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<?xml version="1.0" standalone="yes"?> <Paper uid="P97-1025"> <Title>Planning Reference Choices for Argumentative Texts</Title> <Section position="4" start_page="190" end_page="191" type="metho"> <SectionTitle> 2 The System PROVERB </SectionTitle> <Paragraph position="0"> PROVERB is a text planner that verbalizes natural deduction (ND) style proofs (Gentzen, 1935). Several similar attempts can be found in previous work.</Paragraph> <Paragraph position="1"> The system EXPOUND (Chester, 1976) is an example of direct translation: Although a sophisticated linearization is applied on the input ND proofs, the steps are then translated locally in a template-driven way. ND proofs were tested as inputs to an early version of MUMBLE (McDonald, 1983); the main aim, however, was to show the feasibility of the architecture. A more recent attempt can be found in THINKER (Edgar and Pelletier, 1993), which implements several interesting but isolated proof presentation strategies. PROVERB however can be seen as the first serious attempt for a comprehensive system that produces adequate argumentative texts from ND style proofs. Figure 1 shows the architecture of PROVERB(Huang, 1994a; HuangFiedler, 1997): the macroplanner produces a sequence of PCAs, the DRCC (Derive Reference Choices Component) module of the microplanner enriches the PCAs with reference choices. The TSG (Text Structure Generator) module subsequently produces the text structures as the output of the microplanner. Finally, text structures are realized by TAG-GEN (Kilger and Finkler, 1995), our realization component. In this paper, we concentrate only on the macroplanner and the DRCC component.</Paragraph> <Section position="1" start_page="190" end_page="190" type="sub_section"> <SectionTitle> 2.1 Architecture of the Macroplanner </SectionTitle> <Paragraph position="0"> Most current text planners adopt a hierarchical planning approach (How, 1988; Moore and Paris, 1989; Dale, 1992; Reithinger, 1991). Nevertheless there is psychological evidence that language has an unplanned, spontaneous aspect as well (Ochs, 1979).</Paragraph> <Paragraph position="1"> Based on this observation, Sibun (Sibun, 1990) implemented a system for generating descriptions of objects with a strong domain structure, such as houses, chips, and families. Her system produces text using a technique she called local organization.</Paragraph> <Paragraph position="2"> While a hierarchical planner recursively breaks generation tasks into subtasks, local organization navigates the domain-object following the local focus of</Paragraph> </Section> <Section position="2" start_page="190" end_page="191" type="sub_section"> <SectionTitle> Natural Deduction Proof </SectionTitle> <Paragraph position="0"/> <Paragraph position="2"> PROVERB combines both of these approaches in a uniform planning framework (Huang, 1994a).</Paragraph> <Paragraph position="3"> The hierarchical planning splits the task of presenting a particular proof into subtasks of presenting subproofs. While the overall planning mechanism follows the RST-based planning approach (How, 1988; Moore and Paris, 1989; Reithinger, 1991), the planning operators more resemble the schemata in schema-based planning (McKeown, 1985; Paris, 1988) since presentation patterns associated with specific proof patterns normally contain multiple RST-relations. PROVERB's hierarchical planning is driven by proof patterns that entail or suggest established ways of presentation. For trivial proofs that demonstrate no characteristic patterns, however, this technology will fail. PRO VERB navigates such relatively small parts of a proof and chooses the next conclusion to be presented under the guidance of a local focus mechanism.</Paragraph> <Paragraph position="4"> While most existing systems follow one of the two approaches exclusively, PROVERB uses them as complementary techniques in an integrated framework. In this way, our architecture provides a clear way of factoring out domain-dependent presentation knowledge from more general NLG techniques. While PROVERB's hierarchical planning operators encodes accepted format for mathematical text, its local navigation embodies more generic principles of language production.</Paragraph> <Paragraph position="5"> The two kinds of planning operators are treated accordingly. Since hierarchical planning operators embody explicit communicative norms, they are given a higher priority. Only when none of them is applicable, will a local navigation operator be chosen.</Paragraph> </Section> <Section position="3" start_page="191" end_page="191" type="sub_section"> <SectionTitle> 2.2 Proof Communicative Acts </SectionTitle> <Paragraph position="0"> PCAs are the primitive actions planned by the macroplanner of PROVERB* Like speech acts, they can be defined in terms of the communicative goals they fulfill as well as their possible verbalizations.