Document Structuring à la SDRT
Laurence Danlos
LATTICE – LORIA
U. Paris 7, Case 7003
2, pl. Jussieu
75251 Paris Cedex 05
France
danlos@linguist.jussieu.fr
Bertrand Gaiffe
LORIA
Campus scientifique
BP239
54506 Vandœuvre Cedex
France
gaiffe@loria.fr
Laurent Roussarie
LATTICE
U. Paris 7, Case 7003
2, pl. Jussieu
75251 Paris Cedex 05
France
roussari@linguist.jussieu.fr
Abstract
In this paper, the issue of document
structuring is addressed. To achieve this
task, we advocate that Segmented Dis-
course Representation Theory (SDRT)
is a most expressive discourse frame-
work. Then we sketch a discourse plan-
ning mechanism which aims at pro-
ducing as many paraphrastic document
structures as possible from a set of fac-
tual data encoded into a logical form.
1 Introduction
Using the terms of (Reiter and Dale, 2000), we
consider that the Document Planner architecture
is pipelined: first the content determination task
does its work, and then the document structuring
task takes the result and build a document plan.
Following the work of (Roussarie, 2000), we
adopt SDRT (Asher, 1993; Asher and Lascarides,
1998), which was designed first for text under-
standing, for the document structuring task1.
The input to the document structuring compo-
nent is a set of factual data encoded into a logical
form, as in (1).
(1) a0a2a1a4a3a6a5a7a1a9a8a10a5a12a11a13a5a12a14a16a15a17a1a10a3 –leavea15a18a11a20a19a22a21a23a1a9a8 –fit-of-
tearsa15a18a14a24a19a25a21 causea15a17a1a10a3a26a5a7a1a9a8a27a19a28a21
a11a30a29 Fred a21a30a14a31a29 Mary a21a32a1 a3a34a33a36a35a38a37a26a39 a21a40a1a8a41a33
a35a38a37a26a39 a19
This level of representation is supposed to be
language independent, although we use English-
like predicates for the sake of simplification. (1)
1As far as we know, Roussarie is the first author who has
adopted SDRT for text generation. The work presented here
differs from his work in the following: content determination
and document structuring are pipelined here, while they are
interleaved in his work.
includes a conceptual (language independent) re-
lation, i.e. cause, between the eventsa1a4a3 anda1a9a8 .
A document plan is a SDRS. Our goal is to pro-
duce a wide range of paraphrases from the same
factual data. For example, from the logical for-
m in (1), we want to produce at least all the texts
in (2). These texts have different communicative
structures and so correspond to different commu-
nicative goals. However, these issues will not be
addressed here.
(2) a. Fred left. Therefore, Mary burst into a fit
of tears.
b. Mary burst into a fit of tears because Fred
left.
c. Fred left. His leaving brought Mary into
a fit of tears.
d. Mary burst into a fit of tears. This is due
to Fred’s leaving.
To produce paraphrases, we start by produc-
ing several document plans (i.e. SDRSs) from
the same factual data. The SDRS underlying (2a)
is in (3a) in which the discourse relation Re-
sult between a42 a3 and a42 a8 expresses the predicate
causea15a17a1a10a3a43a5a7a1a27a8a27a19 . The SDRS underlying (2b) is sim-
ilar to (3a) except that Explanationa15a42
a8a44a5
a42
a3a45a19 is in-
volved instead of Resulta15a42 a3a5a42 a8 a19 . The SDRS un-
derlying (2c) is in (3b). It includes the dis-
course relation Commentary2 defined in (Asher,
1993). To ensure the cohesion of texts, we add
the following constraint to his definition: Com-
mentarya15a42 a3a27a5a42 a8a27a19 requires that one element in a42 a8
is coreferent with one element in a42
a3 , as it is the
case in (3b) with a1a27a46a47a29a48a1 a3 . In (3b), the causal
relation has been reified as the discourse referent
f (see section 5). This discourse referent is ex-
2The discourse relation in (2c) is not Result since the
second sentence denotes both the cause and the effect.
pressed through the verb bring into3. The SDRS
underlying (2d) is similar to (3b).
(3) a. a49a51a50a51a49a53a52
a49 a50a38a54
a55
a50a57a56
a56a34a58 Fred
a55
a50 –leavea59a56a53a60
a55
a50a62a61a64a63a66a65a7a67
a49a53a52 a54
a55
a52a69a68
a68a70a58 Mary
a55
a52 –fit-of-tearsa59a68a43a60
a55
a52a71a61a64a63a66a65a7a67
Resulta59a49 a50a12a72a49 a52a73a60
b. a49 a50 a49 a52
a49a51a50 a54
a55
a50a57a56
a56a34a58 Fred
a55
a50 –leavea59a56a53a60
a55
a50 a61a64a63a66a65a7a67
a49 a52a74a54
a55
a52
a55a76a75
a68 f
a68a70a58 Mary
a55
a52 –fit-of-tearsa59a68a43a60
f–causea59a55a75a72a55a52a77a60
a55a76a75
a58
a55
a50
a55
a52 a61a64a63a66a65a7a67
Commentarya59a49 a50a12a72a49 a52a12a60
When provided as input to a “tactical compo-
nent” (microplanner and surface realizer), a given
SDRS leads to zero, one or several texts. It lead-
s to nothing when there is a lexical (or syntac-
tic) gap in the target language. For example, if
there is no verbal predicate semantically equiva-
lent to be due to in the target language, the SDRS
underlying (2d) leads to nothing. Similarly, if a
SDRS includes a discourse relation which cannot
be realized in the target language (e.g. volitional-
Result proposed in (Mann and Thompson, 1987)
cannot be linguistically realized in French (Dan-
los, 2001)), it leads to nothing4. A given SDRS
leads to several texts when there are several lexi-
calizations for at least one predicate.
