But What Do They Mean?
An Exploration Into the Range of Cross-Turn Expectations Denied by “But”
Kavita E. Thomas
School for Informatics, University of Edinburgh
kavitat@cogsci.ed.ac.uk
Abstract
In this paper we hypothesise that Denial of Ex-
pectation (DofE) across turns in dialogue sig-
nalled by “but” can involve a range of different
expectations, i.e., not just causal expectations,
as argued in the literature. We will argue for
this hypothesis and outline a methodology to
distinguish the relations these denied expecta-
tions convey. Finally we will demonstrate the
practical utility of this hypothesis by showing
how it can improve generation of appropriate
responses to DofE and decrease the likelihood
of misunderstandings based on incorrectly in-
terpreting these underlying cross-speaker rela-
tions.
1 Introduction
In this paper, we will continue investigation into Denial
of Expectation (DofE) across turns in dialogue when sig-
nalled by “but”, following work by Thomas and Mathe-
son (2003), and claim that these denied expectations need
not be causal only. That is, we investigate two hypothe-
ses: (1), that “but” can deny noncausal relations across
turns in dialogue, e.g., temporal ordering relations, and
(2) that because “but” is a negative polarity cue (Sanders
et al., 1993), it inverts normal relations, and we will need
to invert DofE dialogues in order to investigate the rela-
tions underlying the original (not denied) expectations.
To this end, we motivate the argument that these de-
nied expectations can involve relations other than causal
ones licensing the inference from A’s turn to B’s. We
will then outline a novel methodology which utilises lin-
guistic substitution tests on Knott’s (1996) taxonomy of
cue phrases to distinguish the underlying expectations de-
nied. The practical utility of distinguishing these rela-
tions arises from discovering ways in which to both rep-
resent and utilise this information for NLG (among other
applications), so we will address these issues in section
4. We show how the Information State (IS) (Matheson
et al., 2000) representing the state of the dialogue in the
PTT (Poesio and Traum, 1998) model of dialogue must
be updated to reflect this new information, with Conver-
sational Acts (Matheson et al., 2000) that do not simply
indicate DofE as in (Thomas and Matheson, 2003), but
also annotate the relation underlying the expectation be-
ing denied. Finally we will demonstrate how a system
incorporating this information can improve generation of
responses to DofE depending on its model of beliefs re-
garding the relation underlying the denied expectation in
DofE dialogues.
2 Motivation
The main motivation behind modelling cross-turn rela-
tions is to get at what expectations and beliefs speakers
might have upon interpreting the previous turn in the di-
alogue. Inferring the relations speakers perceive in cases
where the related material spans speaker turns sheds light
on how they interpret the previous speaker’s turn, which
in turn enables response generation that can specifically
address these implicit relations. Here we focus on cases
involving DofE, where the speaker of the “but” turn in di-
alogues like Ex.1 below has an expectation that beautiful
people a0 marry, where a0 indicates defeasible implica-
tion.
(1) Example 1.
A: Greta Garbo was the yardstick of beauty.
B: But she never married.
Thomas and Matheson (2003) argue that B has the ex-
pectation that beautiful people (usually) marry, and in-
terpreting A’s utterance triggers this expectation, which
B knows does not hold, since he knows that Greta never
married, denying the consequent of the rule. Hence he
generates DofE, and depending on A’s beliefs w.r.t. B’s
assertion that Greta never married or the inferred ex-
pectation that beautiful people marry that is being de-
nied, she can respond accordingly. E.g., if she agrees
with the assertion but disagrees with the expectation, she
can respond “But beautiful people don’t have to marry!”
Thomas and Matheson (2003) focus on modelling DofE
in Task-Oriented Dialogue (TOD). They present TOD ex-
amples like the following,
(2) Example 2.
A: Add the vinegar to the sauce.
B1: (Yeah) But it’s not tangy enough.
B2: (Yeah) But we forgot to add the mushrooms.
where B1 involves an expectation similar to the one above
involving beautiful people marrying, namely, that adding
vinegar makes things tangy, which is a general cause-
effect relationship. However they argue in that paper
that B2 involves satisfaction-precedence (s.p.) between
adding vinegar and adding mushrooms, namely, that B
expects adding mushrooms to be done before adding
vinegar. They then went on to argue that TOD DofE
should be distinguished from Nontask-Oriented Dialogue
(NTOD) DofE, because of examples like Ex.2B2 above,
where the DofE arises from the denial of an ordering of
actions in B’s task-plan.
