Discourse Relations versus Discourse Marker Relations 
Jacques Jayez 
EHESS 
54, Bid Raspail 
75006 Paris FRANCE 
j j ayez~dial, oleane, corn 
Corinne Rossari 
Universit~ de Gen~ve 
D4partement de Linguistique Franqaise 
1211 Gen~ve 4, SWITZERLAND 
Corinne. Kossari~lettres. unige, ch 
Abstract 
While it seems intuitively obvious that many dis- 
course markers (DMs) are able to express discourse 
relations (DRs) which exist independently, the spe- 
cific contribution of DMs - if any - is not clear. In 
this paper, we investigate the status of some conse- 
quence DMs in French. We observe that it is difficult 
to construct a clear and simple definition based on 
DRs for these DMs. Next, we show that the lexi- 
cal constraints associated with such DMs extend far 
beyond simple compatibility with DRs. This sug- 
gests that the view of DMs as signaling general all- 
purpose DRs is to be seriously amended in favor of 
more precise descriptions of DMs, in which the com- 
patibility with DRs is derived from a lexical semantic 
profile. 
1 Introduction 
The idea that discourse markers (DMs) like then or 
anyway signal underlying discourse relations (DRs) 
like cause, opposition, contrast, etc., has been 
adopted in a certain number of works on text and 
conversation structure (see Roulet 1985, Martin 
1992, Knott 1996 for various examples). In itself, the 
idea is reasonably intuitive and appealing and seems 
empirically true to a large extent (Knott 1996). 
However, the linking between DRs and DMs is more 
intricate than is currently assumed. We show here 
that some French consequence DMs akin to therefore 
( donc, par consequent, alors) are difficult to describe 
in terms of DRs. We argue that such clashes are due 
to the semantic profiles of DMs, that is to the way 
DMs 'see' the left and right argument of the seman- 
tic relation they denote. We offer an analysis of the 
profile of the donc class DMs along the lines of Velt- 
man's update semantics (Veltman, 1996). We con- 
clude that the compatibility of DMs with DRs must 
be studied by identifying first the relational core of 
DMs, that is, the semantic relation they denote and 
the types of arguments selected by this relation) 
ll.n this paper, we consider only the deductive use of donc, 
in monologual written speech, a use illustrated for example 
by Paul opened the tuindow, DONC we 90t some fresh air. 
We ignore here other uses of doric. We will also ignore the 
2 The profile problem 
2.1 Observations 
Let us consider the following examples. 
(1) a. Je me suis r4veill4 trop tard. DONC je 
I woke up too late. Therefore I 
n'ai pas pu aller ~ la r4union 
couldn't go to the meeting 
b. Jean n'4tait pas ~ la r4union. DONC 
John wasn't at the meeting. Therefore 
il a dfi se r4veiller trop tard 
he must have waked up too late 
(2) a. Je n'ai pas pu regarder la t@l@, est-ce que 
I couldn't watch the TV, is-it that 
les Red Sox ont gagn4? 
the Red Sox won? 
(I couldn't watch the TV, did the Red Sox 
win?) 
b. Je n'ai pas pu regarder la t@l@, 7?DONC est-ce 
que les Red Sox ont gagn~? 
(I couldn't watch the TV, therefore did the 
Red Sox win?) 
c. Je n'ai pas requ le rapport, DONC 
I didn't receive the report, therefore 
est-ce que le d4partment 1' a envoyS? 
is-it that the department it sent 
(I didn't receive the report, therefore did the 
department send it?) 
(3) a. Ouvre la fen~tre, (et) on aura de 
Open the window, (and) we will get some 
Fair 
air 
(Open the window (and) we'll get some fresh 
air) 
b. Ouvre la fen~tre, ??DONe on aura de Pair 
(Open the window, therefore we'll get some 
fresh air) 
other class of consequence connectives (du coup, de ce/air), 
for which the reader is referred to (Jayez and Kossari, 1998). 
Unless indicated otherwise, doric, alors and par consdquent 
are intersubstitutable in the examples. This does not mean, 
however, that these DMs are synonymous in all contexts (see 
(Jayez and Rossari, 1998) for the difference between doric and 
alors). 