Thanks to the use of SDRT, we are able to give
a formal background to the following assump-
3In the generation community, causative verbal predi-
cates such as bring into or provoke are considered as elemen-
tary ones, although it should not be so. For example, Elixir
provokes an allergic reaction is not analyzed and so is sim-
ply represented as (allergic-reaction (Elixir)) in (Bouayad-
Agha et al., 2000). Whereas, it should get a representation
translating x’s taking Elixir causes x’s having an allergic re-
action with a causal relation between two events.
4We adopt the position that there exists a set of discourse
relations which are likely to be language independent.
tions generally used in bottom-up document-
structuring approaches:
a78 “The content determination mechanism has
produced a set of messages which are re-
quired to be included in the final document
plan” (Reiter and Dale, 2000, p. 114). In for-
mal terms, it translates as follows: a SDRS
a42 built from a logical form LF is such that
the logical form derived from a42 is logical-
ly equivalent to LF. For example, the logi-
cal forms derived from the SDRSs in (3a) and
(3b) are equivalent to that in (1) modulo ax-
ioms which will be presented in section 4.
a78 “The NLG system has a means of determin-
ing what discourse relation (if any) can be
used to link two particular messages or com-
ponent document plans” (Reiter and Dale,
2000, p. 114). Our formal approach is based
on reversing the SDRT conditions to estab-
lish discourse relations. As an illustration, in
SDRT for text understanding, there is the Ax-
iom in (4) for Narration. This axiom states
that if Narration holds between two SDRSs
a42
a3 and
a42
a8 , then the main event (me) of
a42
a3
happens before the main event ofa42
a8 .
(4) a79 a15 Narrationa15a42 a3a9a5a42 a8a9a19a81a80 mea15a42 a3a45a19 a33 mea15a42 a8a27a19a12a19
For text generation, this axiom is reversed in
the rule in (5) which is domain and language
independent. (5) is taken from (Roussarie,
2000, p. 154).
(5) a78 If a82 and a82a51a83 are DRS the main eventuali-
ties of which are not states,
a78 and if the main event of
a82 occurs before
the main event ofa82 a83,
a78 then Narration
a15
a42
a5
a42a20a83
a19 is a valid relation,
wherea42 anda42 a83 respectively labela82 and
a82a51a83.
This paper is organized as follows. Section 2
gives a crash course in SDRT. Section 3 com-
pares our approach to document structuring to
those based on RST. Section 4 explains the ax-
ioms needed to lay down the logical equivalence
of SDRSs such that (3a) and (3b). Section 5 ex-
plains the process for building SDRSs. Section 6
sketches how to generate a text from a SDRS. Sec-
tion 7 illustrates the document structuring strategy
on examples.
2 Crash course in SDRT
2.1 Introduction
SDRT (Segmented Discourse Representation The-
ory) was introduced in (Asher, 1993) as an ex-
tension of DRT (Discourse Representation Theo-
ry, (Kamp and Reyle, 1993)) in order to account
for specific properties of discourse structure.
The original motivation for developing SDRT
can be found in Asher’s study of the reference
to abstract objects in discourse. Asher argues
that a sound discourse theory has to cope with
some anaphora whose antecedents turn out to be
text segments larger than a clause or a sentence.
Moreover, it is necessary to reveal a hierarchical
discourse structure which makes appear the sites
available for anaphora–antecedent binding. Con-
sider the example in (6) taken from (Asher, 1993,
p. 318):
(6) (1) After 38 months, America is back in s-
pace. (2) The shuttle Discovery roared off the
pad from Cape Kennedy at 10:38 this morn-
ing. (3) The craft and crew performed flaw-
lessly. (4) Later in the day the TDRS shut-
tle communication satellite was successfully
deployed. (5) This has given a much needed
boost to NASA morale.
The pronoun this (6.5) can only refer to the w-
hole trip or (possibly) to the last mentioned event
(TDRS launch). Consequently, the structure of
(6) must be such that : i) there exists a constituen-
t which semantically encompasses the whole s-
tory (6.1–4), and ii) neither (6.2) nor (6.3) cor-
respond to available constituents for the anapho-
ra resolution when computing the attachment of
(6.5) in the context. Avaibility (or openness) of
constituents is a formal property that can be ac-
counted for by the use of discourse relations.
