EXPLOITING CONVERSATIONAL IMPLICATURE 
FOR GENERATING CONCISE EXPLANATIONS 
HELMUT HORACEK 
Universit~t Bielefeld 
Fakultlit f'dr Linguistik und Literaturwissenschaft 
Postfach 8640, D-4800 Bielefeld 1, Deutschland 
ABSTRACT 
This paper presents an approach for achieving 
conciseness in generating explanations, which 
is clone by exploiting formal reconstructions of 
aspects of the Gricean principle of relevance to 
simulate conversational implicature. By apply- 
ing contextually motivated inference rules in an 
anticipation feed-back loop, a set of propo- 
sitions explicitly representing an explanation's 
content is reduced to a subset which, in the 
actual context, can still be considered to convey 
the message adequately. 
1. INTRODUCTION 
The task of providing informative natural 
language explanations for illustrating the results 
produced by decision support systems has been 
gtven increased attention recently. The pro- 
posed methods preferably address tailoring of 
explanations to the needs of their addressees, 
including, for instance, object descriptions \[8\] 
and presentation of taxonomic knowledge \[7\]. 
In addition, particular emphasis has been put on 
reactive explanation techniques for selecting an 
appropriate content according to contextual 
interpretation \[6\], and on the way of presenting 
explanations by taking the information Seeking 
person's knowledge into account \[1\]. 
Whereas these approaches attack various issues 
important for the generation of natural language 
explanations, none of them has focussed on the 
conciseness of explanations in a broader con- 
text. Aiming at the production of natural and 
concise texts, we have concentrated our efforts 
on presenting different types of knowledge and 
their interrelations because this kind of infor- 
mation is typically relevant for explanations. 
We formally reconstruct aspects of the Gricean 
principle of relevance \[3\] and exploit the results 
obtained for creating concise explanations to 
questions about solutions proposed by the ex- 
pert system OFFICE-PLAN \[5\]. This system is 
able to appropriately assign a set of employees 
to a set of rooms in offices, which is guided by 
a number of constraints expressing various 
kinds of the persons" requirements. 
2. REPRESENTING DOMAIN 
AND INFERENCE KNOWLEDGE 
Terminological knowledge is represented in a 
sorted type hierarchy, which identifies classes 
of entities and their relevant subsorts, as well as 
relations that may hold between two types of 
entities. Moreover, assertions which refer to the 
referential level must be consistent with the on- 
tology provided by these taxonomic definitions. 
Inferential knowledge is represented in terms of 
rules which express constraints to be satisfied 
in the problem solving process. Rules are 
represented according to the syntax of IRS \[2\], 
which is loosely based on predicate logic. The 
quantifiers used in our system are all, some, 
and unique. The predications contained are re- 
stricted to be one- or two-place predications 
corresponding to class and relation definitions 
introduced in the taxonomic hierarchy. In addi- 
tion, the recta-predicate implies is contained in 
the innermost predication of a rule, which con- 
stitutes the rule's conclusion (see Figure 1). 
The original representation of an explanation to 
a certain question consists of a set of propo- 
sitions (created by the preceeding component in 
the generation process \[4\]) which includes 
inference rules and individual facts that comple- 
tely identify the reasons behind. The task is 
then to reduce this set of propositions as much 
as possible by exploiting a given context so that 
the subset obtained still conveys the same infor- 
mation - in a partially implicit and more concise 
form, but without leading to wrong implica- 
tions. The intuition behind this mechanism is as 
follows: After having asked a certain expla- 
nation seeking question the questioner mentally 
attempts to build links between entities referred 
to in the question and facts or rules provided as 
"explanation'. Hence, if a regularity valid for a 
class of entities is uttered, the person attempts 
to find out which of the entities mentioned pre- 
viously this rule is thought to apply to. 
i i , 
((some r (and (room r) (in r g))) 
(implies (single-room r)))) 
Figure 1: Inference rule I-Rule 1 
1 
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3. EXPRESSING CONVERSATIONAL 
IMPLICATURE 
The reduction of the set of propositions that ori- 
ginally represents the explanation is performed 
by exploiting a set of rules which are contex- 
tually motivated and express conversational im- 
plicature. These rules represent formal recon- 
structions of aspects of the Gricean principle of 
relevance. They have the same format as the 
rules which constitute the system's inferential 
knowledge, but, in addition, they contain meta- 
predications referring to contextual, conversa- 
tional, or processing states associated with the 
individuals referred to (see Figure 2 below). 