While we do not disagree with their claim that these
s.p. DofEs in TOD (e.g., Ex.2B2) are distinct from causal
cases like Ex.2B1, we disagree that these noncausal cases
are unique to TOD; i.e., we argue for a unified treatment
of DofE in TOD and NTOD, where, while search meth-
ods might differ (i.e., searching task-plans in TOD and
private beliefs in NTOD), examples involving noncausal
expectations which are denied are not unique to TOD.
Consider the example below:
(3) Example 3.
A: Greta had a child in ’43.
B: But she married in ’47.
here we interpret B’s “but” as signalling the denial of
his expectation that marriage (usually) precedes having
children in order to coherently interpret his response. The
relation between turns (or antecedent and consequent)
here is temporal ordering, and is very similar to the s.p.
in the previous example (Ex.2B2). Unlike s.p., however,
temporal ordering does not require the actions or states
that temporally precede the later one to be achieved; i.e.,
the accomplishment aspect of s.p. is novel to planning,
where goals are posted and accomplished, and there is
a sense of agency. Temporal ordering relates actions,
events, states, effects, etc, with no notion of agency in-
volved. Prior work on DofE has not focussed much on the
nature of the relation underlying the denied expectation,
and we argue that this information will facilitate much
more adaptive and appropriate response generation.
3 A Methodology for Distinguishing the
Underlying Expectations
We outline a novel methodology for distinguishing fea-
tures involved in these relations using linguistic substi-
tution tests involving the cue phrase taxonomy presented
in Knott’s thesis (1996). Knott presents a taxonomy of
cue phrases distinguished as feature-theoretic constructs
rather than markers of one or more of a set of rhetor-
ical relations as postulated in RST. Rather than finding
data to describe a conceptualised theory of rhetorical re-
lations, he uses data containing cue phrases to drive the
creation of his taxonomy of cue phrases, which reveals
psycholinguistic features involved in conveying or inter-
preting meaning, i.e., the data drives his theory of linguis-
tic production. We enquire into the nature of the relations
underlying these denied cross-turn expectations using the
following methodology:
1. Take original “but” example and determine expectation being denied via
algorithm in (Thomas and Matheson, 2003).
2. Invert example so that the consequent of the expectation is asserted rather
than denied in B’s turn, (i.e., omitting the “but”). (So the dialogue conveys
that the expectation in Step 1 succeeds.)
3. Determine what sort of expectation this inverted pair of turns seems closest
to, given Knott’s taxonomy. Determine whether the cues conveying this
relation are substitutable in this inverted dialogue:
(a) Test all the high-level categories in the taxonomy and see which
ones work by substitution tests involving cues belonging to those
categories. Then determine whether the category chosen captures
the nature of the expectation (i.e., intuitively, following annotator’s
judgment).
(b) If so,
i. test whether hyponyms1 of these high-level cues work in the
inverted dialogue. The most specific hyponyms that work in-
dicate the maximally specific set of features that pertain to the
relation underlying the expectation.
ii. Now confirm that these cues that work in the inverted dialogue
do not also work in the original (denied) dialogue. Those cues
that work in the inverted example but not in the denied (orig-
inal) dialogue are indicative of the nature of the underlying
relation that’s denied in DofE.
iii. Look up the feature-value definitions for the maximally spe-
cific cues that work in this inverted (not denied) case. Compar-
ing these to the feature-value definition of hyponyms of “but”
that deny the same expectation will reveal which feature-
values are denied/inverted in the denied case.
Comparing the intersection of feature-values for hyponyms
that work in the inverted case to the intersection of feature-
values for hyponyms that work in denied case shows precisely
which features are being denied.
(c) If Knott’s taxonomy does not provide a category that works for the
inverted dialogue,
i. check whether any of Knott’s categories fit the original denied
expectation by testing which cues are substitutable in the orig-
inal example; a good place to start is with hyponyms of “but”.
ii. For cues that work, check their hyponyms to determine the
maximally specific set of features that apply to the relation
between turns. Note that this only specifies the relation un-
derlying the denied expectation and does not shed light on the
original (not denied) expectation.
iii. If no cues besides “but” work in the original dialogue, then
“but” must be the maximally specific cue that works, and
we cannot determine more precisely the nature of the denied
expectation, so assume that the turns are related by simple
contingency/co-occurrence.
