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<Paper uid="P94-1009">
  <Title>A HYBRID REASONING MODEL FOR INDIRECT ANSWERS</Title>
  <Section position="3" start_page="58" end_page="60" type="metho">
    <SectionTitle>
2. PRAGMATIC KNOWLEDGE
</SectionTitle>
    <Paragraph position="0"> Linguists (e.g. see discussion in \[Levinson, 1983\]) have claimed that use of an utterance in a dialogue may create shared expectations about subsequent utterances. In particular, a Yes-No question creates the discourse expectation that R will provide R's evaluation of the truth of the questioned proposition p. Furthermore, Q's assumption that R's response is relevant triggers Q's attempt to interpret R's response as providing the requested information. We have observed that coherence relations similar to the subject-matter relations of Rhetorical Structure Theory (RST) \[Mann and Thompson, 1987\] can be used in defining constraints on the relevance of.an indirect answer. For example, the relation between the (implicit) direct answer in (2b) and each of the indirect answers in (2c) - (2e) is similar to RST's relations of Condition, Elaboration, and (Volitional) Cause, respectively.</Paragraph>
    <Paragraph position="1">  2.a. Q: Are you going shopping tonight? b. R: \[yes\] c. if I finish my homework d. I'm going to Macy's e. Winter clothes are on sale  Furthermore, for Q to interpret any of (2c) - (2e) as conveying an affirmative answer, Q must believe that R intended Q to recognize the relational proposition holding between the indirect answer and (2b), e.g. that (2d) is an elaboration of (25). Also, coherence relations hold between parts of an indirect answer consisting of multiple utterances. For example, (le) describes the cause of the failure reported in (ld). Finally, we have observed that different relations are usually associated with different types of answers. Thus, a speaker who has inferred a plausible coherence relation holding between an indirect answer and a possible (implicit) direct answer may be able to infer the direct answer. (If more than one coherence relation</Paragraph>
    <Paragraph position="3"> indirect answer may be ambiguous.) In our model we formally represent the coherence relations which constrain indirect answers by means of coherence rules. Each rule consists of a consequent of the form (Plausible (CR q p)) and an antecedent which is a conjunction of conditions, where CR is the name of a coherence relation and q and p are formulae, symbols prefixed with &amp;quot;?&amp;quot; are variables, and all variables are implicitly universally quantified. Each antecedent condition represents a condition which is true iff it is believed by R to be mutually believed with Q.2 Each rule represents sufficient conditions for the plausibility of (CR q p) for some CR, q, p. An example of one of the rules describing the Obsta2Our model of R's beliefs (and similarly for Q's), represented as a set of Horn clauses, includes 1) general world knowledge presumably shared with Q, 2) knowledge about the preceding discourse, and 3) R's beliefs (including &amp;quot;weak beliefs&amp;quot;} about Q's beliefs. Much of the shared world knowledge needed to evaluate the coherence rules consists of knowledge from domain plan operators.</Paragraph>
    <Paragraph position="4">  operators for Yes and No answers cle relation 3 is shown in Figure 2. The predicates used in the rule are defined as follows: (in-state p /) denotes that p holds during t, (occur p t) denotes that p happens during t, (state z) denotes that the type of x is state, (event x) denotes that the type of x is event, (timeperiod t) denotes that t is a time interval, (before tl t2) denotes that tl begins before or at the same time as t2, (app-cond q p} denotes that q is a plausible enabling condition for doing p, and (unless p) denotes that p is not provable from the beliefs of the reasoner.</Paragraph>
    <Paragraph position="5"> For example, this rule describes the relation between (ld) and (lc), where (ld) is interpreted as (not (in-state (running R-car) Present)) and (lc) as (not (occur (go-shopping R) Future)). That is, this relation would be plausible if Q and R share the belief that a plausible enabling condition of a subaction of a plan for R to go shopping at the mall is that R's car be in running condition.</Paragraph>
    <Paragraph position="6"> In her study of responses to questions, StenstrSm \[Stenstrfm, 1984\] found that direct answers are often accompanied by extra, relevant information, 4 and noted that often this extra information is similar in content to an indirect answer. Thus, the above constraints on the relevance of an indirect answer can serve also as constraints on information accompanying a direct answer. For maximum generality, therefore, we went beyond our original goal of handling indirect answers to the goal of handling what we call full answers. A full answer consists of an implicit or explicit direct answer (which we call the nucleus) and, possibly, extra, relevant information (satellites). s In our awhile Obstacle is not one of the original relations of RST, it is similar to the causal relations of RST.</Paragraph>
    <Paragraph position="7"> 461 percent of direct No answers and 24 percent of direct Yes answers 5The terms nucleus and satellite have been borrowed from RST to reflect the informational constraints within a full answer. Note that according to RST, a property of the nucleus is that its removal remodel, we represent each type of full answer as a (top-level) discourse plan operator. By representing answer types as plan operators, generation can be modeled as plan construction, and interpretation as plan recognition.</Paragraph>
