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    From Dialogue Acts to Dialogue Act Offers: Building Discourse
               Structure as an Argumentative Process
                       J¨rn Kreutel                                        Colin Matheson
                       SemanticEdge                                   Language Technology Group
                           Berlin                                       University of Edinburgh
              joern.kreutel@semanticedge.com                            colin.matheson@ed.ac.uk

                       Abstract                                  mance of a speech act means raising validity claims
Based on the Theory of Communicative Action de-                  that are ‘open to criticism and designed for inter-
veloped by J¨rgen Habermas we propose to analyse
             u                                                   subjective recognition’ (see Habermas (1991)).
the actions of participants in a dialogue in terms of               Habermas assumes that each speech act raises
dialogue act offers that raise validity claims                   the four universal claims of understandability,
to be evaluated by the addressee of a move. We                   propositional truth, normative rightness and ex-
argue that this approach allows us to model dis-                 pressive truthfulness,2 and proposes to classify
putes and misunderstandings in conversations in a                speech acts depending on which is the major claim.
way that minimises revisions of discourse structure              The main debates about his assumptions have fo-
and reconstructs the process of reaching agreement               cussed on this typology, the universality claim (see
in a more natural way than current formal dialogue               for example Goldkuhl (2000)), and on the question
theories.                                                        of whether intention-based approaches to rational
                                                                 interaction or Habermas’ radically intersubjectivist
1    Introduction                                                theory prove to be more powerful and explanatorily
                                                                 adequate (Skjei (1985), Harnad (1991), Dietz and
In the ‘Theory of Communicative Action’ (Haber-                  Widdershoven (1991)).
mas, 1981) J¨rgen Habermas provides an account                      In this paper we want to focus on one aspect
of speech acts that both elaborates and revises John             of Habermas’ analysis that tends to be neglected
Searle’s proposals in Searle (1969). On the one hand,            as it can be considered a minor issue or a mat-
Habermas strengthens the intersubjectivist view of               ter of linguistic expression.3 Throughout his work,
Searle in emphasising that the illocutionary force of            Habermas tends to use the term speech act offer
an utterance can primarily be determined in a con-               (‘Sprechaktangebot’) rather than speech act, thus
ventionalised way on the basis of what has been said             underlining the fact that the contributions of dia-
in a given discourse context and does not require rea-           logue participants (DPs) should be seen as ‘offers’
soning over the intentions of a particular speaker.1             which may then be accepted, (partially) rejected,
On the other hand, he introduces the concept of va-              replied to with a counteroffer, and so on. Dialogue
lidity claims as an alternative to Searle’s notion of            thus is analysed as a genuinely argumentative pro-
acceptability conditions for speech acts. Habermas               cess, where argumentation may take place about
argues that acceptability conditions alone lack an in-           the propositional content of an utterance as well as
tersubjective, ‘pragmatic’, dimension and therefore              about the illocutionary act it is intended to perform.
are not sufficient to reconstruct the orientation to-              We think that this view of dialogue can be very use-
wards mutual agreement as the primary and funda-                 ful in resolving some problems which current formal
mental purpose of language use. A successful in-                 dialogue theories have in analysing all kinds of dis-
teraction essentially requires that the participants             putes, or cases of misunderstanding. We therefore
implicitly or explicitly accept or reject each other’s           propose to analyse dialogue structure, both at the
contributions by making judgements about whether                 level of common ground (see Clark and Wilkes-Gibbs
the conditions for their successful performance are              (1986), Poesio and Traum (1998)) and at the level of
satisfied or violated. What drives the dialogue for-              the individual participants’ point of view, as some-
ward is exactly this process of a speaker raising the            thing that emerges out of the argumentative process
satisfaction of acceptability conditions as an issue             in which DPs a priori engage. According to this
pending evaluation by the addressee, and it is the
                                                                    2 We do not address the claim for understandability (of
notion of validity claims that incorporates this anal-
ysis in the definition of a speech act itself: perfor-            linguistic content) in this paper. The other three claims are
                                                                 discussed in more detail in section 3.1 below.
   1 From this it follows that Habermas must consider indirect      3 See, for example, the argument against Habermas’ use of

speech acts as non-standard uses of language.                    validity claims in Skjei (1985).

