Planning Reference Choices for Argumentative Texts 
Xiaorong Huang* 
Techne Knowledge Systems 
439 University Avenue 
Toronto, Ontario M5S 3G4 
Canada 
xhCFormalSyst ems. ca 
Abstract 
This paper deals with the reference choices in- 
volved in the generation of argumentative text. 
Since a natual segmentation of discourse into 
attentional spaces is needed to carry out this 
task, this paper first proposes an architecture 
for natural language generation that combines 
hierarchical planning and focus-guided naviga- 
tion, a work in its own right. While hierarchi- 
cal planning spans out an attentional hierarchy 
of the discourse produced, local navigation fills 
details into the primitive discourse spaces. The 
usefulness of this architecture actually goes be- 
yond the particular domain of application for 
which it is developed. 
A piece of argumentative text such as the proof 
of a mathematical theorem conveys a sequence 
of derivations. For each step of derivation, the 
premises derived in the previous context and 
the inference method (such as the application 
of a particular theorem or definition) must be 
made clear. Although not restricted to nominal 
phrases, our reference decisions are similar to 
those concerning nominal subsequent referring 
expressions. Based on the work of Reichmann, 
this paper presents a discourse theory that han- 
dles reference choices by taking into account 
both textual distance as well as the attentional 
hierarchy. 
1 Introduction 
This paper describes how reference decisions are 
made in PROVERB, a system that verbalizes 
machine-found natural deduction (ND) proofs. A 
piece of argumentative text such as the proof of a 
mathematical theorem can be viewed as a sequence 
*Much of this research was carried out while the au- 
thor was at Dept. of CS, Univ. of the Saarland, sup- 
ported by DFG (German Research Council). This paper 
was written while the author was a visitor at Dept. of 
CS, Univ. of Toronto, using facilities supported by a 
grant from the Natural Sciences and Engineering Re- 
search Council of Canada. 
of derivations. Each such derivation is realized in 
PROVERB by a proof communicative act (PEA), 
following the viewpoint that language utterances are 
actions. PeAs involve referring phrases that should 
help a reader to unambiguously identify an object of 
a certain type from a pool of candidates. Concretely, 
such references must be made for previously derived 
conclusions used as premises and for the inference 
method used in the current step. 
As an example, let us look at the PeA with the 
name Derive below: 
(Derive Derived-Formula: u * Iv = u 
Reasons : (unit(1u, U, *), u 6U) 
Method : Def-Semigroup*unit) 
Here, the slot Derived-Formula is filled by a new 
conclusion which this PeA aims to convey. It can be 
inferred by applying the filler of Method to the filler 
of Reasons as prernises. There are alternative ways 
of referring to both the Reasons and the Method. 
Depending on the discourse history, the following 
are two of the possible verbalizations: 
1. (inference method omitted): 
"Since 1~ is the unit element of U, and u is 
an element of U, u * lu -- u." 
2. (reasons omitted): 
"According to the definition of unit element, 
u * 1U -- U." 
An explicit reference to a premise or an inference 
method is not restricted to a nominal phrase, as 
opposed to many of the treatments of subsequent 
references found in the literature. Despite this dif- 
ference, the choices to be made here have much in 
common with the choices of subsequent references 
discussed in more general frameworks (Reichman, 
1985; Grosz and Sidner, 1986; Dale, 1992): they 
depend on the availability of the object to be re- 
ferred to in the context and are sensitive to the seg- 
mentation of a context into an attentional hierarchy. 
Therefore, we have first to devise an architecture for 
natural language generation that facilitates a nat- 
ural and effective segmentation of discourse. The 
190 
basic idea is to distinguish between language pro- 
duction activities that effect the global shift of at- 
tention, and language production activities that in- 
volve only local attentional movement. Concretely, 
PROVERB uses an architecture that models text 
generation as a combination of hierarchical planning 
and focus-guided navigation. Following (Grosz and 
Sidner, 1986) we further assume that every posting 
of a new task by the hierarchical planning mecha- 
nism creates new attentional spaces. Based on this 
segmentation, PROVERB makes reference choices 
according to a discourse theory adapted from Reich- 
man (Reichman, 1985; Huang, 1990). 