72 
c. Si tu ouvres la fen~tre, ALORS on 
If you open the window, then we 
aura de l'air 
will get some air 
(4) a. Sois ~ l'heure. Prends l' autoroute 
Be on time. Take the highway 
b. Tu es en retard, DONC prends l' 
You are late, therefore take the 
autoroute 
highway 
c. Sois ~ l'heure, 7?DONC prends l' 
Be on time. therefore take the 
autoroute 
highway 
d. Essaie d'etre h l'heure. Donc prends 
Try to be on time. Therefore take 
1' autoroute 
the highway 
e. Prends l' autoroute. ??DoNC sois h 
Take the highway. Therefore be on 
l'heure 
time 
When it is used to connect two assertions, 
the consequence DONC corresponds either to a 
cause-consequence relation, as in (l-a), or to a 
consequence-cause relation, as in (l-b). In contrast, 
it is not clear how we should analyze the behaviour of 
DONC in the other examples (2-b)-(4-e). The most 
striking fact is that no simple correlation between 
the speech act types (assertion, question, impera- 
tive) and the possibility of using DONC emerges from 
the examples. 
In (3-a), the second proposition appears as a con- 
sequence of the execution of the imperative, as ev- 
idenced by the future tense. 2 DONC is extremely 
clumsy in such contexts, while it may occur after 
imperatives in some others (cf. (4-d)). In (4-a), the 
relation is a means-end one. Taking the highway is a 
possible means to arrive somewhere in due time. To 
explain (4-c), it could be argued that DONC does not 
support means-end relations. But, first, this does 
not square well with (4-b) and, second, the contrast 
(4-c)-(4-d) remains to be explained. 
2.2 Speech acts and semantic profile 
DRs, qua relations, bear on arguments of some 
type(s). We call profile of a DR or DM the types 
of its arguments. It is possible to express pro- 
file distinctions within theories of DRs. For in- 
stance, Sanders et al. (1992) use the primitive 
Source of Coherence with the two values Seman- 
tic and Pragmatic, corresponding respectively to a 
link between propositional contents and between il- 
locutionary meanings (or speech acts). In Cause- 
Consequence or Consequence-Cause relations, the 
~Such pseudo-imperatives are studied in (Clark, 1993). 
value of Source of Coherence is Semantic, while it 
is Pragmatic for Goal-Instrument relations. If we 
assume that questions like (2-a) are grounded on a 
Cause-Consequence relation, the clumsiness of (2-b) 
can be explained by noting that there is no link be- 
tween the propositional contents of the assertion and 
of the question: my watching the TV cannot in- 
fluence the result of the game. Unfortunately, the 
same line of argument predicts that (2-a) itself is 
anomalous. Symmetrically, let us assume that (2-a) 
is rather a Goal-Instrument relation with Goal = 
'the speaker wants to know whether p' and Instru- 
ment = 'the speaker asks whether p'. We could ex- 
plain (2-b) by denying to DONC any compatibility 
with a Goal-Instrument connection. However, this 
is not consistent with the possibility of examples like 
I need a hammer, DONC lend me yours \]or a minute. 
Another variant of the same problem occurs when 
one tries to use commonsense DR categories like jus- 
tification (Roulet et al., 1985; Mann and Thompson, 
1988). DONC normally resists introducing a justi- 
fication, as in (3-b). But, in some cases, it is able 
to introduce a speech act justified by a proposition 
(4-b), while in other cases the very same pattern 
does not license DONC (2-b). 
Knott (1996) proposes that semantic and prag- 
matic connections are sensitive to intended effects. 
The semantic intended effect is that the addressee 
believes the relation associated with the DR to hold 
between the propositional contents of the arguments. 