Bos, Foster & Matheson (eds): Proceedings of the sixth workshop on the semantics and pragmatics of dialogue (EDILOG 2002),
4-6 September 2002, Edinburgh, UK, Pages 85-92.
86                                               Proceedings of EDILOG 2002

view, the interpretations of the DPs’ contributions            DPs themselves, this interpretation is plausible if
will always be seen as preliminary, as ‘speech act             one assumes that A does not know where the secret
offers’, unless the respective addressees have made             valley is located. However, we argue that this inter-
their evaluation evident.                                      pretation strategy not only neglects B’s assumptions
   We first discuss the problems existing theories              about B[2] for the given dialogue step, but also if we
have in analysing conflictive situations in dialogue.           generalise it for the whole dialogue it corresponds to
We then outline the basics of what a formalisation of          a conception of the interpreter as an omniscient ob-
the interpretation process in our model would look             server. This approach is not problematic if one sees
like, and illustrate our proposals with an example             the purpose of a dialogue theory as providing a con-
analysis.                                                      sistent interpretation of the DPs’ actions in terms of
                                                               truth conditional semantics. However, if in addition
2     Disagreements in Dialogue                                the theory is meant to reconstruct the point of view
In this section we will address some of the prob-              of an actual third party observer (not to mention
lems that current formal dialogue theories face in             the DPs’ views), interpretation rules such as those
dealing with situations where there is a mismatch              proposed by Asher and Lascarides seem to be inap-
of the DPs’ opinions with respect to the content               propriate.
of their actions. In particular, we will refer to the             As far as alternative analyses of examples like (1)
way these cases are dealt with in Segmented Dis-               are concerned, Kreutel and Matheson, who use in-
course Representation Theory (SDRT), developed                 formation states5 as developed on the TRINDI6
by Asher and Lascarides.4 SDRT is a framework for              project, would interpret B’s move B[2] as answer,
analysing discourse that has proven very successful            irrespective of A’s belief state, and would keep this
in the analysis of the interdependencies between lin-          interpretation in the common ground as the dia-
guistic content and discourse structure, for which the         logue proceeds, even after A’s actual response in
theory employs a modularised approach which keeps              A[3]. This account corresponds to a rather lax no-
reasoning over information content logically distinct          tion of ‘answerhood’, which is merely seen as ‘a DP’s
from reasoning over discourse structure. However,              attempt to provide a felicitous answer’. It therefore
in the change of emphasis from monologue to dia-               cannot provide a fine-grained semantic analysis of
logue (Asher and Lascarides (1998), Asher and Las-             answers in dialogue, which is a clear strength of the
carides (2001)), the theory exhibits some shortcom-            SDRT model.
ings which, we argue, are manifested in the way ac-            2.2 Building Discourse Structure
tions which are characterised by an explicit or im-            In recent, as yet unpublished, proposals for
plicit disagreement between the DPs’ points of view            analysing disputes in dialogue (Asher, 2002), Asher
are dealt with. We will attempt to illustrate how              and Lascarides have partially revised their ideas
these problems result from the theory’s conception             about the interpreter’s position, assimilating it to
of the interpreter’s position and from its construc-           that of a third party observer such as the reader of a
tion principles for discourse structure.                       textual representation of a dialogue. However, with
2.1 Modelling the Interpreter                                  respect to the way discourse structure is generated
In their 1998 paper on questions in dialogue, Asher            and maintained, the theory still exhibits an arguable
and Lascarides analyse examples such as (1) below,             lack of naturalness which is mainly due to the fact
in which a response to a question does not immedi-             that assignment of rhetorical relations takes place
ately result in a resolution of the latter (Asher and          immediately on the level of what is effectively the
Lascarides, 1998):                                             DPs’ common ground. If the DPs’ actions exhibit
                                                               a conflict between their private beliefs, as in discus-
(1)   A[1]:   How can I find the treasure?.                     sion scenarios, interpretation thus has to revise the
      B[2]:   It’s at the secret valley.                       common ground itself and the discourse structure
      A[3]:   But I don’t know how to get there.               represented therein. We can illustrate this problem
                                                               with an adaption of the kind of example used by
   Here, the rhetorical relation between A’s                   Asher and Lascarides:
question A[1] and B’s answer B[2] is immediately in-
terpreted as nei (‘not enough information’) by the             (2)   A[1]:    John went to jail.
SDRT interpretation rules. As discourse interpreta-                  A[2]:    He was caught embezzling funds.
tion at this step not only has access to the overt con-              B[3]:    No.
tent of what has been said in the given discourse con-               B[4]:    He went to jail because he
                                                                              was convicted of tax evasion.
text, which includes the manifestation of the DPs’
                                                                  5 See Matheson et al. (2000) and Kreutel and Matheson
mental states, but also to the mental states of the
                                                               (2000) for the background to this approach
   4 See Lascarides and Asher (1993). Further references can      6 Telematics Applications Programme, Language Engineer-