2.2 DRSs as formal discourse units
SDRT can be viewed as a super-layer on DRT
whose expressiveness is enhanced by the use of
discourse relations. Thus the DRT structures (Dis-
course Representation Structures or DRS) are han-
dled as basic discourse units in SDRT.
Formally, a DRS is a couple of sets a84 U,Cona85 .
U (the universe) is the set of discourse referents.
Con is a set of conditions which describe the
meaning of the discourse in a truth-conditional
semantics fashion. For instance, the DRS repre-
senting the sentence (7a) is given in (7b).
(7) a. Fred left.
b. a56 a55
a56a34a58 Fred
a55 –leave
a59a56a53a60
a55
a61a64a63a53a65a86a67
Note that in addition to individual referents (a11 ),
U includes event referents (a1 ). DRT adopts a
Davidsonian approach (Davidson, 1967): it con-
siders that events have to be denoted by singu-
lar terms in the logical form of sentences. In the
semantic model, events are handled as world im-
manent entities, and event referents (a1 ) can occur
in argumental slots of certain predicates (like f-
causea15a17a1a46 a5a7a1a27a8a27a19 in (3b)). The statement a1 –leavea15a18a11a62a19
is a predicative notational variant and stands for
“a1 is a leaving ofa11 ”.
DRSs do not correspond to linguistic categories
but are formal units: from the SDRT point of
view, one should see them as (intensional) mean-
ing structures. This is why some discourse ab-
stract objects (such as facts, situations, proposi-
tions...) can be referred to by discourse referents
(we will say that they are reified) and semantical-
ly characterized by (sub-)DRS. (8) is an example
of a fact reading, where a87 is the characterization
predicate (Asher, 1993, p. 145).
(8) a. The fact that Fred left abruptly upset
Mary.
b. a56a88a68 a55a12a89 f
a56a34a58 Fred
fa90
a55
a55 –leave
a59a56a53a60
abrupta59a55a60
a68a91a58 Mary
a55a76a89–upset
a59fa72a17a68a43a60
2.3 Discourse Relations and SDRSs
A SDRS is a couple of sets a84 U,Cona85 . U is a set of
labels of DRS or SDRS which may be viewed as
“speech act discourse referents” (Asher and Las-
carides, 1998). Con is a set of conditions on la-
bels of the form:
a78
a42a93a92a44a94 , where a42 is a label from U and a94 is a
(S)DRS (labelling);
a78 R
a15
a42a69a95
a5
a42a51a96
a19 , where
a42a24a95 and a42a44a96 are labels and R
a discourse relation (structuring).
The set of SDRT relations includes Narration
(for temporal sequence), Background (for tempo-
ral overlap), Elaboration (for whole-part or topic-
development), Explanation and Result (for cau-
sation), Commentary (for gloss).
According to (Asher, 1993, p. 319), (9) sketch-
es the SDR-theoretic analysis of (6) where eacha82a4a95
stands for the DRS representing the content of the
a97 th sentence in (6).
(9) a49 a50 a49 a89
a50 a49a53a98
a49 a50a62a54a6a99a26a50
a49
a89
a50 a54
a49 a52 a49
a75
a49a4a100
a49 a52a74a54a6a99a9a52 a49
a75
a54a6a99
a75
a49a4a100 a54a45a99a100
Commentarya59a49 a52a86a72a49
a75
a60
Narrationa59a49a53a52a72a49 a100a60
Elaborationa59a49a51a50a72a49 a89a50a60
a49a53a98 a54a6a99a98 Commentarya59a49 a50a76a72a49a53a98a60
SDRSs are built by means of non monotonic
rules that encodes discourse properties and world
knowledge. For instance, one rule states that if
a discourse constituent a101 may be connected to a
discourse constituent a102 in the context, then nor-
mally the relation Narrationa15a102 a5a101 a19 holds. Anoth-
er rule states that ifa101 may be connected to a102 and
if the main event of a101 , i.e. mea15a101 a19 , is known as a
cause of mea15a102 a19 , then normally the relation Expla-
nationa15a102 a5a101 a19 holds.
3 Comparison with RST
As nearly everybody in the NLG community us-
es RST (Rhetorical Structure Theory, (Mann and
Thompson, 1987)) as a discourse framework, it
is generally considered that the task of document
structuring is to produce a tree in the RST style.
Since RST is a descriptive theory without any
formal background, there exists a wide range of
interpretations and several notions of Rhetorical
Structure. For some authors, e.g. (Marcu et al.,
2000), the Rhetorical Structure is very surfacic:
it is an ordered tree isomorphic to the linearized
structure of the text and a rhetorical relation can
be viewed as a nickname for a small set of cue
phrases. For other authors, the rhetorical structure
is more abstract: it aims at representing meaning.
For example, in (RAGS Project, 1999; Bouayad-
Agha et al., 2000), the Rhetorical Structure is an
unordered tree in which terminal nodes represen-
t elementary propositions, while non terminal n-
odes represent rhetorical relations which are ab-
stract relations such as cause. This rhetorical rep-
resentation is mapped into a Document Represen-
tation which is an ordered tree reflecting the sur-
facic structure of the text.