If DONC is semantic rather than pragmatic, we can 
account for the clumsiness of (2-b) in the same way 
as Sanders et al.: watching the TV cannot influence 
the result of the game. However, this is not consis- 
tent with the impossibility of (3-b). The pragmatic 
intended effect is that some relation actually holds 
between the intended effects associated with the ar- 
guments. In (2-a), the intended effect of the asser- 
tion is that the addressee believes that the speaker 
did not watch TV. The intended effect of the ques- 
tion is that the addressee answers the question, if 
possible at all. The intended eSect of the whole is 
that the first belief causes the addressee to answer 
the question. If DONC is pragmatic and expresses a 
consequence relation, the intended effect of the first 
argument must have the intended effect of the sec- 
ond as one of its consequences. This seems to be the 
case in (2-b). Yet the linking is not natural. 
These hypotheses seem to suffer from calibration 
problems. The possible profiles they allow us to 
construct tend to overlicense or underlicense the ob- 
served combinations. 
2.3 Towards a dynamic notion of profile 
The difference between (3-a) and (3-b) hints at what 
is happening. In (3-a), obeying the command results 
in a situation in which the window is open. This sit- 
uation is not real but only potential. Using accom- 
73 
modation (Lewis, 1979), we can consider a potential 
version of the real world in which this situation is 
realized. In such a version, it is legitimate to con- 
clude that we'll get some fresh air. Although the 
technical details of accommodation are somewhat 
intricate (see Frank 1996 for a recent survey), the 
general principle remains constant. Accommodation 
gives us the opportunity of importing information in 
a possible world. 
How is it that DONC seems to block accommo- 
dation in (3-b), although there is a clear Cause- 
Consequence relation between opening a window 
and getting some fresh air? Generally speak- 
ing, DONC requires that we construct an inferential 
bridge between the representation of the first sen- 
tence and that of the second sentence. In (3-b), 
obeying the command creates a potential world 
where the window is open. Assertions consist basi- 
cally in updating a world with the information con- 
veyed by the asserted sentence. So, they are func- 
tions from a state of some world to another state 
of the same world. This granted, there are several 
options. 
(i) The assertion in (3-b) is evaluated in the poten- 
tial world where the window is open. There is no 
reason why the sentence should be odd. 
(ii) The opening of the window is evaluated in the 
world where the assertion is, that is, presumably, 
the real world. Again, there is no explanation for 
the oddness of (3-b). 
(iii) The opening of the window and the assertion 
are evaluated in different worlds. This could explain 
the oddness of (3-b). 
So, the Option (iii) seems to be the right candidate, 
but the only difference between (3-b) and (3-a) is 
the occurrence of DONC in the former. Therefore, 
DONC must be responsible for the phenomenon. 
Specifically, we make two assumptions. 
(i) DONC signals some consequence connection be- 
tween two semantic constructs. 
(ii) This connection is evaluated in one type of world 
at one time. It may not link two constructs from two 
different types of world at the same time. 
(i) is unobjectionable. One of the roles of a con- 
sequence DM is to signal a consequence relation. 
Which notion of consequence is appropriate remains 
to be seen, however. From (i) we derive the observa- 
tion that the left construct must have the type of a 
proposition (or, more generally, of a judgment). (ii) 
explains why we cannot freely mix speech act types 
with DONC. We can go from assertions to assertions 
or from imperatives to imperatives because we stay 
in the same type of world. We can go from assertions 
to imperatives because there is some reflection of the 
world of assertions in that of imperatives. 3 This is 
3Concerning {./--clauses, there is a sharp diIfererLce between 
ALORS and DONC and PAR CONSEQUENT whose compatibility 
as expected if we consider that, in a consequence re- 
lation, the premise and the conclusion must have the 
same modal status (belong to the same world). 
Condition (i) echoes the current belief that ques- 
tions do not introduce propositions, that is, semantic 
constructs evaluated as true or false (in some world). 
If consequence DMs need propositional premises, 
they cannot follow questions. 4 That imperatives 
have a propositional behavior, on a par with asser- 
tions and in contrast with questions, is evidenced by 
tt-,e following contrasts. 
(~} a. It a ouvert la fen~tre, ce qui a rafrMchi 
He opened the window, which cooled 
la piece 
the room 
b. Ouvre la fen~tre, ce qui rafredchira la 
Open the window, which will cool the 
piece 
room 
c. Est-ce qu' il a ouvert la fen~tre? 