</Paragraph> <Paragraph position="1"> The simplest one conveying the derivation of a new intermediate conclusion is illustrated in the introduction. There are also PCAs that convey a partial plan for further presentation and thereby update the reader's global attentional structure. For instance, creates two attentional spaces with A and B as the assumptions, and Formula as the goal by producing the verbalization: &quot;To prove Formula, let us consider the two cases by assuming A and B.&quot;</Paragraph> </Section> <Section position="4" start_page="191" end_page="191" type="sub_section"> <SectionTitle> 2.3 Hierarchical Planning </SectionTitle> <Paragraph position="0"> Hierarchical planning operators represent communicative norms concerning how a proof is to be presented can be split into subproofs, how the subproofs can be mapped onto some linear order, and how primitive subproofs should be conveyed by PCAs.</Paragraph> <Paragraph position="1"> Let us look at one such operator, which handles proof by case analysis. The corresponding schema of such a proof tree I is shown in Figure 2, where</Paragraph> <Paragraph position="3"> the subproof rooted by ?L4 leads to F V G, while subproofs rooted by ?L2 and ?L3 are the two cases proving Q by assuming F or G, respectively* The applicability encodes the two scenarios of case anMysis, where we do not go into details. In both circumstances this operator first presents the part leading to F V G, and then proceeds with the two cases. It also inserts certain PCAs to mediate between parts *We adopt for proof tree the notation of Gentzen.</Paragraph> <Paragraph position="4"> Each bar represents a step of derivation, where the formula beneath the bar is derived from the premises above the bar. For the convenience of discussion, some formulae are given an identifying label, such as ?L1.</Paragraph> <Paragraph position="5"> of proofs. This procedure is captured by the planning operator below.</Paragraph> <Paragraph position="6"> Case-Implicit * Applicability Condition: ((task ?L1) V (local-focus ?L4)) A (not-conveyed (?L2 ?L3)) * Acts: 1. if ?L4 has not been conveyed, then present ?L4 (subgoal 1) 2. a PCA with the verbalization: &quot;First, let us consider the first case by assuming F.&quot; 3. present ?L2 (subgoal 2) 4. a PCA with the verbalization: &quot;Next, we consider the second case by assuming G.&quot; 5. present ?L3 (subgoal 3) 6. mark ?L1 as conveyed .features: (hierarchical-planning compulsory implicit) null</Paragraph> </Section> <Section position="5" start_page="191" end_page="191" type="sub_section"> <SectionTitle> 2.4 Planning as Navigation </SectionTitle> <Paragraph position="0"> The local navigation operators simulate the unplanned part of proof presentation. Instead of splitting presentation goals into subgoals, they follow the local derivation relation to find a proof step to be presented next.</Paragraph> <Paragraph position="1"> The node to be presented next is suggested by the mechanism of local focus. In PROVERB, our local focus is the last derived step, while focal centers are semantic objects mentioned in the local focus. Although logically any proof node that uses the local focus as a premise could be chosen for the next step, usually the one with the greatest semantic overlap with the focal centers is preferred* In other words, if one has proved a property about some semantic objects, one will tend to continue to talk about these particular objects, before turning to new objects.</Paragraph> <Paragraph position="2"> Let us examine the situation when the proof below is awaiting presentation.</Paragraph> <Paragraph position="3"> \[1\]: P(a,b) \[1\]: P(a,b), \[3\]: S(c) \[ 2\] Q(a;b)' \[4\]: R(b,c) \[5\]: Q(a, b) A R(b, c) Assume that node \[1\] is the local focus, {a, b} is the set of focal centers, \[3\] is a previously presented node and node \[5\] is the root of the proof to be presented* \[2\] is chosen as the next node to be presented, since it does not introduce any new semantic object and its overlap with the focal centers ({a,b}) is larger than the overlap of \[4\] with the focal centers ({b}). For local focus mechanisms used in another domain of application, readers are referred to (McKeown, 1985).</Paragraph> </Section> </Section> <Section position="5" start_page="191" end_page="193" type="metho"> <SectionTitle> 3 The Attentional Hierarchy </SectionTitle> <Paragraph position="0"> The distinction between hierarchical planning and local navigation leads to a very natural segmentation NNo S;D Formula 7. 7; ~- group(F, *) A subgroup(U, F, *) A unit(F, 1, *) A unit(U, lt\], *) 8. 7; ~- U C F 9. 7; I- lrr EU 10. 7; I- 3zx E U 11. ;11 I- u E U 12. 7;11 b u* lt\] = u 13. 7;11 b u E F 14. 7;11 I- It\] E F 15. 7;11 I- semigroup(F, *) 16. 7;11 b solution(u, u, lu, F, *) 17. 7;11 b u* 1 = u 18. 7;11 I- 1 E F 19. 7;11 I- solution(u, u, 1, F, *) 20. 7;11 b- 1 = lrr 21. 