be found at http://www.cogsci.ed.ac.uk/alex/papers.html        ing Project LE4-8314.
                           Kreutel & Matheson / Building Discourse Structure as an Argumentative Process            87

   The main point to be emphasised here is that                and SDRT’s rhetorical relations will be dealt with
only the rhetorical relation connecting A[1] and               as argumentation acts. Following Habermas’ termi-
A[2], which Asher and Lascarides interpret as                  nology we will use the term dialogue act offer
explanation, is disputed by B[3] and B[4]; the                 (dao) rather than ‘dialogue act’ in the remainder of
contents of the assertions themselves are accepted.            this paper.
However, as the interpretation of the rhetorical re-
                                                               3.1 Validity Claims
lation is added to the common ground immediately
after A[2] is processed, it is necessary to change the         Our primary goal in this paper is to analyse the way
representation of the dialogue structure as the anal-          in which daos are managed in the course of a con-
ysis progresses. Specifically, it is necessary to re-           versation, and we therefore do not give an exhaus-
place explanation with Dis(explanation), where                 tive description of how the validity claims raised by a
the Dis predicate indicates that the relation is dis-          dao can be represented. Briefly, we propose to iden-
puted. In this case, then, the process of building             tify the content of the truth claim with the proposi-
dialogue representations is non-monotonic.                     tional content π of the dao and its presuppositions.
   We feel that the truth-conditional complexities             We further think one can determine the contents of
which arise in such cases can be avoided if one as-            the claims of rightness and truthfulness on the basis
sumes that after the performance of A[2] the con-              of π and the type of dao that has been performed.
tent of the move, including the rhetorical relation            As for truthfulness, we argue that its content can be
between A[1] and A[2], has to be acknowledged, ei-             seen as the intention that is conventionally associ-
ther explicitly or implicitly, before it can be con-           ated with a dao of a certain type, for example the
sidered part of the common ground. Seeing the ac-              intention that some content π become shared-belief
tions of DPs thus as principally pending for acknowl-          and be resolved with assert and ask acts, respec-
edgement, interpretation of the whole dialogue can             tively. From intentions that express interactive goals
proceed monotonically even if no or only partial ac-           of this kind, we can then infer the sincerity con-
knowledgement takes place, as in (2).                          ditions of dialogue acts in Searle’s terms (Searle,
   The following section outlines such an alterna-             1969), i.e. that the speaker believes π and wants to
tive approach to the examples discussed above using            know π, respectively.
Habermas’ notion of speech act offer to analyse how                As for the claim of rightness, there is an ongoing
the interpretations of speech acts, including rhetor-          discussion of how to generalise Habermas’ standard
ical relations,7 are managed by the DPs during an              example for rightness claims as given in his analysis
interaction. Our theory can be formulated in a way             of requests (see Goldkuhl (2000)): When requesting
that is compatible with most of SDRT’s assumptions             π, speakers claim that there is a social norm that
about how speech act assignment and interpretation             entitles them to make the request, hence the right-
of linguistic content takes place.                             ness claim is related to the acceptability of an action
                                                               in a certain social context. Given this generalisa-
3    The Interpretation Process                                tion, the rightness claim for assertions and questions
                                                               could, first of all, be modelled in terms of conditions
In this section we sketch an interpretation process            that require that the respective contribution be in-
based on Habermas’ notion of speech act offer. Our              formative. However, in addition to this, the right-
objective is to model the process of the introduction          ness claim will also comprise the appropriateness of
and evaluation of speech act offers independently               the topic that has been raised in the given social
from other aspects of interpretation, such as speech           context, so in the following example, B’s response
act assignment and interpretation of linguistic con-           can be seen as a rejection of the rightness claim of
tent. In thus keeping the interpretation algorithm             A’s question:
as modularised as possible, our proposals are com-
patible with both SDRT and dialogue models which               (3)   A[1]:   Is it true that John went to jail?
use a TRINDI-style approach based on the notion of                   B[2]:   I don’t want to talk about this now.
information state.                                                In his discussion of Habermas’ universality as-
   The basic notions we employ adhere to the pro-              sumption for the validity claims, Goldkuhl remarks
posals in Poesio and Traum (1998) and decompose                that the rightness claim has become a sort of ‘resid-
speech acts into dialogue acts of different types.              ual category’ in academic discussion which covers all
We use core speech acts such as ask or assert,                 aspects of social interaction (Goldkuhl, 2000). As
on the one hand, and argumentation acts like                   it is evident that social interaction cannot fully be
answer, request-evidence, and correct, on the                  reduced to issues of concordance to norms, the ques-
other. Argumentation acts can be seen as expressing            tion is whether one should extend the repertoire of
the context dependent aspects of a core speech act,            validity claims as proposed by Goldkuhl or rather re-
   7 See Asher and Lascarides (2001) for a discussion of the   lax the definition of the rightness claim as adherence
interpretion of rhetorical relations as speech acts.           to actual social norms. Given this unresolvedness,
88                                               Proceedings of EDILOG 2002