Is-it that he opened the window? 
??Ce qui rafrMchira la piece 
Which will cool the room 
Did he open the window? Which will cool 
the room 
The remaining problem is that DONC accepts ques- 
tions on its right, as in (2-c). DONe does not accept 
just any question, however, but only those questions 
which convey some propositional link between one of 
the possible answers and the proposition/judgment 
on the left. In (2-c), in view of the fact that the 
speaker did not receive the report, it is more plau- 
sible, other things being equal, that the department 
did not send it than the contrary. The constraint 
that the proposition on the left should impinge on 
the possible answers to the question explains why 
(2-b) is strange. My (not) watching the TV can- 
not possibly exert any influence on the result of the 
game. The observations show that DMs of the DONC 
class connect speech acts only if the left speech act is 
a judgment and conveys information which renders 
the right speech act propositionally successful. We 
define a speech act to be propositionally successful 
if the states of affairs it represents as true or pre- 
supposes to be possible in a given (set of) world(s), 
by means of its propositional content, are actually 
true or possible in this (these) world(s). The restric- 
tion by means o/its propositional content is essen- 
tial. It distinguishes between propositional success 
with conditional structures is poor. See (Jayez and Rossari, 
1998) for a discussion of this problem. 
4Recall that we consider here the deductive use of donc. As 
shown in (Rossari and ,)ayez, 1997), DONC may follow ques- 
tions when it hm a rephrasing use corresponding to in other 
~errns (Tanaka, 1997). Deductive consequence connectives, 
however, are strange after questions. 
74 
and pragmatic felicity. The question in (2-a) is felici- 
tous if we assume that the speaker does not know the 
answer. But it is not necessarily propositionally suc- 
cessful given the first assertion I couldn't watch the 
TV. The possibility that the Red Sox won is neither 
implied nor entailed in any reasonable sense by the 
first sentence. DONe resists the consequence relation 
in this case because it does not 'see' speech acts as 
such, but their underlying informational structure. 
So, the semantic/pragmatic distinction is of no avail 
in the case of DONC. We need to construct specific 
objects to which DONC is sensitive. This sensitiv- 
ity constitutes the profile of DONC and of its mates 
( alors and par consgquent). 
The difference on the left between questions and 
the other speech acts points to a notion of dynamic- 
ity: assertions and imperatives update information 
structures, questions just test them, that is, check 
that certain conditions are satisfied. Veltman's up- 
date logic (Veltman, 1996; Groeneveld, 1995) pro- 
vides a convenient framework for studying the dy- 
namics of information at an abstract level. Roughly, 
updating an information state with an expression ¢ 
amounts to suppress all worlds where -~¢ is true. An 
expression Might ¢ holds in an information state if 
the state is consistent with ¢. Unfortunately, the 
difference between a possibility Might ¢ introduced 
by an assertion and that associated with a question 
is extremely difficult to express in this framework. 
There is no substantial difference between the static 
truth of Might ¢ (a test triggered by a question) 
and a dynamic update with Might ¢ (an assertion 
of possibility, as in Mary is late, so she might have 
missed the train). In the next section, we describe 
informally a modification of the framework which 
allows us to take into account this difference. 
2.4 Speech.acts and DONC 
An information state is a set of worlds (epistemic 
alternatives, possibilities). We consider the basic 
epistemic objects to be sets of information states. 
Information states and updates in Veltman's sense 
are called V-states and V-updates. Non-modal as- 
sertions (without Might) update a set of states by 
V-updating each member of this set (i.e. each V- 
state). Imperatives have a similar effect, but they 
bear on a set of ideal future V-states. Might ¢ as- 
sertions update states by withdrawing every V-state 
where Might ¢ is false. Questions only test whether 
there is some V-state in which a given appropriate 
answer is possible. So, they do not update anything 
in a strong sense (they are static or non-eliminative). 
However, questions, like genuine updates, are func- 
tions: applied to a state, they return this state or the 
absurd state (the empty set of V-states). Consider 
the two examples below. 
(6) a. It's not Paul, neither Henry, so who did it? 
b. This is obvious, so who would say the con- 
trary? 