The rules expressing conversational implicature 
allow variables to denote propositions, though 
in an extremely limited sense only: a variable x 
denoting a proposition must always be restrict- 
ed by the predication (newinfo x) so that the eva- 
luation process can rely on a definite set of en- 
tities when generating legal instances of x. 
We have defined three rules that constitute a 
fundamental repertoire for exploiting conversa- 
tional implicature (see Figure 3). They express 
contextually motivated inferences of a fact from 
another one, of a fact from an inference rule, 
and the relevance of an inference rule justified 
by a fact. Moreover, logical substitution is ap- 
plied to those domain inference rules which be- 
come bound to variables of a contextually moti- 
vated inference rule at some processing stage. 
The first rule, C-Rule 1, refers to two (sets of) 
entities el and e2, which have been both addres- 
sed (expressed by topic) in the question and 
share the most general superclass (topclass). If 
, ,,,, ,, J , , 
Predicate ~¢a.0Jag 
(topic a) the entity referred to by a is mentioned 
in the explanation seeking question 
(topclass a) the most general class a is a subclass 
of (the root node does not count) 
(unknown p) the truth value of proposition p is 
considered to be unknown to the user 
(newinfo p) p is contained in the set of propo- 
sitions constituting the explanation 
(no-newinfo a) the information about the entity refer-! 
red to by variable a is not effected by 
the explanation given 
(subst p a b) b is substituted for a in proposition p I 
(contains p a) proposition p refers to entity a \[ 
(aboutfa c) formulafcontains a proposition asser- 
ting variable a to belong to class c 
(not-falsep) p is either unknown to the user ori 
considered by him/her to be true 
(relevant gr ir) rule gr is relevant for instantiation ir 
Figure 2: Meta-predications and their meanings 
the explanation also contains new facts p (newin- 
fo) about el and the same assertion also applies 
to e2 (expressed by subst), and nothing is said 
about e2 (no-newinfo), conversational relevance 
dictates that the contrary of the newly introdu. 
ted facts p is true for e2 (otherwise, the relevant 
part of the message would also mention e2). 
C-Rule 2 may be applicable if the explanation 
contains an inference rule r (referred to by new. 
info). In that case an attempt is made to establish 
a link between a class el which occurs (about) in 
the rule's premise and all entities e2 mentioned 
in the prior question (topic) which could fit (not- 
false) the class membership of el. ff this is suc- 
cessful for some e2, their class membership 
concerning el is considered to be valid. 
Finally, C-Rule 3 tries to strenghten the rele- 
vance of a proposition (newinfo) concerning an 
entity el. First, a unique inference rule r has to 
be found (in the addressee's mental state) 
which contains a variable e2 in its premise such 
that el could fit (not-false) the class membership 
of e2. Secondly, the rule's conclusion must be 
consistent with the information available so far; 
hence, it must be possible to associate all vari- 
ables e3 occurring in the conclusion with vari- 
ables e4 by means of a class membership rela, 
tion. Then the rule is considered to be relevant. 