Our approach is closer to the RAGS’one if we
consider our logical form as equivalent to their
Rhetorical Structures. However, we differ ba-
sically on the following point: their Rhetorical
Structure is a tree, while our logical form, when
graphically represented, is a (connex) graph and
not a tree. Let us justify our position by consider-
ing the discourses in (10).
(10) a. Fred run the vacuum cleanera103 while Sue
was sleepinga104 in order to bother hera105 .
b. Fred run the vacuum cleanera103 while Sue
was sleepinga104 in order to please hera105 .
They can be given various meanings, however
we focus on the following:
a78 for (10a), running the vacuum cleaner is sup-
posed to be noisy and Fred attempts to both-
er Sue by making something noisy exactly
when she is sleeping,
a78 for (10b), running the vacuum cleaner is sup-
posed to be an awful chore and Fred attempts
to please Sue by relieving her of a chore. It
just happens that he run the vacuum cleaner
while she was sleeping.
In RST, both (10a) and (10b) are given the tree
representation in (11), in which CIRC abbreviates
CIRCUMSTANCE.
(11) CIRC a106
a107 a108
N S
SN
PURPOSE
The semantic interpretation of a rhetorical tree
is given by the “nuclearity principle” (Marcu,
1996): whenever two large spans are connected
through a rhetorical relation, that rhetorical rela-
tion holds also between the most important part-
s of the constituent spans. In (11), the nucleari-
ty principle amounts to saying that there is only
one interpretation, namely that in which the nu-
cleus argument of PURPOSE is a109 , which is the
nucleus argument of CIRCUMSTANCE. This is the
right interpretation for (10b). However, (11) can-
not represent the meaning of (10a) for which the
first (nucleus) argument of PURPOSE is the sub-
tree rooted at CIRCUMSTANCE. In conclusion, a
RST tree structure is too poor: it cannot account
for the expressiveness of texts. This can be ac-
counted for by the use of representations which
correspond graphically to (connex) graphs. The
graphical representations of (10a) and (10b) and
their equivalent in pseudo logical forms are re-
spectively shown in (12a) and (12b)5.
(12) a. PURPOSE
1 2
a110a111
a112
CIRC
a113 a114
a109 a115
a116a118a117
a119a88a120 a121
a122a20a123
a72a17a124a125a72a127a126a74a72a129a128 a59a128 –CIRCa59
a123
a72a129a124a88a60a44a130 PURPOSEa59a128a131a72a132a126a25a60a17a60
b. PURPOSE CIRC
2 1 1 2
a121 a109 a115
a122a20a123
a72a17a124a125a72a127a126 a59 CIRCa59
a123
a72a129a124a88a60a53a130 PURPOSEa59
a123
a72a129a126a25a60a17a60
(12a) is a tree in which the first argument of
PURPOSE is
a120
, the sub-tree rooted at CIRCUM-
STANCE. It is the interpretation of the RST tree
in (11) without the nuclearity principle. (12b) is
a graph in whicha109 is part of two relations6. This
graph corresponds to the interpretation of the RST
tree in (11) given by the nuclearity principle. This
principle makes that a109 is part of both the rela-
tion PURPOSE with a121 and the relation CIRCUM-
STANCE with its satellitea115 .
The SDRSs underlying (10a) and (10b) are
shown respectively in (13a) and (13b) (the nota-
tion a94a64a103 stands for the DRS representing a109 and
so on). Here we replace CIRCUMSTANCE by the
SDRT relation Background for temporal overlap7.
5The arguments of a binary semantic predicate are noted
as 1 and 2 after the fashion of MTT (Meaning to Text Theory,
(Mel’ˇcuk, 1988)) and not as Nucleus and Satellite in the RST
tradition.
6This graph can be annotated to mark the element(s)
which are focused on.
7Actually, the SDR-theoretical representations of (13)
should be more complex with a pseudo-topic that would s-
(13) a. a49 a75 a49a4a100
a49
a75
a54
a49a51a50a57a49a53a52
a49a51a50 a54a134a133a2a135 a49a53a52 a54a134a133a125a136
Backgrounda59a49 a50a76a72a49 a52a12a60
a49a4a100 a54a6a133a125a137
Purposea59a49
a75
a72a49a4a100a60
b. a49a51a50a57a49a53a52a69a49 a75
a49 a50a38a54a6a133 a135 a49 a52a71a54a134a133 a136 a49
a75
a54a134a133a125a137
Backgrounda59a49a51a50a72a49a4a52a60
Purposea59a49 a50a12a72a49 a75a60
In (13a), the first argument of Purpose is a42
a46
which groups a94 a103 and a94 a104 which are linked
through Background. In (13b), a42 a3 is part of t-
wo discourse relations. The graphical represen-
tations of (13a) and (13b) (in which Ra15a42 a3a134a5a42 a8a27a19 is
represented as a tree rooted at R) have the same
topology as (12a) and (12b) respectively.