2 The System PROVERB 
PROVERB is a text planner that verbalizes natural 
deduction (ND) style proofs (Gentzen, 1935). Sev- 
eral similar attempts can be found in previous work. 
The system EXPOUND (Chester, 1976) is an exam- 
ple 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 ar- 
chitecture. A more recent attempt can be found in 
THINKER (Edgar and Pelletier, 1993), which imple- 
ments several interesting but isolated proof presenta- 
tion 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) mod- 
ule of the microplanner enriches the PCAs with ref- 
erence choices. The TSG (Text Structure Genera- 
tor) module subsequently produces the text struc- 
tures 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 macroplan- 
ner and the DRCC component. 
2.1 Architecture of the Macroplanner 
Most current text planners adopt a hierarchical plan- 
ning approach (How, 1988; Moore and Paris, 1989; 
Dale, 1992; Reithinger, 1991). Nevertheless there 
is psychological evidence that language has an un- 
planned, spontaneous aspect as well (Ochs, 1979). 
Based on this observation, Sibun (Sibun, 1990) im- 
plemented 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. 
While a hierarchical planner recursively breaks gen- 
eration tasks into subtasks, local organization navi- 
gates the domain-object following the local focus of 
Natural Deduction Proof 
i- ............................................................ :~lacroplanner 
,, 
: i&p\]An-e; ............ ........................ 
V 
PMs 
7 
................................. L LT_e_x_t_S_t__m_c_t_u_r_ e ............... 
Transformer ) 
(  e ,izo  ) 
Figure 1: Architecture of PROVERB 
attention. 
PROVERB combines both of these approaches 
in a uniform planning framework (Huang, 1994a). 
The hierarchical planning splits the task of present- 
ing 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 es- 
tablished ways of presentation. For trivial proofs 
that demonstrate no characteristic patterns, how- 
ever, 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. 
While most existing systems follow one of the two 
approaches exclusively, PROVERB uses them as 
complementary techniques in an integrated frame- 
work. In this way, our architecture provides a clear 
way of factoring out domain-dependent presenta- 
tion 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 
191 
language production. 
The two kinds of planning operators are treated ac- 
cordingly. Since hierarchical planning operators em- 
body explicit communicative norms, they are given 
a higher priority. Only when none of them is appli- 
cable, will a local navigation operator be chosen. 
2.2 Proof Communicative Acts 
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. 
The simplest one conveying the derivation of a new 
intermediate conclusion is illustrated in the intro- 
duction. There are also PCAs that convey a partial 
plan for further presentation and thereby update the 
reader's global attentional structure. For instance, 
the PCA 
(Begin-Cases Goal : Formula 
Assumptions: (A B)) 
creates two attentional spaces with A and B as the 
assumptions, and Formula as the goal by producing 
the verbalization: 
"To prove Formula, let us consider the two cases 
by assuming A and B." 
2.3 Hierarchical Planning 
Hierarchical planning operators represent commu- 
nicative norms concerning how a proof is to be pre- 
sented can be split into subproofs, how the subproofs 
can be mapped onto some linear order, and how 
primitive subproofs should be conveyed by PCAs. 
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 
F G 
: : : 
?L4 : F V G ~ ?L3 :~ CASE ?L1 :A~-Q 
Figure 2: Proof Schema Case 
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 anM- 
ysis, where we do not go into details. In both circum- 
stances 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. 
Each bar represents a step of derivation, where the for- 
mula beneath the bar is derived from the premises above 
the bar. For the convenience of discussion, some formu- 
lae are given an identifying label, such as ?L1. 
of proofs. This procedure is captured by the plan- 
ning operator below. 
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: "First, let us 
consider the first case by assuming F." 
3. present ?L2 (subgoal 2) 
4. a PCA with the verbalization: "Next, we con- 
sider the second case by assuming G." 
