwise 
impossible). For example, Washing-Machine's reali- 
zation contains a superset of the open-class words 
used in the realization of Machine, so the basic-level 
preference of Section 6 indicates that Washing- 
Machine should be lexically preferred over Machine, 
while the realization-subset preference indicates that 
Machine should be lexically preferred over 
Washing-Machine. The basic-level preference 
should take priority in such cases, so Washing- 
Machine is the true lexicaUy-preferred class in this 
example. 
7.3. Generalizability of Results 
For the task of generating attributive descrip- 
tions as formalized in Reiter (1990a, 1990b), the 
Local Brevity, No Unnecessary Components, and 
Lexieal Preference rules are effective at prohibiting 
utterances that carry unwanted conversational impli- 
catures, and also can be incorporated into a 
polynomial-time generation algorithm, provided that 
some restrictions are imposed on the underlying 
knowledge base. The effectiveness and tractability 
of these preference rules for other generation tasks is 
an open problem that requires further investigation. 
The Full Brevity and No Unnecessary Words 
preference rules are computationally intractable for 
the attributive description generation task (Reiter 
1990b), and it seems likely that they will be intract- 
able for most other generation tasks as well. Because 
global maxima are usually expensive to locate, 
finding the shortest acceptable utterance will prob- 
ably be computationally expensive for most genera- 
tion tasks. Because the 'new parse' problem arises 
whenever the preference function is staled solely in 
terms of the surface form, detecting unnecessary 
words will also probably be quite expensive in most 
situations. 
8. Conclusion 
Referring expressions and other object descrip- 
tions need to be brief, to avoid unnecessary elements, 
and to use lexically preferred classes; otherwise, they 
may carry unwanted and incorrect conversational 
implicatures. These principles can be formalized by 
requiring referring expressions to be maximal under 
the Local Brevity, No Unnecessary Components, and 104 
Lexical Preference preference rules. These prefer- 
ence rules can be incorporated into a polynomial- 
time algorithm for generating free-of-false- 
implicatures referring expressions, while some alter- 
native preference rules (Full Brevity and No 
Unnecessary Words) make this generation task NP- 
Hard. 
AckmowJedgements 
Many thanks to Robert Dale, Joyce Friedman, Barbara 
Grosz, Joe Marks, Warren Plath, Candy Sid~er, Jeff Siskind, Bill 
Woods, and the anonymous reviewers for their help and sugges- 
tions. This work was partially supported by a National Science 
Foundatiou Graduate Fellowship, an IBM Graduate Fellowship, 
and a contract from U S WEST Advanced Technologies. Any 
opinions, findings, conclusions, or recommendations are those of 
the author and do not necessarily reflect the views of the National 
Science Fotmdation, IBM, or U S WEST Advanced Technologies. 
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