In summary, in document structuring ap-
proaches based on RST, a rhetorical structure is
always a tree, whenever understood as abstract
representation or a more surfacic one. This cannot
be maintained. First, if the rhetorical structure is
an abstract conceptual representation closed to a
logical form, its graphical representation is a con-
nex graph (and not always a tree). Second, if the
rhetorical structure is a discourse representation,
as it is the case for SDRS, its graphical represen-
tation is also a connex graph.
This criticism is not the only one against RST.
This discourse framework has already been criti-
cized in the generation community (de Smedt et
al., 1996). So we advocate the use of SDRT. This
theory presents the following advantages :
a78 it is a formalized theory which benefits of al-
l the progress in formal semantics most of-
ten realized in the understanding perspective
around DRT or SDRT.
a78 adopting SDRT for text generation by “re-
versing” the rules (see (4) reversed in (5)) al-
lows us to have reversible systems: the same
linguistic data can be used for both text un-
derstanding and generation.
a78 as it will be shown in section 5, the document
structuring component à la SDRT gives hint
on referring expressions: it indicates when a
pan the Background-related constituents. See (Asher and
Lascarides, 1998) for details.
discourse referent should be expressed as an
anaphoric NP.
a78 a SDRS (i.e. a document plan) can be given
to existing microplanners and surface real-
izers with perhaps some modifications (see
section 6). For example, a SDRS can be giv-
en as input to G-TAG (Danlos, 2000) imple-
mented in CLEF (Meunier and Reyes, 1999)
provided small fits are realized.
In conclusion, we think that SDRT is a better
discourse framework than RST (for both text gen-
eration and understanding).
4 Equivalence between logical forms
Recall that we want to compute both the SDRS in
(3a) with Result and the SDRS in (3b) with Com-
mentary from the logical form in (1). Let us show
that the logical forms derived from these SDRSs
are equivalent. In SDRT, there is an axiom for Re-
sult from which one can entail the rule in (14),
which is similar to the axiom in (4) for Narration.
(14) Resulta15a42 a3a9a5a42 a8a9a19a81a80 causea15a18a138a139a1a44a15a42 a3a45a19a86a5a12a138a139a1a44a15a42 a8a43a19a12a19
Therefore, the logical form derived from (3a)
is (1) repeated in (15) without the temporal infor-
mation.
(15) a0a2a1 a3a5a7a1a8 a5a12a11a13a5a12a14a16a15a17a1 a3 –leavea15a18a11a20a19a22a21a23a1a8 –fit-of-
tearsa15a18a14a24a19a25a21 causea15a17a1a10a3a26a5a7a1a9a8a27a19a28a21
a11a30a29 Fred a21a30a14a31a29 Marya19
The discourse relation Commentary per se
does not add information. Therefore, the logical
form derived from (3b) is (16).
(16) a0a2a1a4a3a6a5a7a1a9a8a10a5 fa5a12a11a71a5a12a14a140a15a17a1a10a3 –leavea15a18a11a62a19a38a21
a1a27a8 –fit-of-tearsa15a18a14a24a19a62a21 f–causea15a17a1a4a3a9a5a7a1a9a8a27a19a38a21a28a11a30a29
Freda21a140a14a141a29 Marya19
The difference between (15) and (16) consists
in considering the causal relation between the two
events either as only a predicate or as a variable
plus a predicate. However, the axioms in (17a)
and (17b) can be laid down. With these axioms,
(15) and (16) are equivalent since they are both e-
quivalent to (18), in which the causal relation gets
represented twice. In other words, we have the
following logical entailments: (15), (17a) a142 (18),
and (16), (17b) a142 (18).
(17) a. a143 a11a13a5a12a14 causea15a18a11a13a5a12a14a24a19a88a80a144a0a146a145a147a145 –causea15a18a11a71a5a12a14a146a19
b. a143 a11a13a5a12a14a148a5a76a145a131a145 –causea15a18a11a13a5a12a14a24a19a81a80 causea15a18a11a13a5a12a14a24a19
(18) a0a2a1a10a3a6a5a7a1a9a8a10a5 fa5a12a11a13a5a12a14a140a15a17a1a4a3 –leavea15a18a11a20a19a38a21
a1a9a8 –fit-of-tearsa15a18a14a146a19a62a21 f–causea15a17a1a4a3a9a5a7a1a9a8a27a19a38a21
causea15a17a1a10a3a9a5a7a1a27a8a27a19a62a21a28a11a16a29 Freda21a28a14a31a29 Marya19
Let us underline that the content determination
task may arbitrarily result in (15), (16) or even
(18). Therefore, the document structuring task
has to produce SDRS such as (3a) and (3b) from
one of these logical forms.
There is a an important difference between
SDRSs and logical forms. SDRSs represent dis-
courses and their variables are discourse refer-
ents. Logical forms represent meanings and their
variables are pure logical variables. To compute
a SDRS from a logical form, one has to decide
which variables from the logical form become
discourse referents, as explained in the next sec-
tion.
5 Building SDRSs
5.1 Basic principles
To get a recursive process, first, we translate the
logical form into a DRS8. In case of a purely exis-
tential formula such as those we have been deal-
ing with so far, this just amounts to putting all the
variables into the universe of the DRS and split
the formula into elementary conjoined condition-
s9. The document structuring task amounts then
in building a SDRS from a DRS. The simplest way
to do that is simply to transform :
universe
conditions into
a49
a49 :
universe
conditions
.