5. present ?L3 (subgoal 3) 
6. mark ?L1 as conveyed 
.features: (hierarchical-planning compulsory im- 
plicit) 
2.4 Planning as Navigation 
The local navigation operators simulate the un- 
planned part of proof presentation. Instead of split- 
ting presentation goals into subgoals, they follow the 
local derivation relation to find a proof step to be 
presented next. 
2.4.1 The Local Focus 
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. Al- 
though 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 ob- 
jects, one will tend to continue to talk about these 
particular objects, before turning to new objects. 
Let us examine the situation when the proof below 
is awaiting presentation. 
\[1\]: 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 do- 
main of application, readers are referred to (McKe- 
own, 1985). 
3 The Attentional Hierarchy 
The distinction between hierarchical planning and 
local navigation leads to a very natural segmentation 
192 
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 
unit(U, lt\], *) :=~ 1 = It\] 
Reason 
(Hyp) 
(Def-subgroup 7) 
(Def-unit 7) 
(::1 9) 
(Hyp) 
(Def-unit 7 11) 
(Def-subset 8 11) 
(Def-subset 8 9) 
(Def-group 7) 
(Def-sohition 12 13 14 15) 
(Def-unit 7 13) 
(Def-unit 7) 
(Def-soluti0n 13 17 18 15) 
(Th-solution 17 16 19) 
(Choice 10 20) 
(Ded 7:21) 
Figure 3: Abstracted Proof about Unit Element of Subgroups 
of a discourse into an attentional hierarchy, since fol- 
lowing the theory of Grosz and Sidner (Grosz and 
Sidner, 1986), there is a one-to-one correspondence 
between the intentional hierarchy and the atten- 
tional 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. 
The definitions of semigroup, group, and unit are 
obvious, solution(a, b, c, F, ,) stands for "c is a so- 
lution of the equation a, z = b in F." 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. 
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. Chil- 
dren of nodes are given in the order they have been 
presented. The circles denote nodes which are first 
2The first 6 lines are definitions and theorems used in 
this proof, which are omitted. 
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 oper- 
ators. For example, attentional space U2 has two 
subordinate spaces U3 and U4. This reflects a natu- 
ral shift of attention between a subproof that de- 
rives 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. Elemen- 
tary attentional spaces are often composed of multi- 
ple 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. 
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. 
-The active attentional space is the innermost 
attentional space that contains the local focus. 
-The controlling attentional space is the inner- 
most proof unit that contains the active atten- 
tional space. 
-precontrol attentional spaces are attentional 
spaces that contain the controlling attentional 
space. 
193 
U4 
U5 ~ U6 
U1 
Figure 4: Proof Tree as Discourse Model 
• Closed spaces are attentional spaces without open 
goals. 
4 A Classification of Reference 
Forms 
A referring expression should help a reader to iden- 
tify an object from a pool of candidates, This sec- 
tion presents a classification of the possible forms 
with which mathematicians refer to conclusions pre- 
viously proved (called reasons) or to methods of in- 
ference available in a domain. 
4.1 Reference Forms for Reasons 
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. 
2. The explicit form: where a reason is literally re- 
peated. 
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 in- 
stance, in the verbalization below 
"Since u is an element in U, u • 1u = u by 
the definition of unit." 
the first reason of the PCA in Section 1, "since 
1v is the unit element of U" is hinted at by the 
inference method which reads "by the definition 
of unit". 
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. 
4.2 Reference Forms for Methods 
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: "by the def- 
inition of unit element", or "by the uniqueness of 
solution." ND rules have usually standard verbal- 
izations. 
2. the omit form: in this case a word such as "thus" 
or "therefore" will be used. 
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. 
5 Reference Choices in PROVERB 
5.1 Referring to Reasons 
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 ac- 
count for this phenomenon , concepts like activat- 
194 
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 Sid- 
net, 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 influ- 
enced by other aspects of human preference. For ex- 
ample, easily perceivable attributes and basic-level 
attributes values are preferred (Dale and Haddock, 
1991; Dale, 1992; Reiter and Dale, 1992). 