    <Paragraph position="8"> Examples of (top-level) operators describing a full Yes answer and a full No answer are shown in Figure 3. 6 To explain our notation, s and h are constants denoting speaker (R) and hearer (Q), respectively. Symbols prefixed with &amp;quot;?&amp;quot; denote propositional variables. The variables in the header of each top-level operator will be instantiated with the questioned proposition. In interpreting example (1), ?p would be instantiated with the proposition that R is going shopping tonight.</Paragraph>
    <Paragraph position="9"> Thus, instantiating the Answer-No operator in Figure 3 with this proposition would produce a plan for answering that P~ is not going shopping tonight. Applicability conditions are necessary conditions for appropriate use of a plan operator.</Paragraph>
    <Paragraph position="10"> For example, it is inappropriate for R to give an affirmative answer that p if R believes p is false.</Paragraph>
    <Paragraph position="11"> Also, an answer to a Yes-No question is not appropriate unless s and h share the discourse expectation that s will provide s's evaluation of the truth of the questioned proposition p, which we denote as (discourse-ezpectation (informif s h p)).</Paragraph>
    <Paragraph position="12"> Primary goals describe the intended effects of the plan operator. We use (BMB h s p) to denote that h believes it mutually believed with s that p \[Clark and Marshall, 1981\].</Paragraph>
    <Paragraph position="13"> In general, the nucleus and satellites of a discourse plan operator describe primitive or non-primitive communicative acts. Our formalism elsuits in incoherence. However, in our model, a direct answer may be removed without causing incoherence, provided that it is inferable from the rest of the response.</Paragraph>
    <Paragraph position="14">  lows zero, one, or more occurrences of a satellite in a full answer, and the expected (but not required) order of nucleus and satellites is the order they are listed in the operator. (inform s h p) denotes the primitive act of s informing h that p.</Paragraph>
    <Paragraph position="15"> The satellites in Figure 3 refer to non-primitive acts, described by discourse plan operators which we have defined (one for each coherence relation used in a full answer). For example, Use-obstacle, a satellite of Answer-no in Figure 3, is defined in  To explain the additional notation in Figure 4, (cr-obstacle q p) denotes that the coherence relation named obstacle holds between q and p. Thus, the first applicability condition can be glossed as requiring that s believe that the coherence relation holds. In the second applicability condition, (Plausible (cr-obstacle q p)) denotes that, given what s believes to be mutually believed with h, the coherence relation (cr-obstacle q p) is plausible. This sort of applicability condition is evaluated using the coherence rules described above.</Paragraph>
    <Paragraph position="16"> Stimulus conditions describe conditions motivating a speaker to include a satellite during plan construction. They can be thought of as triggers which give rise to new speaker goals. In order for a satellite to be selected during generation, all of its applicability conditions and at least one of its stimulus conditions must hold.</Paragraph>
    <Paragraph position="17"> While stimulus conditions may be derivative of principles of cooperativity \[Grice, 1975\] or politeness \[Brown and Levinson, 1978\], they provide a level of precompiled knowledge which reduces the amount of reasoning required for contentplanning. For example, Figure 5 depicts the discourse plan which would be constructed by R (and  must be inferred by Q) for (1). The first stimulus condition of Use-obstacle, which is defined as holding whenever s suspects that h would be surprised that p holds, describes R's reason for including (le). The second stimulus condition, which is defined as holding whenever s suspects that the Yes-No question is a prerequest \[Levinson, 1983\], describes R's reason for including (ld). 7</Paragraph>
  </Section>
  <Section position="4" start_page="60" end_page="62" type="metho">
    <SectionTitle>
3. INTERPRETATION
</SectionTitle>
    <Paragraph position="0"> We assume that interpretation of dialogue is controlled by a Discourse Model Processor (DMP), which maintains a Discourse Model \[Carberry, 1990\] representing what Q believes R has inferred so far concerning Q's plans. The discourse expectation generated by a Yes-No question leads the DMP to invoke the answer recognition process to be described in this section. If answer recognition is unsuccessful, the DMP would invoke other types of recognizers for handling less preferred types of responses, such as I don't know or a clarification subdialogue. To give an example of where our recognition algorithm fits into the above framework, consider (4).</Paragraph>
    <Paragraph position="1">  4a. Q: Is Dr. Smith teaching CSI next fall? b. R: Do you mean Dr. Smithson? c. Q: Yes.</Paragraph>
    <Paragraph position="2"> d. R: \[no\] e. He will be on sabbatical next fall.</Paragraph>
    <Paragraph position="3"> f. Why do you ask?  Note that a request for clarification and its answer are given in (4b) - (4c). Our recognition algorithm, when invoked with (4e) - (4f) as input, would infer an Answer-no plan accounting for (4e) and satisfying the discourse expectation generated by (4a). When invoked by the DMP, our interpretation module plays the role of the questioner Q. The inputs to interpretation in our model consist of 7Stimulus conditions are formally defined by rules encoded in the same formalism as used for our coherence rules. A full description of the stimulus conditions used in our model can be found in \[Green, in preparation\].</Paragraph>