1Hyponyms inherit the features of their parent (higher-level)
cues in the directed acyclic graph structure of the taxonomy.
So all hypernyms (higher-level parents) should also be substi-
tutable in the given case. Hypernyms are far less specific and
therefore less precise.
Table 1: Feature-Values Denied in Ex.1
Features Asserted Denied
indeed despite this
even then again
Polarity Positive Negative
Source of Coherence – Pragmatic
Anchor – Cause-driven
Focus of Polarity Anchor Counterpart
Presuppositionality Non-presupposed Non-presupposed
Modal Status Actual Actual
3.1 An example
So to determine how A and B might be related (in B’s per-
spective) for Ex.1, we find that the following cues work in
the inverted dialogue below with the expectation asserted
rather than denied:
(4) Example 4.
A: Greta was beautiful.
B: (Yes) a0 indeeda1 she a0 evena1 married.
The asserted expectation works with Knott’s “additional
information” category of cues, and “even” and “indeed”
are the most specific of these cues which work. In the
original denied example below, (with “*” indicating un-
acceptable cues):
(5) Example 5.
A: Greta was beautiful.
B: a0 However/even so/in spite of this/all the same/despite
this/nevertheless/then again/*indeeda1 she never married.
two of the most specific of these negative polarity cues
which work are “despite this” and “then again”, which
differ from “indeed” and “even” in polarity (the former
are negative, the latter positive) and focus of polarity (the
former are anchor-based, the latter, counterpart-based).
Also, the cues which work in the inverted case do not
work in the denied case. Furthermore, these negative po-
larity cues are defined for some values which are unde-
fined for these additional information cues, and the two
pairs also share some feature-values in common. But the
features that are defined for both and differ are the ones
which are the most informative; they specify which fea-
tures are being denied in the DofE case, and which ones
asserted in the inverted case. So here we find that DofE
involves denying polarity and focus of polarity in the un-
derlying expectation.
4 Modelling Issues
Although this methodology requires human judgment to
assess the results of the substitution tests, it is a first
step towards distinguishing underlying relations in DofE.
We address how this information might be modelled in
the PTT (Poesio and Traum, 1998) model of dialogue
by adapting the Information State (IS) (Matheson et al.,
2000) in order to facilitate more responsive generation
from the system upon hearing the DofE.
4.1 Utilising Knott’s Feature Definitions
Knott argues that his data-driven definition of relations
is compatible with the view that relations are planning
operators with preconditions and effects, where the rela-
tions’ preconditions are defined via the speaker’s inten-
tions and applicability conditions specified for what the
speaker wants to convey, and the effects are simply the
intended effects the conveyed relation has on the hearer.
More practically speaking, the features are defined in
terms of variable bindings and relationships which de-
scribe the relations concisely. For example, the polar-
ity feature describes whether the defeasible rule a2 a0a4a3
holds, based on whether A=P and C=Q (positive) or A=P
and C is inconsistent with Q (negative), where A and
C are the propositional contents of the two respective
related clauses. To address how polarity might be de-
termined in a dialogue situation, if a speaker believes
a2
a0a5a3 , then this is in her Private Beliefs field in the
IS. If her turn is mapped onto Q, and the prior turn is
mapped successfully onto P by matching first-order logic
representations of the material in the two turns, then if
her turn maps onto Q, we can assume positive polarity; if
her turn maps onto a negated Q, then we assume negative
polarity.
While mapping speakers’ turns onto the variables
which define Knott’s features might be difficult, we can
automate some of the feature assignment to update the
IS by maintaining an exhaustive (i.e. complete) static ta-
ble of cue-phrase definitions2. This way, once the most
specific cue-phrases that work in the inverted and denied
expectations are determined, we can automatically assign
feature-value-pair bundles to these dialogues which de-
scribe the underlying relation being denied. Then com-
paring the feature-values for the maximally specific cues
for both the asserted and denied cases (as we saw in the
previous section), we can determine precisely which fea-
tures are being denied in a given DofE, and the IS can
be updated with this information, so that in the next turn
of the dialogue, the speaker can compare these feature-
value assignments to his own (in his private beliefs) and
respond accordingly with a highly specific response to
the DofE which targets precisely where he disagrees or
agrees.
