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<Paper uid="E91-1033">
  <Title>EXPLOITING CONVERSATIONAL IMPLICATURE FOR GENERATING CONCISE EXPLANATIONS</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2. REPRESENTING DOMAIN
AND INFERENCE KNOWLEDGE
</SectionTitle>
    <Paragraph position="0"> 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 ontology provided by these taxonomic definitions.</Paragraph>
    <Paragraph position="1"> 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 restricted to be one- or two-place predications corresponding to class and relation definitions introduced in the taxonomic hierarchy. In addition, the recta-predicate implies is contained in the innermost predication of a rule, which constitutes the rule's conclusion (see Figure 1).</Paragraph>
    <Paragraph position="2"> The original representation of an explanation to a certain question consists of a set of propositions (created by the preceeding component in the generation process \[4\]) which includes inference rules and individual facts that completely 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 information - in a partially implicit and more concise form, but without leading to wrong implications. The intuition behind this mechanism is as follows: After having asked a certain explanation seeking question the questioner mentally attempts to build links between entities referred to in the question and facts or rules provided as &amp;quot;explanation'. Hence, if a regularity valid for a class of entities is uttered, the person attempts to find out which of the entities mentioned previously this rule is thought to apply to.</Paragraph>
    <Paragraph position="4"/>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3. EXPRESSING CONVERSATIONAL
IMPLICATURE
</SectionTitle>
    <Paragraph position="0"> The reduction of the set of propositions that originally represents the explanation is performed by exploiting a set of rules which are contextually motivated and express conversational implicature. These rules represent formal reconstructions 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 metapredications referring to contextual, conversational, or processing states associated with the individuals referred to (see Figure 2 below).</Paragraph>
    <Paragraph position="1"> 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 restricted by the predication (newinfo x) so that the evaluation process can rely on a definite set of entities when generating legal instances of x.</Paragraph>
    <Paragraph position="2"> We have defined three rules that constitute a fundamental repertoire for exploiting conversational 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 applied to those domain inference rules which become bound to variables of a contextually motivated inference rule at some processing stage.</Paragraph>
    <Paragraph position="3"> The first rule, C-Rule 1, refers to two (sets of) entities el and e2, which have been both addressed (expressed by topic) in the question and share the most general superclass (topclass). If</Paragraph>
    <Paragraph position="5"> (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 propositions 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 asserting 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  the explanation also contains new facts p (newinfo) 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).</Paragraph>
    <Paragraph position="6"> 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 (notfalse) the class membership of el. ff this is successful for some e2, their class membership concerning el is considered to be valid.</Paragraph>
    <Paragraph position="7"> Finally, C-Rule 3 tries to strenghten the relevance 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 variables e3 occurring in the conclusion with variables e4 by means of a class membership rela, tion. Then the rule is considered to be relevant.</Paragraph>
    <Paragraph position="8"> ((all p (and (proposition p) (newinfo p))) ((all el (and (entity el) (topic el) (contains p el)))</Paragraph>
    <Paragraph position="10"> (implies (not (subst p el C/2)))))) C-Rule 1 : Inferring a fact from another fact ((all r (and (rule r) (newinfo r))) ((all el (about (premise r) el c))</Paragraph>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4. THE INFERENCE MECHANISM
</SectionTitle>
    <Paragraph position="0"> 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 successful application of a contextually motivated rule only C-Rule 1 and logical substitution arc taken into account for further inferencing. This process is continued until all propositions conmined 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 contradictions have been derived (it is also implicature-free) - hence, the hypothesis considered represents a valid explanation. The hypotheses are created by starting with the smallest subsets, 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 achieved by shorter utterances than by expressing the inference rule explicitly. This heuristics has its source in the Gricean principle of brevity.</Paragraph>
  </Section>
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