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 segmenta- 
tion 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 re- 
ferring to an object using English, namely, by using 
a pronoun, by name, by a description, or implicitly. 
Our theory uses the notions of structural closeness 
and textual closeness, and takes both of these factors 
into account for argumentative discourse. 
5.1.1 Structural Closeness 
The structural closeness of a reason reflects the 
foreground and background character of the inner- 
most attentional space containing it. Reasons that 
may still remain in the focus of attention at the cur- 
rent point from the structural perspective are con- 
sidered 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 con- 
trast, 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. 
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. 
1. Reasons in the active attentional space are struc- 
turally close. 
2. Reasons in the controlling attentional space are 
structurally close. 
3. Reasons in closed attentional spaces: 
(a) reasons that are the root of a closed attentional 
space immediate subordinate to the active at- 
tentional space are structurally close. 
(b) Other reasons in a closed attentional spac e are 
structurally distant. 
4. Reasons in precontrol attentional spaces are struc- 
turally distant. 
Note that the rules are specified with respect to 
the innermost proof unit containing a proof node. 
Rule 3 means that only the conclusions of closed 
subordinated subproofs still remain in the reader's 
focus of attention. 
5.1.2 Textual Closeness 
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 dis- 
course. 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 conclu- 
sions, which is calculated from textual distance be- 
tween the last mentioning of a reason and the current 
sentence where the reason is referred to. 
5.1.3 Reference Rules 
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. 
Referring Expressions for Reasons 
1. If a reason is both structurally and textually close, 
it will be omitted. 
2. If a reason is structurally close but textually dis- 
tant, first try to find an implicit form; if impossi- 
ble, use an explicit form. 
3. If a reason is structurally distant but textually 
close, first try to find an implicit form; if impossi- 
ble, omit it. 
4. An explicit form will be used for reasons that are 
both structurally and textually far. 
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. 
Fourteen PCAs are generated by the macroplanner 
of PROVERB for our example in Figure 3. The 
195 
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, respec- 
tively. According to the definition of unit ele- 
ment, 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 para- 
graphs, 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. 
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 men- 
tioned 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. 
6 Conclusion 
This paper describes the way in which PROVERB 
refers to previouslyderived results while verbalizing 
machine-found proofs. By distinguishing between 
hierarchical planning and focus-guided navigation, 
PROVERB achieves a natural segmentation of con- 
text into an attentional hierarchy. Based on this 
segmentation, PRO VERB makes reference decisions 
according to a discourse theory adapted from Reich- 
man for this special application. 
PROVERB works in a fully automatic way. The 
output texts are close to detailed proofs in text- 
books and are basically accepted by the community 
of automated reasoning. With the increasing size of 
proofs which PROVERB is getting as input, inves- 
tigation is needed both for longer proofs as well as 
for more concise styles. 
Although developed for a specific application, we 
believe the main rationales behind of our system ar- 
chitecture are useful for natural language generation 
in general. Concerning segmentation of discourse, a 
natural segmentation can be easily achieved if we 
could distinguish between language generation ac- 
tivities affecting global structure of attention and 
those only moving the local focus. We believe a 
global attentional hierarchy plays a crucial role in 
choosing reference expressions beyond this particu- 
lar domain of application. Furthermore, it turned 
out to be also important for other generation deci- 
sions, such as paragraph scoping and layout. Finally, 
the combination of hierarchical planning with local 
navigation needs more research as a topic in its own 
right. For many applications, these two techniques 
are a complementary pair. 
Acknowledgment 
Sincere thanks are due to all three anonymous re- 
viewers of ACL/EACL'97, who provided valuable 
comments and constructive suggestions. I would like 
to thank Graeme Hirst as well, who carefully read 
the final version of this paper. 

References 
Chester, Daniel. 1976. The translation of formal 
proofs into English. Artificial Intelligence, 7:178- 
216. 