In (6-a) and (6-b), the speaker seems to be prepared 
to accept Nobody you might know and Nobody as ap- 
propriate answers. It is often the case that questions 
impose a hierarchy of speaker-oriented expectations 
on the set of appropriate answers. We will speak of 
expected answers in this case. The effect of questions 
is to test whether appropriate answers are possible. 
When the question does not imply some preference 
of the speaker, the set of expected answers and the 
set of appropriate answers coincide. 5 
Let O(¢) DONC O'(¢) be the logical form of a X 
DONC Y construction, where O and O' are opera- 
tions (updates, etc.) on ¢ and ¢. DONC signals 
that there is some set of rules, say R, such that the 
possibility of updating/testing successfully the way 
we do on the right (O'(¢)) is predictable from the 
update on the left (O(¢)). DONC warns us that, 
for some R, R and O(¢) jointly predict that O'(¢) 
cannot always fail. 6 In other terms, DONC connect 
operations of certain kinds, not propositional con- 
tents, nor speech acts in the traditional sense. This 
is because speech acts signal operations that they 
are sometimes (mis)taken for the arguments of the 
D O N C-relation. 
3 A dynamic model of profile 
3.1 Basics 
In update semantics, information states are sets of 
worlds. Updating an information state with some 
formula ¢ consists in eliminating from the informa- 
tion state all the worlds where ¢ does not hold. 
Def. 1 --Information states and updates 
Let P be a set of atomic propositions p, q .... and B(P) 
the set of boolean combinations of members of P. Mem- 
bers of B(P) are called expressions and axe denoted by 
¢, ~b,.... A world (w, w',... ) is a set of expressions. A 
V-state (s, s',... ) is a set of worlds. 
An expression ¢ holds in a world w, in symbols w ~ ¢, 
iff ~ E w. There is no expression ¢ and no world w such 
that w ~¢andw~¢. 
The update of s with ¢, in symbols s + ¢, is defined by: s+p= {w:w esAw ~p},s+~¢= s-{w:w ~¢}, 
s + ¢ V ~ = s + ¢ U s + ¢. Usual boolean equivalences 
hold. ¢ is called the update expression. 
A V-state s accepts an expression ¢, in symbol s If- ¢ 
iff s ÷ ¢ = s. A V-state s tolerates an expression ¢ iff 
s+¢¢0. 
5In a series of works, Ginzburg has proposed to extend the 
notion of appropriate answer used in the current literature 
on questions (see Ginzburg 1998 for a global presentation). 
Assessing the (possible) usefulness of this extension for our 
current purpose is beyond the scope of this paper, however. 
We ignore also, for space reasons, the problem of the 'negative 
value' of questions (Ducrot 1984, 227-228). 
6That the DONC sentence does not (always) sound redun- 
dant comes from the fact that the rules are not explicitly 
indicated, but are to be reconstructed via some abductive process. 
75 
Note that the empty V-state (or absurd V-state) accepts 
anything and tolerates nothing. 
This basic language is extended by considering ex- 
pressions of possibility of the form Might ¢. The 
update notion is extended as follows. 
Def. 2 --Update for Might expressions 
s + Might q~ : s if s + ¢ -~ @, O otherwise. 
Obviously, for s ¢ 0, s tolerates ~ iff s tolerates Might ¢, 
and s accepts Might ~b iff s tolerates Might ¢. 
3.2 Information states 
An information state (henceforth simply state) is a 
set of V-states. We distinguish two types of states 
corresponding to assertions and imperatives. They 
are noted S ~ss~t and S i'np respectively. A boolean 
expression without Might is called classical. A state 
accepts ¢ iff each of its V-states accepts ¢. 
Def. 3 -- Assertive and imperative updates 
The update of S ~sse~t with a classical expression ¢, noted 
S °'s~' ~q~, is the set of non-empty V-states s such that, 
for some s' in S ~se~t. s = s' + ¢. 
The update of S a'~'~ with Might ~, where ¢ is classi- 
cal, noted S ..... ~ ~ Might ¢, is the set of V-states s in 
S ..... * such that s tolerates ~b. 