                µ,δ,π                                          who manipulatively exploits the way validity claims
                                                               and their acceptance influence the intersubjectively
                generate(µ, {δ})
                                                               shared assumptions of DPs.
                        i                                         Rather than associating daos with beliefs that ap-
                                                               ply to the content of some action itself, we think a
                                                               dao should be seen as expressing an agent’s assump-
                              name(j,John)                     tions about the impact the presentation of this con-
                        π:    jail(p)
                δ:                                             tent may have on the addressee of the action. This
                              goto(j,p)                        way, it will be possible to model agents who act in-
                                                               sincerely, for instance by asserting something which
                        assert(π)                              they do not believe to be true, but which for strate-
                                                               gic reasons they wish to convince their addressees
                                                               of. We therefore assume a more complex modality
                                                               for daos, which can, preliminarily, be described as
     Figure 1: Interpretation of John went to jail.            in (4) (note that the formalisations in this paper are
                                                               relatively shallow and do not cover the temporal se-
                                                               mantics which would be needed for a complete model
we will currently not provide an explicit represen-            of the processes described here):
tation of the contents of the rightness claim given
a dao of some type, and only represent the claims              (4) If a dialogue act offer δ is made by some agent A
of truth and truthfulness, on which there is relative             towards an addressee B, then BelA (accept(B, δ)).
agreement in the research community.
                                                                  The performance of a dao with some content Kδ
   Depending on the theoretical framework, the as-             is primarily seen as expressing an agent’s belief that
signment of validity claims to some dao can be ex-             Kδ may become part of the common ground of the
pressed by the discourse interpretation algorithm ei-          DPs via the acceptance of the dao by the addressee.
ther in terms of SDRT-style axioms for dialogue act            This semantics leaves open whether the agent actu-
types or alternatively as update rules in the TRINDI           ally believes Kδ itself or not, and can thus account
framework similar to the ones in Kreutel and Math-             for both cooperative and strategic behaviour of dis-
eson (to appear). In Figure 1 we have sketched an              course participants.
example of what the full analysis of an assertion in a            However, in order to have the semantics re-
zero context would be after interpretation rules have          flect Habermas’ critique of the expressive power of
applied, where µ, δ and π denote the move that has             Searle’s acceptability conditions it is necessary to ex-
been made by A, the dialogue act offer made in µ                tend this analysis and to augment the modal oper-
and the propositional content of µ, respectively. i            ator described in (4) with an interactive dimension,
denotes the intention conventionally associated with           which is not provided by the simple association of
an assertion of content π, which we have identified as          daos with the beliefs of a speaker about a future ac-
expressing the truthfulness claim. Following propos-           tion of an addressee. Only this way can we account
als by Poesio and Traum (Poesio and Traum, 1997)               for the fact that a claim is made by the speaker and
we further assume a generate relation between a                directed towards an addressee. An intuitive way to
move that is made by a DP and the set of dialogue              model this is to assume that a dialogue act offer
act offers that is performed therewith.8                        introduces a discourse obligation9 on the ad-
   Making a dialogue act offer thus is interpreted as           dressee to take a position with respect to it. The
first of all producing some propositional content with          intersubjective nature of daos is thus accounted for
some illocutionary force that may be associated with           by having daos enforce a reaction on the part of the
an intention related to the former. As for the formal          addressee, be it an acceptance or a rejection. In the
semantic interpretation of DRSs such as that in Fig-           definition below, the action, which an addressee is
ure 1, we propose to interpret the DRS Kδ that rep-            obliged to perform, is classified as address, where
resents the content of a dao δ as being in the scope of        addressing can be realised explicitly or tacitly:
some modal operator. In a first approximation this
operator could be seen as expressing the beliefs of            (5) Semantics of Dialogue Act Offers
the relevant speaker, however this would mean mod-                An agent A makes a dialogue act offer δ towards an
elling agents in dialogue as genuinely sincere. Our               addressee B iff
model could not then account for a strategic agent
                                                                    1. BelA (accept(B, δ)) and
     8 Poesio
           and Traum assume generate as holding between             2. obligedB (address(B, δ)).
locutionary acts, i.e. a speaker uttering something, and the
performance of dialogue acts, which in their framework are        9 See Traum and Allen (1994) for the basis of the use of