    <Paragraph position="4">  1) the set of discourse plan operators and the set of coherence rules described in section 2, 2) Q's beliefs, 3) the discourse expectation (discourseexpectation (informif s h p)), and 4) the semantic representation of the sequence of utterances performed by R during R's turn. The output is a partially ordered set (possibly empty) of answer discourse plans which it is plausible to ascribe to R as underlying It's response. The set is ordered by plausibility using preference criteria. Note that we assume that the final choice of a discourse plan to ascribe to R is made by the DMP, since the DMP must select an interpretation consistent with the interpretation of any remaining parts of R's turn not accounted fo~ by the answer discourse plan, e.g. (4f).</Paragraph>
    <Paragraph position="5"> To give a high-level description of our answer interpretation algorithm, first, each (top-level) answer discourse plan operator is instantiated with the questioned proposition from the discourse expectation. For example (1), each answer operator would be instantiated with the proposition that R is going shopping tonight. Next, the answer interpreter must verify that the applicability conditions and primary goals which would be held by R if R were pursuing the plan are consistent with Q's beliefs about It's beliefs and goals. Consistency checking is implemented using a Horn clause theorem-prover. For all candidate answer plans which have not been eliminated during consistency checking, recognition continues by attempting to match the utterances in R's turn to the actions specified in the candidates. However, no candidate plan may be constructed which violates the following structural constraint. Viewing a candidate plan's structure as a tree whose leaves are primitive acts from which the plan was inferred, no subtree Ti may contain an act whose sequential position in the response is included in the range of sequential positions in the response of acts in a subtree Tj having the same parent node as 7~. For example, (5e) cannot be interpreted as related to  (5c) by cr-obstaele, due to the occurrence of (5d) between (5c) and (5e). Note that a more coherent response would consist of the sequence, (5c), (5e), (Sd). 5.a. O: Are you going shopping tonight? b. R: \[no\] c. My car's not running.</Paragraph>
    <Paragraph position="6"> d, Besides, I'm too tired.</Paragraph>
    <Paragraph position="7"> e. The timing belt is broken.</Paragraph>
    <Paragraph position="8">  To recognize a subplan for a non-primitive action, e.g. Use-obstacle in Figure 4, a similar procedure is used. Note that any applicability condition of the form (Plausible (CR q p)) is defined to be consistent with Q's beliefs if it is provable, i.e., if the antecedents of a coherence rule for CR are true with respect to what Q believes to be mutually believed with R. The recognition process for non-primitive actions differs in that these operators contain existential variables which must be instantiated. In our model, the answer interpreter first attempts to instantiate an existential variable with a proposition from R's response. For example (1), the existential variable ?q of Use-obstacle would be instantiated with the proposition that R's car is not running. However, if (ld) was not explicitly stated by R, i.e., if R's response had just consisted of (le), it would be necessary for ?q to be instantiated with a hypothesized proposition, corresponding to (ld), to understand how (le) relates to R's answer. The answer interpreter finds the hypothesized proposition by a subprocedure we refer to as hypothesis generation.</Paragraph>
    <Paragraph position="9"> Hypothesis generation is constrained by the assumption that R's response is coherent, i.e., that (le) may play the role of a satellite in a subplan of some Answer plan. Thus, the coherence rules are used as a source of knowledge for generating hypotheses. Hypothesis generation begins with initializing the root of a tree of hypotheses with a proposition p0 to be related to a plan, e.g. the proposition conveyed by (le). A tree of hypotheses is constructed by expanding each of its nodes in breadth-first order until all goal nodes (as defined below) have been reached, subject to a limit on the depth of the breadth-first search, s A node containing a proposition Pi is expanded by searching for all propositions Pi+l such that for some coherence relation CR which may be used in the type of answer being recognized, (Plausible ( CR pi pi+l)) holds from Q's point of view. (The search is implemented using a Horn clause theorem prover.) The plan operator invoking hypothesis generation has a partially instantiated applicability condition of the form, (Plausible (CR ?q p)), where CR is a coherence relation, p is the proposition that was used to instantiate the header variable of the operator, and ?q is the operator's existential variable. Since the purpose of the search is to find a proposition q with which to instantiate ?q, a goal node is defined as a node containing a proposition q satisfying the above condition. (E.g. in Figure 6 P0 is the proposition conveyed by (le), Px is the proposition conveyed by (ld), P0 and Pl are plausibly related by er-obstaele, P2 is the proposition conveyed by a No answer to (la), Pl and P2 are plausibly related by cr-obstacle, P2 is a goal node, and therefore, Pl will be used to instantiate the existential variable ?q in Use-obstacle.) After the existential variable is instantiated, plan recognition proceeds as described above at SPlacing a limit on the maximum depth of the tree is reasonable, given human processing constraints.  to (lc) the point where the remaining conditions are checked for consistency. 9 For example, as recognition of the Use-obstacle subplan proceeds, (le) would be recognized as the realization of a Use-obstacle satellite of this Use-obstacle subplan. Ultimately, the inferred plan would be the same as that shown in Figure 5, except that (ld) would be marked as hypothesized.</Paragraph>