Dale, Robert. 1992. Generating Referring Expres- 
sions. ACL-MIT PressSeries in Natural Language 
Processing. MIT Press. 
Dale, Robert and Nicholas Haddock. 1991. Con- 
tent determination in the generation of referring 
expressions. Computational Intelligence, 7(4). 
Edgar, Andrew and Francis Jeffry Pelletier. 1993. 
Natural language explanation of natural deduc- 
tion proofs. In Proc. of the first Conference of the 
Pacific Association for Computational Linguistics, 
Vancouver, Canada. Centre for Systems Science, 
Simon Fraser University. 
Gentzen, Gerhard. 1935. Untersuchungen fiber das 
logische SchlieBen I. Math. Zeitschrift, 39:176-210. 
Grosz, Barbara J. and Candace L. Sidner. 1986. At- 
tention, intentions, and the structure of discourse. 
Computational Linguistics, 12(3):175-204. 
Hovy, Eduard H. 1988. Generating Natural Lan- 
guage under Pragmatic Constraints. Lawrence 
Erlbaum Associates, Hillsdale, New Jersey. 
Huang, Xiaorong. 1990. Reference choices in math- 
ematical proofs. In L. C. Aiello, editor, Proc. of 
9th European Conference on Artificial Intelligence, 
pages 720-725. Pitman Publishing. 
Huang, Xiaorong. 1994. Planning argumentative 
texts. In Proc. of COLING-94, pages 329-333, 
Kyoto, Japan. 
Huang, Xiaorong. 1996. Human Oriented Proof 
Presentation: A Reconstructive Approach. Infix, 
Sankt Augustin. 
Huang, Xiaorong and Armin Fiedler 1997. Proof 
Verbalization as an Application of NLG. In Proc. 
of IJCA1-97, Nagoya, Japan, forthcoming. 
Kilger, Anne and Wolfgang Finkler. 1995. Incre- 
mental generation for real-time applications. Re- 
search Report RR-95-11, DFKI, Saarbriicken, Ger- 
many. 
McDonald, David D. 1983. Natural language gen- 
eration as a computational problem. In Brady 
and Berwick: Computational Models of Discourse. 
MIT Press. 
McKeown, Kathleen. 1985. Text Generation. Cam- 
bridge University Press, Cambridge, UK. 
Moore, Johanna and C6cile Paris. 1989. Plan- 
ning text for advisory dialogues. In Proc. 27th 
Annual Meeting of the Association for Compu- 
tational Linguistics, pages 203-211, Vancouver, 
British Columbia. 
Ochs, Elinor. 1979. Planned and unplanned dis- 
course. Syntax and Semantics, 12:51-80. 
Paris, C~cile. 1988. Tailoring object descriptions to 
a user's level of expertise. Computational Linguis- 
tics, 14:64-78. 
Pattabhiraman, T. and Nick Cercone. 1993. 
Decision-theoreticsalience interactions in lan- 
guage generation. In Ruzena Bajcsy, editor, 
Proc. of IJCAI-93, volume 2, pages 1246-1252, 
Chamb~ry, France. Morgan Kaufmann. 
Reichman, Rachel. 1985. Getting Computers to Talk 
Like You and Me. Discourse Context, Focus, and 
Semantics. MIT Press. 
Reiter, Ehud and Robert Dale. 1992. A fast algo- 
rithm for the generation of referring expressions. 
In Proc. of COLING-92, volume 1, pages 232-238. 
Reithinger, Norbert. 1991. Eine parallele Architek- 
tur zur inkrementellen Generierung multimodaler 
Dialogbeitriige. Ph.D. thesis, Universit~t des Saar- 
landes. Also available as book, Infix, Sankt Au- 
gustin, 1991. 
Sibun, Penelope. 1990. The local organization of 
text. In K. McKeown, J. Moore, and S. Niren- 
burg, editors, Proc. of the fifth international nat- 
ural language generation workshop, pages 120-127, 
Dawson, Pennsylvania. 