analysed as conversational events.                             discourse obligations in dialogue modelling.
                            Kreutel & Matheson / Building Discourse Structure as an Argumentative Process                     89

   Note that the obligation to address a dialogue act              Consider again as an example the dialogue below,
offer that is introduced by the performance of a dao              introduced in (1) above:
is distinct from the obligation that may be intro-
duced once the addressee has accepted the offer, for              (6)   A[1]:    How can I find the treasure?.
                                                                       B[2]:    It’s at the secret valley.
example the obligation to answer a question one has
                                                                       A[3]:    But I don’t know how to get there.
been asked.10 Whereas the latter obligations are
specific to the type of dao, the obligation to address               We assume that B’s answer B[2] to A’s question
a dao is generic and does not depend on the type of              A[1] introduces two daos of type assert (δ1 ) and
dialogue act that was meant to be performed.11 As                answer (δ2 ). A’s response A[3] can then be inter-
the following section will outline, it is the fact that          preted as fully grounding δ1 , in particular its propo-
an addressee acts according to these generic obliga-             sitional content π, but only as partially grounding
tions that may result in the DPs’ shared assumption              δ2 . While A does not reject the truthfulness of
that a dialogue act of some type actually has been               B’s answer, and thus grounds B’s intention that A’s
performed.                                                       question be resolved,12 A does reject the claim that
                                                                 in asserting π B provides an answer that actually
3.2    Evaluating Dialogue Act Offers                             does resolve the question. Depending on what types
As our discussion in the previous section has shown,             of dialogue acts one assumes, this rejection could be
we think it is a rather natural and intuitive approach           seen as A interpreting the relation between A[1] and
to conceive of the evaluation of dialogue act offers by           B[2] as nei (as in Asher and Lascarides (1998)), thus
the addressee of a move as a process of grounding.               introducing a counteroffer δ2 to B’s claim in δ2 that
In this respect, our analysis can be seen as an elab-            the relation is actually answer. Now, B has basically
oration of some proposals made by members of the                 two options: one is to revise the belief that A knows
TRINDI consortium, in particular the work of Poe-                a way to the secret valley, accept the rejection, and
sio and Traum (Poesio and Traum (1997), Matheson                 come up with an alternative answer. However, if
et al. (2000)).                                                  there is reason for B to assume that A is not sincere
   In contrast to earlier proposals in Traum (1994),             in A[3], B may reject this claim and provide argu-
Poesio and Traum (1997) assume that the domain                   ments for the view that B[2] provides an acceptable
of the grounding process is a discourse unit that                answer to A[1].
comprises the full interpretation of a dialogue move.               Our assumptions about the introduction and eval-
Our model adds a further level of granularity to this            uation of the daos that underlie this analysis can be
analysis and proposes to have grounding apply to                 summarised in the following way:
the single daos into which a move can be broken
                                                                 (7) Discourse Interpretation Algorithm
down, and to determine for each dao whether all of
its content can be grounded or whether it contains                     1. For each move µ determine the set ∆µ of dia-
information that must be exempt from the ground-                          logue act offers generated by µ applying com-
ing process and be made subject to argumentation.                         mon interpretation rules such as those in SDRT
   Our analysis is thus closer, on the one hand, to                       or in TRINDI models.
the ideas in Traum (1994), which describe ground-                         (a) If µ performs a mere acceptance or correc-
ing processes on the basis of an abstract communi-                            tion δ and if there is a subsequent move µ+1
cation recipe. Here, dialogue is analysed on the                              by the speaker of µ then ∆µ = {δ} ∪ ∆µ+1 .
conceptual level as a number of acts of presenting                     2. If there is a move ν by the addressee of µ that
and acknowledging content – in a generic sense – at                       precedes µ and if ∆ν contains ungrounded dia-
a granularity finer than the actions of discourse par-                     logue act offers, then
ticipants. On the other hand, our model retains the                       (a) Check for each ungrounded δi ∈ ∆ν whether
advantages of the highly structured account of the                            µ grounds δi or whether there is some δj ∈
overt realisation of dialogue as provided by a theory                         ∆µ that exempts parts of the content of
of discourse which is based on the notions of dialogue                        δi from being grounded and/or provides a
acts and validity claims.                                                     counteroffer δi to δi .
                                                                          (b) If a counteroffer is provided, add δi to
  10 See Kreutel and Matheson (2000) for how these obliga-
                                                                              ∆µ , otherwise merge δi with the common
tions can be employed for modelling the actions of DPs.                       ground.
  11 In a similar fashion, Poesio and Traum (1997) assume