The update of S ~'~p with ~b, noted S "~ ~¢, is defined as 
in the S a~'~'* case, provided that S ~mt' does not accept 
¢, in which case the update returns the empty set. 
The conditional update of S imp with ¢, noted S ''~p ~ ¢, 
returns S imp itself if S ~mp accepts ~b, and S i'~p ~ ¢ oth- 
erwise. 
The conditional update of S ~ is not different from 
the standard update: S ~ ~c ¢ = S~ ~ ¢. 
When the update of 5 with ¢ is (not) the empty set, we 
say that the update fails (succeeds). When S ~ Might 
succeeds, we say that S tolerates ¢. ~b is called the up- 
date expression. 
Assertive updates with classical expressions consist 
in V-updating each member of the state with the 
expressions. For Might ¢ expressions, we keep only 
the V-states where ¢ is not a priori excluded. Im- 
perative updates with ¢ also amount to force the 
realization of ¢, whenever it is not already accepted. 
A global state S is a pair (S assent, S'm~). Global 
states are subject to two conditions on imperative 
states. A faithfulness condition ensures that im- 
perative states reflect assertive states: every expres- 
sion accepted in an assertive state is also accepted 
in the associated imperative state. So, imperative 
states are 'realistic': they take true states of affairs 
into account. To avoid conflicts, we use conditional 
updates for imperatives: S imp is not updated with 
¢ ff it contains ¢. The second condition, labelled 
Must ~ Might, stipulates that an obligatory state 
of affairs is always possible. In a more intuitive form, 
one does not issue commands which cannot be exe- 
cuted. 7 
7See (yon Wright, 1971) on this and related topics. Must¢ 
expressions are considered to be classical in the context of this paper. 
Def, 4 -- Must ~ Might 
If S accepts Must ¢, S ~ Might ¢ succeeds. 
Def. 5 -- Global states 
A global state S is a pair (SaS'ert,S imp) where every 
expression accepted in every V-state of S ~sert is 
accepted in every V-state of S imp. A global state 
(S,S') is degenerate when S or S' is the empty set. It 
accepts an expression ~b when S and S' accept ¢ 
Def. 6 -- Propositional denotation 
The propositional denotation of a sentence P, noted 
\[p\]i, is a set of pairs of global states, where the second 
member of each pair is obtained by updating/testing 
the first member. 
If the sentence P consists in asserting that ¢, 
S? .... ' $ ¢ and S~ rnp = S~ rnp @c ¢}. 
If the sentence P consists in commanding that ¢, 
l\kul ~ ~-'1 \]1 k'-.,'l ' ~"'2 11 : v2 : 
s; ~ • ¢}. 
If the sentence P is a question which respect to 
which @ is an answer, \[P\]~'~ = {((S ..... ~,S'~P), 
(S ..... *, S'mP)) : S ..... * tolerates ¢}. 
To shorten notation, we write S ~ ¢ instead of 
(S ..... t $ ~b, S "~p ~c ¢) when S = (S ..... *, S"~P). 
The faithfulness condition is implemented by impos- 
ing a parallel update on S ~e~* and S i'~p in asser- 
tions. The definition separates updates and tests. 
Updates correspond to assertions and imperatives. 
They consist in changing V-states by eliminative 
V-updates. Tests correspond to questions. They 
consist in checking that a state tolerates a certain 
expression. Since, in this case, the expression is not 
uniformly true nor possible across V-states, it can- 
not provide a stable premise from which to draw a 
conclusion. This explains why consequence connec- 
tives, which mimic the game of drawing conclusions 
from premises, cannot be preceded by questions in 
monologues. Note that, in line with the remarks of 
section 2.3, we do not consider the denotation of sen- 
tences in general, but only those denotations (propo- 
sitional denotations) which are 'seen' by DONC. 
3.3 Rules 
We will not attempt to discuss here the nature of 
the commonsense rules and inference schemas which 
are used in theories of semantic interpretation. In 
the context of this paper, we only need to make two 
simplistic assumptions. 
1. A rule is an implicative structure of form ¢1 A 
... A ¢,~ ~ ¢, with its traditional semantics: ~b is 
true whenever ¢1 ... ¢n are. 