7; t- 1 = 1u 22. ; I- group(F, *) A subgroup(U, F, *) A unit(F, 1, *) A of a discourse into an attentional hierarchy, since following the theory of Grosz and Sidner (Grosz and Sidner, 1986), there is a one-to-one correspondence between the intentional hierarchy and the attentional hierarchy. In this section, we illustrate the attentional hierarchy with the help of an example, which will be used to discuss reference choices later. The input proof in Figure 3 is an ND style proof for the following theorem2: Theorem: Let F be a group and U a subgroup of F. If i and lv are unit elements of F and U respectively, then 1=1u.</Paragraph> <Paragraph position="1"> The definitions of semigroup, group, and unit are obvious, solution(a, b, c, F, ,) stands for &quot;c is a solution of the equation a, z = b in F.&quot; Each line in the proof is of the form: Label A F- Conclusion (Justification reasons) where Justification is either an ND inference rule, a definition or theorem, which justifies the derivation of the Conclusion using as premises the formulas in the lines given as reasons. A can be ignored for our purpose.</Paragraph> <Paragraph position="2"> We assume a reader will build up a (partial) proof tree as his model of the ongoing discourse. The corresponding discourse model after the completion of the presentation of the proof in Figure 3 is a proof tree shown in Figure 4. Note that the bars in Gentzen's notion (Figure 2) are replaced by links for clarity. The numbers associated with nodes are the corresponding line numbers in Figure 4. Children of nodes are given in the order they have been presented. The circles denote nodes which are first this proof, which are omitted.</Paragraph> <Paragraph position="3"> derived at this place, and nodes in the form of small boxes are copies of some previously derived nodes (circled nodes), which are used as premises again. For nodes in a box, a referring expression must have been generated in the text. The big boxes represent attentional spaces (previously called proof units by the author), created during the presentation process. The naturalness of this segmentation is largely due to the naturalness of the hierarchical planning operators. For example, attentional space U2 has two subordinate spaces U3 and U4. This reflects a natural shift of attention between a subproof that derives a formula of the pattern 3,P(z) (node 10, 3,x E U), and the subproof that proceeds after assuming a new constant u satisfying P (node 11, u E U). When PROVERB opens a new attentional space, the reader will be given information to post an open goal and the corresponding premises. Elementary attentional spaces are often composed of multiple PCAs produced by consecutive navigation steps, such as U5 and U6. It is interesting to note that elementary attentional space cannot contain PCAs that are produced by consecutive planning operators in a pure hierarchical planning framework.</Paragraph> <Paragraph position="4"> Adapting the theory of Reichman for our purpose (Reichman, 1985), we assume that each attentional space may have one of the following status: * an attentional space is said to be open if its root is still an open goal.</Paragraph> <Paragraph position="5"> -The active attentional space is the innermost attentional space that contains the local focus. -The controlling attentional space is the innermost proof unit that contains the active attentional space.</Paragraph> <Paragraph position="6"> -precontrol attentional spaces are attentional spaces that contain the controlling attentional space.</Paragraph> <Paragraph position="8"/> </Section> <Section position="6" start_page="193" end_page="193" type="metho"> <SectionTitle> 4 A Classification of Reference </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="193" end_page="193" type="sub_section"> <SectionTitle> Forms </SectionTitle> <Paragraph position="0"> A referring expression should help a reader to identify an object from a pool of candidates, This section presents a classification of the possible forms with which mathematicians refer to conclusions previously proved (called reasons) or to methods of inference available in a domain.</Paragraph> </Section> <Section position="2" start_page="193" end_page="193" type="sub_section"> <SectionTitle> 4.1 Reference Forms for Reasons </SectionTitle> <Paragraph position="0"> Three reference forms have been identified by the author for reasons in naturally occurring proofs (Huang, 1990): 1. The omit form: where a reason is not mentioned at all.</Paragraph> <Paragraph position="1"> 2. The explicit form: where a reason is literally repeated. null 3. The implicit form: By an implicit form we mean that although a reason is not verbalized directly, a hint is given in the verbalization of either the inference method, or of the conclusion. For instance, in the verbalization below &quot;Since u is an element in U, u * 1u = u by the definition of unit.