    <Paragraph position="10"> The set of candidate plans inferred from a response are ranked using two preference criteria. 1deg First, as the number of hypothesized propositions in a candidate increases, its plausibility decreases. Second, as the number of non-hypothesized propositions accounted for by the plan increases, its plausibility increases.</Paragraph>
    <Paragraph position="11"> To summarize the interpretation algorithm, it is primarily expectation-driven in the sense that the answer interpreter attempts to interpret R's response as an answer generated by some answer discourse plan operator. Whenever the answer interpreter is unable to relate an utterance to the plan which it is currently attempting to recognize, the answer interpreter attempts to find a connection by hypothesis generation. Logical inference plays a supplementary role, namely, in consistency checking (including inferring the plausibility of coherence relations) and in hypothesis generation.</Paragraph>
  </Section>
  <Section position="5" start_page="62" end_page="63" type="metho">
    <SectionTitle>
4. GENERATION
</SectionTitle>
    <Paragraph position="0"> The inputs to generation consist of 1) the same sets of discourse plan operators and coherence rules used in interpretation, 2) R's beliefs, and 3) the same discourse expectation. The output is a 9Note that, in general, any nodes on the path between p0 and Ph, where Ph is the hypothesis returned, will be used as additional hypotheses (later) to connect what was said to ph.</Paragraph>
    <Paragraph position="1"> 1degAnother possible criterion is whether the actual ordering reflects the default ordering specified in the discourse plan operators. We plan to test the usefulness of this criterion.</Paragraph>
    <Paragraph position="2"> discourse plan for an answer (indirect, if possible). Generation of an indirect reply has two phases: 1) content planning, in which the generator creates a discourse plan for a full answer, and 2) plan pruning, in which the generator determines which parts of the planned full answer do not need to be explicitly stated. For example, given an appropriate set of R's beliefs, our system generates a plan for asserting only the proposition conveyed in (le) as an answer to (lb). 11 Content-planning is performed by top-down expansion of an answer discourse plan operator.</Paragraph>
    <Paragraph position="3"> Note that applicability conditions prevent inappropriate use of an operator, but they do not model a speaker's motivation for providing extra information. Further, a full answer might provide too much information if every satellite whose operator's applicability conditions held were included in a full answer. On the other hand, at the time R is asked the question, R may not yet have the primary goals of a potential satellite. To overcome these limitations, we have incorporated stimulus conditions into the discourse plan operators in our model. As mentioned in section 2, stimulus conditions can be thought of as triggers or motivating conditions which give rise to new speaker goals.</Paragraph>
    <Paragraph position="4"> By analyzing the speaker's possible motivation for providing extra information in the examples in our corpus, we have identified a small set of stimulus conditions which reflect general concerns of accuracy, efficiency, and politeness. In order for a satellite to be included in a full answer, all of its applicability conditions and at least one of its stimulus conditions must hold. (A theorem prover is used to search for an instantiation of the existential variable satisfying the above conditions.) The output of the content-planning phase, a discourse plan representing a full answer, is the input to the plan-pruning phase. The goal of this phase is to make the response more concise, i.e. to determine which of the planned acts can be omitted while still allowing Q to infer the full plan. To do this, the generator considers each of the acts in the frontier of the full plan tree from right to left (thus ensuring that a satellite is considered before its nucleus). The generator creates trial plans consisting of the original plan minus the nodes pruned so far and minus the current node. Then, the generator simulates Q's interpretation of the trial plan. If Q could infer the full plan (as the most preferred plan), then the current node can be pruned. Note that, even when it is not possible to prune the direct answer, a benefit of this approach is that it generates appropriate extra information with direct answers.</Paragraph>
    <Paragraph position="5"> 11The tactical component must choose an appropriate expression to refer to R's car's timing belt, depending on whether (ld) is omitted.</Paragraph>
  </Section>
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