2. The set of rules does not form a theory in any 
logically interesting sense. It is just a package of 
resources. We can freely use any subset of rules to 
obtain a given conclusion and we have no warranty 
that the set of rules is classically consistent, s This 
S A well-known cause of inconsistency is the coexistence in 
a rule database of monotonic rules like R1 and R2:R1 -~ ~b 
76 
can remedied by imposing a non-monotonic struc- 
ture on the inferential relation ~ as in (Veltman, 
1996). However, this is not a move we will consider 
here. We will rather focus on the definition of an 
appropriate entailment relation. We need a slightly 
more subtle notion than that of entailment between 
expressions. The next definition says that some op- 
eration (update/test) entails some other operation 
modulo "R whenever successfully executing the first 
entails modulo ~ that we can successfully execute 
the second. 
Def. T -- Operation entailment 
Let 7~ be a set of rules and O(¢) and 0'(¢) two opera- 
tions of update or test with ¢ and ¢, we say that O(¢) 
T~--entails O'(¢) iff, for every global state S, applying 
O(¢) to S results in a state S = O(¢)\[S\] for which there 
exists a rule r = ¢ =~X in T~ such that, if S" = S' ~B r 
is non-degenerate, O'(¢)\[S"\] is non-degenerate. 
Since operations correspond to sets of pairs of global 
states which themselves correspond to sentences, the 
last definition readily extends to sentences and prac- 
tically gives us the denotation of DONC. 
3.4 DONC semantic profile 
We now define the denotation of a sentence pair of 
form P DONC Q, where DONC has its deductive sense. 
It is the set of pairs of global states (S,S") such 
that there is an intermediate global state S' that one 
reaches from S by a conditional P-update and whose 
update by a finite subset of 7~ warrants a successful 
conditional Q-update or Q-test. We require the op- 
erations to be conditional because we want to draw 
a distinction between cases where imperative speech 
acts are infelicitous in view of the context and cases 
where conditions on DONC are not satisfied. E.g., 
a command that ¢ is infelicitous if ¢ already holds. 
However, the same command is not necessarily in- 
compatible with the constraints on DONC. 
Def. 8 -- DONC semantic profile 
Let 7~ a set of rules, ¢ and ~b two expressions. I 
P DONC Q\] with respect to 7~, ¢, ~b is the set of pairs 
S, S") such that: 
a. O(~) is the conditional version of the operation asso- 
ciated with P and is an update,90 ' (¢) is the conditional 
version of the operation associated with Q. 
b. There exists S' such that (S,S') E \[p\]1,~ and 
<s', s") e \[q\] 
c. O(¢) T~-entails O'(¢). 
To motivate informally this definition, consider (2-b) 
again. The first assertion results in updating S~ ''~t 
and ¢irnp with an expression not watch TV. This 
\[¢assert oimP~ results into a state v~2 ,o 2 ; which accepts 
not watch TV. Let us assume that we have a rule 
¢, R2 = ¢ ^ X ~ "~¢. When ¢ and X are both true ¢ and ~g, 
are both true. 
9Actually, we could eliminate this condition by defining a 
more general notion of stability, but this would require some 
extra technical machinery. 
in 7~: not watch TV ~ not know result. Then, 
~,mp with the rule results in updating S~ 8serf and ~,2 
a global state where the two members accept not 
know result. The question Did the Red Sox win is 
interpreted as connected with answers like Red Sox 
win or Red Sox not win. But, clearly, the fact that 
not know result is accepted does not warrant that 
Red Sox win is tolerated by any V-state in the ques- 
tion test on S~ sSert. The same holds for Red Sox 
not win. So, we are in no position to conclude that 
the test will be successful, unless we ascribe to the 
sentence some contrived interpretation. 
The definition distinguishes between (i) the con- 
ditional operations which are used to check out 7~- 
entailment and (ii) (absolute) operations associated 
with P and Q. This allows for situations in which 7~- 
entailment holds, but there are still problems with P 
and/or Q, which is precisely the case in (4-c). In the 
next section, we show how the proposed constraints 
shed light upon other observations. 