that all core speech acts introduce an obligation on the ad-       12 We think that this intention could be assigned – and

dressee to perform an understanding act expressing acknowl-      grounded – also in an interpretation that analysed B’s re-
edgement. In addition, they propose the introduction of an       sponse as a hint rather than as an answer. On the other
address obligation for some classes of core speech acts. In      hand, if B was considered to be insincere, just trying to tease
the context of Habermas’ theory of validity claims, this anal-   A, the intention would be assigned to the dao but then A’s
ysis can be extended to all classes of core speech acts and      response could be interpreted as a rejection of the truthfulness
argumentation acts.                                              claim.
90                                                  Proceedings of EDILOG 2002

   In general the merge of a dialogue offer δ with the                           µ1 ,µ2 ,δ1 ,δ2 ,δ3 ,π1 ,π2
common ground mentioned in the algorithm can – in
a DRT-based formalisation – be thought of as join-                              generate(µ1 ,{δ1 })
ing the sets of discourse referents and conditions of                           generate(µ2 ,{δ2 , δ3 })
the DRS Kδ that contains the content of δ with the                                    i1
corresponding sets of that DRS that contains the                                        π1 :Kπ1
grounded information.13 In the particular frame-                                δ1 :    assert(π1 )
work of SDRT the site where the merge takes place                                       i1 :shared-belief(π1 )
will be determined by the way dialogue act offers at-
tach to the previous dialogue context. Assuming a
model that integrates our notion of dialogue act of-                                    i2
fers with Lascarides and Asher’s algorithms for dis-                                    π2 :Kπ2
course interpretation, we propose to merge the con-                             δ2 :    assert(π2 )
tent of a dao with the content of that SDRS that                                        i2 :shared-belief(π2 )
contains the condition δ : Kδ .
3.3 Example Analysis
We will now give a more elaborate analysis of exam-                             δ3 :    explain(π2 ,π1 )
ple (2), repeated here as (8):
(8)   A[1]:    John went to jail.
      A[2]:    He was caught embezzling funds.
      B[3]:    No.                                                          Figure 2: Dialogue State after A[2]
      B[4]:    He went to jail because he
               was convicted of tax evasion.
                                                                   intention that the fact that explanation holds be-
  Figure 2 shows the result of applying step 1 of                  tween two propositional contents π1 and π2 become
the algorithm to A’s moves A[1] and A[2], which are                shared belief.
represented by the discourse referents µ1 and µ2 .                    Apart from the mere fact that two moves have
We see that three daos, assigned the types assert                  been made, raising daos δ1 -δ3 with contents π1 and
(δ1 , δ2 ) and explain (δ3 ), are introduced. Note                 π2 , Figure 2 shows that all the actual content gener-
that whereas δ1 and δ2 comprise propositional con-                 ated by µ1 and µ2 is embedded under the modality
tent (π1 ,π2 ), δ3 , being an argumentation act, simply            associated with daos. Step 2 of the algorithm does