More complex structures are obtained by split-
ting the DRS into sub-DRSs as illustrated below.
8This DRS is considered as a logical representation. It is
not yet a discourse representation.
9More complex formulas are not considered here.
universe
conditiona50
conditiona52
conditiona75
conditiona100
conditiona98
conditiona149
conditiona150
a151a10a152
a49 a50 a49 a52 a49
a75
a49a51a50 :
universea50
conditiona50
conditiona150
a49 a52 :
universea52
conditiona52
conditiona98
a49
a75 :
universea75
conditiona100
a153
a50a59a49 a50a73a72a49 a52a12a60a57a154 condition
a75
a153
a52a59a49a53a52a72a49
a75
a60a57a154 conditiona149
a155 a3a27a15
a42
a3a9a5
a42
a8a27a19a41a156 conditiona46 means that the dis-
course relation a155 a3 to be established between a42 a3
and a42 a8 must have conditiona46 among its conse-
quences: no other element is in charge of express-
ing conditiona46 .
In SDRT for text understanding, the condition-
s are not ordered. However, in text generation, a
document plan indicates the order of its compo-
nents. As a consequence, when a document plan
is a SDRS, its components (labelleda42a24a95 ) have to be
ordered. In the pseudo SDRS above, it is supposed
thata42 a3 precedesa42 a8 which precedesa42 a46 .
Let us examine the principles governing the s-
plitting of the conditions and the universes. For
the splitting of the conditions, the whole con-
tent of the factual database has to be verbalized.
Therefore all the conditions in the DRS have to be
expressed in the SDRS. Two cases appear:
a78 either a condition in the DRS appears as a
condition in one of the sub-DRS; that is the
case fora157a37a43a35a38a158 a97a129a159a77a97a37a26a35 a3 in the DRS labelleda42 a3 ;
a78 or it is expressed through a discourse rela-
tion; that is the case for a157a37a26a35a38a158 a97a127a159a132a97a37a26a35 a46 . One of
the criteria for choosing an appropriate dis-
course relation is that its consequences have
to contain the condition involved. For ex-
ample, the condition causea15a17a1a10a3a9a5a7a1a9a8a27a19 can be ex-
pressed through Resulta15a42 a3a9a5a42 a8a27a19 whena42 a3 and
a42
a8 label the sub-DRSs that contain the de-
scriptions ofa1a10a3 anda1a9a8 respectively.
Let us now look on how to determine the uni-
verses of the sub-DRSs, i.e. the discourse refer-
ents. First, there are technical constraints, name-
ly:
a78 the arguments of any condition in a sub-DRS
must appear in the universe of this DRS;
a78 the universes of all the sub-DRSs have to be
disjoint. This constraint is the counterpart
of the following constraint in understanding:
“partial DRSs introduce new discourse refer-
ents” (Asher, 1993, p. 71).
These two constraints are not independent. As-
suming that the first constraint is respected, the
second one can be respected with the following
mechanism: if a variable a11 already appears in a
preceding sub-DRS labelled a42a24a160 , then a brand new
variablea14 is created in the universe of the curren-
t sub-DRS labelled a42a24a161 and the condition a14a162a29a163a11
is added into the conditions of a42a69a161 . The discourse
referent a14 will be generated as an anaphora if a42a24a160
is available to a42a69a161 (see section 2.1), otherwise it
will be generated as a definite or demonstrative
NP.
Secondly, as mentioned in section 4, it has
to be decided which variables become dis-
course referents. When we have for instance
a0 fa5a7a1 a3a5a7a1a8 f–causea15a17a1 a3a5a7a1a8 a19 , we can decide to apply
axiom (17b), and then remove the variable f and
every condition having f as an argument (in par-
ticular the condition f–causea15a17a1a10a3a9a5a7a1a27a8a27a19 ). In order for
such an operation to be valid, we have to ensure
that no information is lost. In practice, this sup-
poses that no other condition than f–causea15a17a1a4a3a9a5a7a1a9a8a27a19
has f as an argument. We call this operation de-
reification. Conversely from such a formula as
a0a146a1a4a3a6a5a7a1a9a8 causea15a17a1a10a3a43a5a7a1a9a8a27a19 , we can apply axiom (17a),
and then remove the condition causea15a17a1a4a3a9a5a7a1a9a8a27a19 . We
call this operation reification. Contrarily to de-
reification, no information can be lost. These two
operation are a mix between something which is
pure logic (that adds information) and a discourse
operation that deals with discourse referents. As
our objective is to build as much dicourse plans
as possible, reification and de-reification are sys-
tematically performed whenever possible.
The process is recursive: once all this is done
(splitting the conditions, universes determina-
tion (including reification and de-reification) and
choice of discourse relations), the process can ap-
ply recursively on each of the embedded DRSs
(this is the reason why the logical form is first
translated into a DRS).
5.2 Algorithm
A naive solution to implement these principles
will be first described. Next some refinements
will be proposed.