4 Applications 
Assertion-Imperative 
This the (4-b) case. • 
You are late : (S~'"'t,S'l '~p) ---+ = 
¢irnp ¢imp ec late) (by def. 6 S~ ssert ~ late, ~2 : ~1 
and 8). 
We assume a rule r: late ~ Must highway. When 
somebody is late, she must take the highway (in 
certain circumstances). 
¢irnp ~c r) accepts 2vlust highway. (S~ .... t • r, ~2 
Take the highway : (S ~r, S~mP~BCr~.BChighway) ~sser~ 
> • r, s; # ¢). 
Success is warranted because the principle 
Must ~ Might entail that any conditional 
update with highway will be succesful. Of course, 
(4-b) could be issued in a context where the 
addresse is already on the highway. It would then 
be infelicitous, but DONC is not responsible for this 
communication clash. 
Imperative-Imperative Let us explain the 
contrast (4-c)-(4-d). In (4-c), we have: 
Be on time : (S 1 ,S 1 ) ~ = 
sassert ¢irnp ~irnp ec time). 1 , ~2 = '-,1 on 
We assume there is a rule r = on time ~ highway. 
This rule is intended to mean that somebody who 
is on time is on the highway or took the highway. 
q~mp ec r) accepts highway. (S~ 's~'~ • r, ~2 
\[ Sasser~ m r S~mP eCr~ehighway) Take the highway : ~ 2 ~ , 
¢imp • r, # ¢)" 
7~-entailment holds, but the imperative update 
associated with Q (=take the highway) is bound 
~imp to fail, since ~'2 accepts highway. This is a case 
where satisfying the DONC constraint amounts to an 
77 
illocutionary suicide: the rule which licenses DONC 
forbids us to update non-conditionally on the right 
sentence. A similar explanation goes for (4-e). If 
the rule links the event of taking the highway and 
its result (being on time), any update with on time 
fails or is infelicitous, since the addressee is asked to 
obtain a result (being on time) which is anyway, in 
the imperative world, an unescapable consequence 
of what she 'did' (taking the highway) in the same 
world. 
In (4~d), we have: 
Try to be on time: (S~ sser~,S~ rnp) ~ (S~ ssert = 
Sasser~ ¢irnp imp c time). 1 ,"2 = S 1 $ try on 
We assume that there is a rule r = try on time 
Must highway, which is intended to mean that 
somebody who wants to be on time is going to take 
the highway. 
(S~ "Se't @ r, ~mp @c r) accepts Must highway. ~2 
Take the highway: (ST'BettOr, S~mP $Cr~Ch£ghway) 
~irap (S~ s'er~ $ r,~ ¢ ~). Success is warranted 
because of the Must ~ Might constraint of defini- 
tion 4. 
As noted above, questions on the left are not 
updates and are thus blocked by def. 8. In con- 
trast, Might assertions are treated on a par with 
assertions. So, Paul might come, DONC he might 
meet Henry would analyzed with the help of rules 
like Might come ~ Might meet, possibly based 
over non-modal rules like come ~ meet in T~. Fi- 
nally, assertion-assertion structures are essentially 
unproblematic. 
5 Conclusion 
Although the analysis presented here is limited, it 
shows that the view of DMs as manifestations of very 
general communication-oriented DRs is oversimpli- 
fying. Some DMs are able to signal DRs only insofar 
as their own lexical constraints are satisfied. These 
constrains pertain to the semantic relation and to 
the argument types associated with particular DMs. 
An open question is whether the importance of se- 
mantic profile is particular to some class(es) of DMs. 
Consequence connectives are inferential, in the sense 
of (Jayez and Rossari, 1998). The other classes of 
inferential DMs are oppositive (yet, however) and 
rephrasing (anyway). In subsequent work, we will 
address primarily th e following questions. Is the im- 
portance of a specific semantic profile particular to 
the category of inferential DMs? Are the profile re- 
strictions inside the class of inferential DMs just the 
reflection of the inferential processes these DMs sig- 
nal, or have they a (partly) independent status? 

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