((all p (and (proposition p) (newinfo p))) 
((all el (and (entity el) (topic el) (contains p el))) 
((all e2 (and (entity e2) (topic e2) 
(equal (topclass e2) (topclass el)) 
(no-newinfo e2) 
(unknown (subst p el e2)))) 
(implies (not (subst p el ¢2)))))) 
C-Rule 1 : Inferring a fact from another fact 
((all r (and (rule r) (newinfo r))) 
((all el (about (premise r) el c)) 
((all e2 (and (entity e2) (topic e2) 
(not.false (subclass (class e2) c)))) 
(implies (equal (class e2) c))))) 
C-Rule 2 : Inferring a fact from a rule 
i 
((all p (and (proposition p) (newinfo p))) 
((all el (and (entity el) (topic el) (contains p el))) 
((unique r (and (rule r) (knows user r))) 
((all e2 (and (about (premise r) e2 cl) 
(not-false (subclass (class el) cl)))) 
((all e3 (about (conclusion r) e3 c2)) 
((some o4 (and (topic e4) 
(not-false (or (subclass (class e4) c2) 
(subclass c2 (c "lass o4)))))) 
(implies (relevant r (subst r e2 ¢1)))))))) 
C-Rule 3 : Inferring a rule from a fact 
Figure 3: Contextually motivated rules 
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4. THE INFERENCE MECHANISM 
The inference mechanism is applied by using a 
simulated anticipation feed-back loop fed by 
heuristically generated hypotheses. They are 
subsets of the set of propositions that originally 
represent the explanation. After the first suc- 
cessful application of a contextually motivated 
rule only C-Rule 1 and logical substitution arc ta- 
ken into account for further inferencing. This 
process is continued until all propositions con- 
mined in the explanation's explicit form occur 
• in the current hypothesis, or 
• in the user model, or 
• in the set of propositions inferred, 
(thus, the explanation is complete) and no con- 
tradictions have been derived (it is also impli- 
cature-free) - hence, the hypothesis considered 
represents a valid explanation. The hypotheses 
are created by starting with the smallest sub- 
sets, so that the first valid hypothesis can be 
expected to be the best choice. In addition, all 
inference rules referred to in the explicit form of 
the explanation and unknown to the user are 
also contained in each hypothesis, as there is no 
chance to infer the relevance of a rule without 
being acquainted with it (see the clause (knows 
user r) in C-Rule 3). Even if the addressee is 
familiar with a certain rule, this rule must either 
be mentioned or it must be inferable, because 
evidence for its relevance in the actual instance 
is required. In fact, hypotheses not including 
such a rule are preferred because u'iggering the 
inference of a rule's relevance by means of 
uttering an additonal fact can usually be achiev- 
ed by shorter utterances than by expressing the 
inference rule explicitly. This heuristics has its 
source in the Gricean principle of brevity. 
5. EXAMPLES 
The mechanism described has been implement- 
ed in CommonLisp on a SUN4. We demon- 
strate the system's behavior by means of the 
effects of three different user models when 
expressing most adequately the expIanation 
(represented in Figure 4) to the question: "Why 
is person A in room B and not in room C?" 
The user models applied comprise stereotypes 
for a "local employee" (he/she is acquainted 
with all information about the actual office), for 
a "novice" (who does not know anything), and 
for an "office plan expert" (who is assumed to 
know I-Rule 1 (1) only). Fact (5) is known to 
anybody, as it is presupposed by the question. 
The process is simple for the "local employee': 
Since he/she also knows facts (2) to (4), the 
first hypothesis (I-Rule 1) provides the missing 
information. The first hypothesis is identical for 
the "novice', but a series of inferences is need- 
ed to prove its adequacy. First, a part of C-Rule 
2 matches (1) and, as A is the only person refer- 
red to in the question, it is inferred that A is a 
group leader, which is what fact (2) expresses. 
Then, substituting A and B in I-Rule 1 results in 
the evidence that B is a single room, thus prov- 
ing fact (3) as well. Finally, C-Rule 1 is appli- 
cable by substituting B and C for the variables 
el and e2, respectively, concluding that C is not 
a single room (and, in fact, a double room if 
this is the only other possible type of room). 
The first hypothesis for the "expert" consists of 
(2) only. Because experts are assumed to be ac- 
quainted with I-Rule 1, C-Rule 3 can be applied 
proving the relevance of (1). Then, processing 
can continue as this is done after the first infer- 
ence step for the "novice', so that fact (2) is 
obtained as the best explanation for the expert. 
,m i ,,Jl i 
(1) (and (Rule 1) "Group leaders must 
be in single rooms" 
(2) (group-leader A) "A is a group leader" 
(3) (single-room B) "B is a single room" 
(4) (double-room (2) "(2 is a double room" 
(5) (in B A)) "A is in room B" 
Figure 4:Representing an explanation 
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