4.2 Information State Modification
We propose, given information about the nature of
the underlying relation via the feature-value differ-
ences involved in the DofE as well as broader in-
formation about the category(ies) to which a cue-
phrase belongs in Knott’s taxonomy, to include this
in the a6a8a7a10a9a12a11 Conversational Act as follows for Ex.3:
2Knott provides a partial table of cue-phrase definitions like
this in Appendix D.1 of his thesis.
a6a8a7a10a9a12a11a1a0a3a2a5a4a7a6a8 a11a7a9a11a10 a7a13a12a15a14a17a16 a7a13a12 a6 a11a7a12a13a18a20a19a22a21a22a0a23a9a24a14a1a12a13a12a13a25a17a18a26a19a22a21a27a0a29a28a30a4a31a8a31a32a33a4
a34
a14a36a35a1a18a20a19a22a21 a37
a34
a18a38a16 a6a36a12 a11a39a19a40a0a23a28a41a4a31a8a43a42a44a32a33a45a46a8a48a47a49a8a43a42a44a32a38a50a26a4a7a6a50a29a32 , where we replace
a0 with the more specific temporal ordering relation as
the link between A and B’s turns; the last field includes
specific features being denied.
4.3 Responding to DofE Appropriately
Upon hearing B’s DofE, A must then respond appropri-
ately. If A also infers the nature of B’s denied expecta-
tion, this can lead to much more responsive generation.
(Thomas and Matheson, 2003) address how interpreting
DofE in the IS can facilitate better generation. We argue
that their algorithm cannot predict the correct expecta-
tions in cases involving noncontingency related expecta-
tions (i.e., cases unlike Ex.1). E.g., in Ex.3, their algo-
rithm would predict that B has the expectation that “hav-
ing a child in ’43 a0 not married in ’47”, since accord-
ing to their original formulation of defeasible rules, B’s
turn is negated to form the consequent, so depending on
A’s beliefs he would respond accordingly. E.g., If A dis-
agrees with both B’s assertion and inferred expectation,
then neither must be in his beliefs, and he might respond:
“She didn’t marry in ’47, and anyway just because she
had a child in ’43 doesn’t mean she should be married in
’47.” (I.e., A does not understand that B sees the events
as temporally ordered.)
With our added information about the nature of this
expectation, namely that it involves temporal ordering,
we can improve upon Thomas and Matheson’s scheme
by predicting the following more appropriate responses.
Notice that given this added information about the rela-
tion underlying the DofE, denying the DofE now means
denying the underlying relation licensing the expectation.
This means that A can be much more relevant when gen-
erating a response:
1. If A disagrees with both B’s assertion and inferred expec-
tation, then neither must be in his beliefs, and he might
respond: “She married before ’43, and anyway lots of peo-
ple back then had children before marrying.”
2. If A only agrees with B’s assertion, then this assertion
must be in his private beliefs, and he might respond:
“Yeah, but lots of people back then had children before
marrying.”
3. If A only agrees with B’s expectation, then this must be
in his private beliefs, and he might say: “But she married
before ’43.”
4. If A agrees with both B’s assertion and expectation, he
might say (minimally): “Yes, that’s odd.”
Notice that these responses indicate that A has under-
stood B’s temporal ordering that underlies these events
and is the source of the denied expectation, and this al-
lows B to correct possible misunderstandings. E.g., if
B realises that A thinks she believes that people need to
marry before having children, and this is an incorrect in-
ference on A’s part, she can indicate this by responding,
e.g., to the situation in which A disagrees with both B’s
inferred expectation and assertion, B: “OK, but I don’t
think that people had to marry before having children.” B
needs to recognise specifically that A failed to interpret
her temporal ordering expectation in order to correct A’s
misassumption. In cases in which specific features are
the precise source of the DofE, if the hearer of the DofE
can recognise that the wrong polarity is being attributed
to his utterance, he (A) might indicate this misassumption
by saying “but not marrying is common among beautiful
people” (Ex.1).
5 Conclusions and Future Work
We present a novel treatment of DofE, in which we argue
that the expectation denied in DofE across turns arises
from a specific relationship between the antecedent and
consequent. We then demonstrate a novel methodology
for distinguishing the nature of this underlying relation
via linguistic substitution tests on Knott’s taxonomy of
cue phrases. Finally, we show how this information can
be used to generate more relevant responses that indicate
explicitly what speakers have inferred from the preced-
ing turn, allowing for faster detection and resolution of
misunderstandings.

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