The naive solution amounts to considering all
the possible splittings of the set of conditions. If
there are a35 conditions, the number of sub-SDRSs
ranks from a113 toa35 . In the hypothesis of a splitting
into a164 sub-SDRSs, each condition may be put in
any of thea164 sub-SDRSs or in any of thea164a166a165 a113 sets
of conditions to be expressed by a discourse re-
lation10. Next the universes of the sub-SDRSs are
built according to the principles described above.
This leads to availability constraints (e.g. a42a69a160 is
available toa42a69a161 ) to be checked later on. In the nex-
t step, the possible discourse relations are com-
puted according to their consequences. At this
step, a lot of hypotheses are ruled out. For ex-
ample, any hypothesis assuming that a condition
such as a1 –leavea15a18a11a71a5a12a14a146a19 is to be expressed through
a discourse relation will be ruled out. Finally, the
availability constraints have to be checked using
the same rules as in understanding.
With this naive solution, a lot of documen-
t plans will be rejected by the linguistic compo-
nent. As an illustration, each sub-SDRS has to be
verbalized as a clause (see section 6). Therefore,
any sub-SDRS that does not include an eventuality
or a fact will be rejected by the linguistic compo-
nent.
This naive solution is theoretically valid, how-
ever it is not usable in practice. A lot of possible
failures can be foreseen. For example, the con-
ditions that can be expressed through a discourse
relation, e.g. causea15a17a1 a3a5a7a1 a8 a19 , should be considered
first. If it is decided that such a condition is in-
deed expressed by a discourse relation, e.g. Re-
sulta15a42 a3a27a5a42 a8a6a19 , then the sub-SDRSs a42 a3 and a42 a8 are
created with the conditions concerning a1a4a3 and a1a27a8
respectively.
To sum up, the process of splitting the condi-
tions should not be blind. The content of the con-
ditions has to be taken into account in order to
guide the splitting and avoid thereby failures that
can be foreseen. However, the details of this opti-
mization will not be presented here.
10In SDRT, any element in the universe of a SDRS must
be linked to another element. Therefore, a SDRS witha167 sub-
SDRSs must include (at least)a167 a151a140a168 discourse relations.
6 Generating a text from a SDRS
A SDRS, i.e. a document plan, is given to a micro-
planner and surface realizer which computes one
or several texts. It is the topic of another paper to
explain in detail this process. Here we will only
give the basic principles which guide the choices
to be made in the tactical component.
The process to generate a text from a SDRS
a84 U,Cona85 is basically recursive:
a78 an element
a42a69a95 in U has to be generated as
a clause if a42 a95 labels a DRS and recursively
as a text (possibly a complex sentence) if a42a69a95
labels a SDRS.
a78 a condition R
a15
a42a69a95
a5
a42a51a96
a19 in Con has to be gener-
ated as a text “a169 a95a77a170 a121a41a171 a1 a169 a96a4a170” or as a complex
sentence “a169a148a95 a121a172a171 a1 a169a146a96 a170”, where a169a148a95 generates
a42a24a95 , a169a146a96a70a42a44a96 , and a121a172a171
a1 is a cue phrase lexicaliz-
ing R (a121a172a171 a1 may be empty).
a78 a condition
a42a93a92a57a94 in Con where a94 is a DRS
a84 U,Cona85 has to generated as a clause accord-
ing to the following constraints:
– in analysis, a discourse referent is the
trace of either a determiner or an in-
flexion mark. Therefore, in generation,
a discourse referent has to be generat-
ed as an NP or a tensed verb (noted
V). Such an information is noted as e.g.
a1 a3 :NP/V;
– the conditions guide the lexical choic-
es. The conditions a11a173a29 Fred corre-
spond to proper names which is noted
asa11 :PN[Fred]. The equality conditions
between discourse referents (e.g. a11a174a29
a14 ) give rise to (pronominal or nominal)
anaphora which is noted as a11 :ANA[a14 ].
The other conditions are associated to
lexical predicates.
With these constraints, an element which is
reified, e.g. f–causea15a17a1a10a3a9a5a7a1a27a8a27a19 , gives rise to an
NP or a verb (a cause of, provoke) and an ele-
ment which is not reified, e.g. causea15a17a1a10a3a9a5a7a1a27a8a27a19 ,
gives rise to a modifier on a1 a3 or a1 a8 with a1 a3
anda1a27a8 generated either as verbs or NPs.
This process results in a list such as:
– a1a10a3 :NP/V[a1a10a3 –leave(a11 )],
– a11 :PN[Fred(a11 )],
– f:NP/V[f–cause(a1a10a3 , a1a9a8 )],
– a1a9a8 :NP/V[a1a27a8 –fit-of-tears(a14 )],
– a14 :PN[Mary(a14 )].
Such a list guides the lexical choices
and syntactic realization performed by the
micro-planner.
7 Illustration on examples
Let us show how to compute the SDRSs in (3a)
and (3b) from the logical form in (1). First, this
formula is translated in the DRS in (19), in which
the conditions are numbered for the sake of con-
venience.