&quot; the first reason of the PCA in Section 1, &quot;since 1v is the unit element of U&quot; is hinted at by the inference method which reads &quot;by the definition of unit&quot;.</Paragraph> <Paragraph position="2"> Although omit and implicit forms lead to the same surface structure, the existence of an implicit hint in the other part of the verbalization affects a reader's understanding.</Paragraph> </Section> <Section position="3" start_page="193" end_page="193" type="sub_section"> <SectionTitle> 4.2 Reference Forms for Methods </SectionTitle> <Paragraph position="0"> PROVERB must select referring expressions for methods of inference in PCAs as well. Below are the three reference forms identified by the author, which are analogous to the corresponding cases for reasons: 1. the explicit form: this is the case where a writer may decide to indicate explicitly which inference rule he is using. For instance, explicit translations of a definition may have the pattern: &quot;by the definition of unit element&quot;, or &quot;by the uniqueness of solution.&quot; ND rules have usually standard verbalizations. null 2. the omit form: in this case a word such as &quot;thus&quot; or &quot;therefore&quot; will be used.</Paragraph> <Paragraph position="1"> 3. The implicit form: Similar to the implicit form for the expression of reasons, an implicit hint to a domain-specific inference method can be given either in the verbalization of the reasons, or in that of the conclusion.</Paragraph> </Section> </Section> <Section position="7" start_page="193" end_page="194" type="metho"> <SectionTitle> 5 Reference Choices in PROVERB </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="193" end_page="194" type="sub_section"> <SectionTitle> 5.1 Referring to Reasons </SectionTitle> <Paragraph position="0"> Because reasons are intermediate conclusions proved previously in context, their reference choices have much in common with the problem of choosing anaphoric referring expressions in general. To account for this phenomenon , concepts like activat- null edness, foregroundness and consciousness have been introduced. More recently, the shift of focus has been further investigated in the light of a structured flow of discourse (Reichman, 1985; Grosz and Sidnet, 1986; Dale, 1992). The issue of salience is also studied in a broader framework in (Pattabhiraman and Cercone, 1993). Apart from salience, it is also shown that referring expressions are strongly influenced by other aspects of human preference. For example, easily perceivable attributes and basic-level attributes values are preferred (Dale and Haddock, 1991; Dale, 1992; Reiter and Dale, 1992).</Paragraph> <Paragraph position="1"> In all discourse-based theories, the update of the focus status is tightly coupled to the factoring of the flux of text into segments. With the segmentation problem settled in section 3, the DRCC module makes reference choices following a discourse theory adapted from Reichman (Reichman, 1985). Based on empirical data, Reichman argues that the choice of referring expressions is constrained both by the status of the discourse space and by the object's level of focus within this space. In her theory, there are seven status assignments a discourse space may have. Within a discourse space, four levels of focus can be assigned to individual objects: high, medium, low, or zero, since there are four major ways of referring to an object using English, namely, by using a pronoun, by name, by a description, or implicitly.</Paragraph> <Paragraph position="2"> Our theory uses the notions of structural closeness and textual closeness, and takes both of these factors into account for argumentative discourse.</Paragraph> <Paragraph position="3"> The structural closeness of a reason reflects the foreground and background character of the innermost attentional space containing it. Reasons that may still remain in the focus of attention at the current point from the structural perspective are considered as structurally close. Otherwise they are considered as structurally distant. If a reason, for instance, is last mentioned or proved in the active attentional space (the subproof which a reader is supposed to concentrate on), it is likely that this reason still remains in his focus of attention. In contrast, if a reason is in a closed subproof, but is not its conclusion, it is likely that the reason has already been moved out of the reader's focus of attention.</Paragraph> <Paragraph position="4"> Although finer differentiation may be needed, our theory only distinguishes between reasons residing in attentional spaces that are structurally close or structurally distant. DRCC assigns the structural status by applying the following rules.</Paragraph> <Paragraph position="5"> 1. Reasons in the active attentional space are structurally close.</Paragraph> <Paragraph position="6"> 2. Reasons in the controlling attentional space are structurally close.