adds illocutionary force to µ2 claiming that π2 ac-                not apply here as we are at a discourse initial state
tually provides an explanation for π1 .14 Our inter-               and there is no preceding move by B. The result
pretation currently does not comprise an intention                 of grounding parts of A’s contribution through B’s
associated with δ3 . However, for an argumentation                 performance of B[3] and B[4], represented by µ3 and
act like explain, we can extend interpretation rules               µ4 , is then shown in Figure 3. Here, we see, first
of the kind described in Kreutel and Matheson (to                  of all, that in addition to issuing a dao δ4 typed as
appear), which conventionally associate intentions                 correct, two further assert daos are introduced
with dialogue acts in the following way:                           (δ5 and δ6 ). Furthermore, δ7 claims that explain
                                                                   holds between the contents of the assertions.
(9) explainDP (π2 , π1 )                                              As B’s No is a simple correction which is followed
     iDP : shared-belief (explanation(π1 , π2 ))
                                                                   by another move by B, step 1a of the algorithm
  According to this rule, if some DP makes a dao                   applies in this case, and µ1 and µ2 are evaluated
of type explain, we can infer that they have the                   against {δ4 } ∪ {δ5 , δ6 , δ7 } according to step 2. Note
  13 see Poesio and Traum (1997) for a formalisation of the
                                                                   further that we interpret correct acts – as well as
merge operation in terms of Compositional DRT.
                                                                   accept acts – as anaphoric, applying to some set of
  14 One could, nevertheless, associate a propositional content    daos ∆, the reference of which is not resolved before
with an argumentation act such as explain(π2 ,π1 ), assum-         the application of step 2.
ing that it expresses the fact that explanation(π1 , π2 ) holds.      Considering the propositional content of δ5 and δ6 ,
Note that in a two-level approach to discourse interpretation,     we then can assume that µ3 and µ4 , first of all, fully
explanation will be a predicate in the language of informa-
tion content whereas explain will belong to the language used      ground δ1 , the content of which is echoed in δ5 .15 In
for reasoning over discourse structure. As noted, Asher and        addition, the proposed interpretation assumes that
Lascarides do not distinguish the level of the actions of a DP     δ2 is accepted as well, where the DRS shows the
from the level of rhetorical relations, whereas our model can      result of merging the contents of δ1 and δ2 with the
derive the latter in a secondary step as information content
given the interpretation that some act has been performed,           15 δ and δ are not fully represented in the DRS. The ;
                                                                         5      6
which, on its part, will be achieved by applying the logics of     symbol should be read as introduction of the indicated dis-
dicourse structure.                                                course referents.
                               Kreutel & Matheson / Building Discourse Structure as an Argumentative Process              91