(19) a55a50 a55a52 a56a175a68
conda50 : a55a50 –leavea59a56a53a60
conda52 : a55a52 –fit-of-tearsa59a68a26a60
conda75 : causea59
a55
a50a12a72
a55
a52a73a60
conda100 :a56a34a58 Fred
conda98 :a68a70a58 Mary
conda149 : a55a50a38a61a64a63a66a65a7a67
conda150 : a55a52 a61a64a63a66a65a7a67
From (19), one possibility is to express conda46
through Resulta15a42 a3a9a5a42 a8a9a19 in which a42 a3 and a42 a8 label
the sub-DRSs grouping the conditions on a1a10a3 and
a1a9a8 respectively. Therefore,
a42
a3 has to group conda3
and conda176 . As conda3 introduces the variable a11 ,
conda177 has to figure also in a42 a3 11. The universe
of the DRS labelled by a42 a3 is a178 a1a4a3a9a5a12a11a38a179 . Similar-
ly for a42 a8 , its universe is a178 a1a9a8a10a5a12a14a180a179 , its conditions
are conda8 , conda181 and conda182 . All the conditions
of (19) are therefore expressed in (3a) which is a
well-formed document plan. Following the rules
sketched in section 6, (3a) will be generated in
(2a) by the linguistic component, if Result is lex-
icalized as the cue phrase therefore which links
two sentences.
From (19), another possibility is to split all the
conditions into two sub-DRSs: the first one la-
belleda42
a3 grouping the conditions ona1a4a3 (as in the
previous possibility), the second one labelled a42 a8
grouping all the other conditions. conda46 ina42 a8 has
a1a10a3 as argument. This variable already appears in
a42
a3 . Therefore a brand new variable a1a46 is created
in the universe of a42
a8 and the condition a1 a46 a29a183a1a4a3
11This is an optimization: if cond
a100 were not included in
a49a51a50 , the surface realizer would fail ona49a51a50 and the hypothesis
would be ruled out.
is added ina42 a8 . As all the conditions are split into
the sub-DRSs, a42 a3 and a42 a8 have to be linked with a
discourse relation which adds no information (i.e.
which has no consequence). Commentary is such
a discourse relation, and it is valid here since its
constraint (one element ina42 a8 has to be coreferent
with one element in a42 a3 , see section 1) is respect-
ed with the coreference relation a1 a46 a29a184a1a4a3 . At this
step, the SDRS in (20) has been built.
From (20), one possibility is to transmit this
SDRS as it is to the tactical component. If Com-
mentary is lexicalized as an empty cue phrase
linking two sentences, (20) will be generated in
(21) where causea15a17a1a46 a5a7a1a27a8a27a19 , which is not reified, is
expressed through the modifier because of.
(20) a49 a50 a49 a52
a49a44a50 a54
a55
a50a51a56
a56a34a58 Fred
a55
a50 –leavea59a56a53a60
a55
a50a38a61a64a63a53a65a86a67
a49 a52a185a54
a55
a52
a55a76a75
a68
a68a91a58 Mary
a55
a52 –fit-of-tearsa59a68a43a60
causea59a55a75a72a55a52a12a60
a55a7a75
a58
a55
a50
a55
a52 a61a64a63a53a65a86a67
Commentarya59a49 a50a12a72a49 a52a73a60
(21) Fred left. Mary burst into a fit of tears be-
cause of that.
In text understanding, (21) is likely to
be analyzed with the discourse relation
Narrationa15a42 a3a9a5a42 a8a27a19 , which has for consequence
a1a4a3 a33 a1a27a8 . This condition is compatible with those
in a42
a8 since causea15a17a1 a46 a5a7a1a9a8a27a19 with a1a46 a29a186a1a4a3 implies
a1 a3a187a33 a1 a8 . So, there is no conflict between the
understanding and the generation of (21).
From (20), another possibility is to reify
causea15a17a1a9a46a10a5a7a1a8 a19 in a42 a8 . The SDRS in (20) becomes
that in (3b). If f–cause is lexicalized as bring in-
to (a colloquial variant of cause when the second
argument is a fit of tears), (2c) will be generated.
8 Conclusion
We have dealt with the document structuring task,
considering that it should be able to produce sev-
eral outputs so that it can cope, among other
things, with real lexical gaps in the target lan-
guage (and also actual gaps in a realistic surface
realizer). We therefore aim at producing as much
document plans as possible.
We suppose that the content determination
component provides a logical form encoding the
factual data to be linguistically verbalized. Ax-
ioms may apply on this logical form which en-
able reifications and de-reifications. As a conse-
quence, some predicates may be realized either as
a verb, an NP or a modifier.
The document structuring component is based
on SDRT, a formalized discourse framework
which can account for the expressiveness of texts,
contrarily to RST. A document plan is a SDRS.
This level of representation is likely to be lan-
guage and domain independent and can be pro-
vided to existing surface realizers. Building
SDRSs from a logical form is a recursive process
for which a basic strategy has been presented and
exemplified.
No implementation has been realized yet, how-
ever we foresee to do it and to interface it with the
tactical component CLEF (Meunier and Reyes,
1999).

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