</Paragraph> <Paragraph position="7"> 3. Reasons in closed attentional spaces: (a) reasons that are the root of a closed attentional space immediate subordinate to the active attentional space are structurally close.</Paragraph> <Paragraph position="8"> (b) Other reasons in a closed attentional spac e are structurally distant.</Paragraph> <Paragraph position="9"> 4. Reasons in precontrol attentional spaces are structurally distant.</Paragraph> <Paragraph position="10"> Note that the rules are specified with respect to the innermost proof unit containing a proof node.</Paragraph> <Paragraph position="11"> Rule 3 means that only the conclusions of closed subordinated subproofs still remain in the reader's focus of attention.</Paragraph> <Paragraph position="12"> The textual closeness is used as a measure of the level of focus of an individual reason. In general, the level of focus of an object is established when it is activated, and decreases with the flow of discourse. In Reichman's theory, although four levels of focus can be established upon activation, only one is used in the formulation of the four reference rules. In other words, it suffices to track the status high alone. Therefore, we use only two values to denote the level of focus of individual intermediate conclusions, which is calculated from textual distance between the last mentioning of a reason and the current sentence where the reason is referred to.</Paragraph> <Paragraph position="13"> We assume that each intermediate conclusion is put into high focus when it is presented as a newly derived conclusion or cited as a reason supporting the derivation of another intermediate result. This level of focus decreases, either when a attentional space is moved out of the foreground of discussion, or with the increase of textual distance. The DRCC component of PRO VERB models this behavior with the following four reference rules.</Paragraph> </Section> </Section> <Section position="8" start_page="194" end_page="195" type="metho"> <SectionTitle> Referring Expressions for Reasons </SectionTitle> <Paragraph position="0"> 1. If a reason is both structurally and textually close, it will be omitted.</Paragraph> <Paragraph position="1"> 2. If a reason is structurally close but textually distant, first try to find an implicit form; if impossible, use an explicit form.</Paragraph> <Paragraph position="2"> 3. If a reason is structurally distant but textually close, first try to find an implicit form; if impossible, omit it.</Paragraph> <Paragraph position="3"> 4. An explicit form will be used for reasons that are both structurally and textually far.</Paragraph> <Paragraph position="4"> Note that the result of applying rule 2 and rule 3 depends on the availability of an implicit form, which often interacts with the verbalization of the rest of a PCA, in particular with that of the inference method. Since the reference choice for methods is handled independent of the discourse segmentation (Huang, 1996), however, it is not discussed in this paper.</Paragraph> <Paragraph position="5"> Fourteen PCAs are generated by the macroplanner of PROVERB for our example in Figure 3. The microplanner and the realizer of PROVERB finally produces: Proof: Let F be a group, U be a subgroup of F, 1 and 1u be unit elements of F and U, respectively. According to the definition of unit element, 1v E U. Therefore there is an X, X E U. Now suppose that u is such an X. According to the definition of unit element, u * ltr = u. Since U is a subgroup of F, U C F. Therefore lv E F. Similarly u E F, since u E U. Since F is a group, F is a semigroup. Because u*lv -= u, 1v is a solution of the equation u * X --= u. Since 1 is a unit element of F, u* 1 = u. Since 1 is a unit element of F, 1 E F. Because u E F, 1 is a solution of the equation u * X = u. Since F is a group, 1v = 1 by the uniqueness of solution. Some explanations are in order. PROVERB's microplanner cuts the entire text into three paragraphs, basically mirroring the larger attentional spaces U3, U5 and U6 in Figure 4. Since nodes 22 and 21 are omitted in this verbalization, node 20 (the last sentence) is merged into the paragraph for U6.</Paragraph> <Paragraph position="6"> Let's examine the reference choices in the second last sentence: Because u E F, 1 is a solution of the equation which is actually line 19 in Figure 3 and node 19 in Figure 4. Among the four reason nodes 13, 17, 18, 15, only node 13 is explicitly mentioned, since it is in a closed attentional space (U5) and is mentioned five sentences ago. Node 17 and 18 are in the current space (U6) and was activated only one or two sentence ago, they are therefore omitted. Node 15 is also omitted although also in the same closed space U5, but it was mentioned one sentence after node 13 and is considered as near concerning textual distance.</Paragraph> </Section> class="xml-element"></Paper>