         µ1 ,µ2 ,µ3 ,µ4 ,δ1 ,δ2 ,δ3 ,δ3 ,δ4 ,δ5 ,δ6 ,δ7 ,          in the previous example (6), given the state repre-
         π1 ,π2 ,π3 ,π4 ,π5 ,i1 ,i2                                sented in Figure 3, A now has the options of either
                                                                   acknowledging B’s claims, including δ3 , or starting
         generate(µ1 ,{δ1 })                                       a discussion to provide arguments in support of δ3 .
         generate(µ2 ,{δ2 , δ3 })                                     Given these example analyses, we think that an
         generate(µ3 ,{δ4 })                                       algorithm of the kind described in (7) is powerful
         generate(µ4 ,{δ5 , δ6 δ7 , δ3 })                          enough to account not only for an intuitive analysis
         π1 :Kπ1                                                   of cases like (6) and (8), but also for situations such
         assert(π1 )                                               as the one exemplified in (10) below, in which an
         i1 :shared-belief(π1 )                                    utterance is misinterpreted by the addressee:
         π2 :Kπ2
         assert(π2 )                                               (10)    A[1]:   Where’s the water tap?
         i2 :shared-belief(π2 )                                            B[2]:   You shouldn’t drink the water here.
         δ1 :Kδ1                                                                   There’s mineral water in the fridge.
         δ2 :Kδ2                                                           A[3]:   I actually just wanted to water
         δ3 :{}{explain(π2 , π1 )}                                                 the plants.
                                                                           B[4]:   Oh, I see. It’s downstairs in
                 ∆                                                                 the cellar.
                 π3 : K π 3                                                A[5]:   Thanks.
         δ4 :    correct(π3 ,∆)
                                                                      Here, B’s response B[2] grounds the overt content
                 ∆ = {δ3 }
                                                                   of A[1] and, in addition, introduces a dao containing
                                                                   B’s assumptions about A’s motives underlying A[1].
         δ5 :Kδ5 ; π4 ≡ π1
                                                                   In the same way as in the examples discussed above,
         δ6 :Kδ6 ; π5
                                                                   A[3] then provides a counteroffer to this interpreta-
         δ7 :{}{explain(π5 , π1 )}
                                                                   tion, which is finally grounded and responded to in
         δ3 :{}{FAIL(explain(π2 , π1 ))}

                                                                   4      Conclusion
          Figure 3: Dialogue State after B[4]
                                                                   In this paper we propose an approach to dialogue
                                                                   modelling that is based on Habermas’ notion of
root DRS. Given the correct and explain daos δ4                    speech act offer, incorporated in our theory as di-
and δ7 , we can further assume that what is rejected               alogue act offer. Leaving aside how all the validity
by B is actually δ3 , which allows us to resolve the               claims raised by a dao will actually be represented
anaphor ∆ to {δ3 }.16 In addition, we propose to have              for the different types of daos, we have concentrated
δ4 -δ7 introduce a counteroffer δ3 to δ3 , which claims             our argument on the general issue of how a discourse
that π2 does not actually provide an explanation for               interpretation algorithm can be formulated on top of
π1 .                                                               these basic assumptions.
   As Figure 3 demonstrates, our analysis is very                     As the discussion of the example dialogues has
close to that in SDRT as far as the successfully                   made clear, an algorithm of the kind proposed in
grounded information is concerned.17 However, in                   (7) is powerful enough to analyse various situations
contrast to the SDRT analysis of (8), our interpre-                in which DPs have contrary assumptions about the
tation builds discourse structure monotonically; in                interaction in a way that does not require any revi-
particular it maintains the information in δ3 while                sion of the discourse structure that was built before
at the same time expressing the fact that it is dis-               the conflict became evident. On the other hand, it
puted by the presence of the counteroffer δ3 .18 As                 is able to reconstruct the third party perspective of
                                                                   an interpreter who does not have to be seen as om-
  16 An alternative interpretation of µ and µ would be to
                                       3        4                  niscient, but rather as an interpreter for whom the
assume that only δ1 is grounded and to resolve ∆ to {δ2 , δ3 }.    representation of the dialogue emerges out of the
  17 In particular with respect to the example dialogue (8)

in Asher (2002). What is not represented here, however, is         observable actions of the discourse participants and
the fact that µ1 and µ2 are grouped together and trigger a         the interpretation rules that are conventionally as-
package of information which some rhetorical relation could        sociated with these actions.
refer to as a whole.
  18 Whereas Lascarides and Asher’s Dis operator marks some
rhetorical relation as being under discussion, the application
of the FAIL operator to some dialogue act α indicates that the     Nicholas Asher and Alex Lascarides. 1998. Ques-
speaker considers the performance of the act as not felicitous.      tions in dialogue. Linguistics and Philosophy,
The fact that some dialogue act offer of action type α is under       23(3).
discussion is thus reflected by having the dialogue state com-
prise both α and FAIL(α) embedded under the belief operator        for daos.
92                                         Proceedings of EDILOG 2002

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