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<Paper uid="W98-0313">
  <Title>Discourse Relations versus Discourse Marker Relations</Title>
  <Section position="4" start_page="0" end_page="74" type="metho">
    <SectionTitle>
2 The profile problem
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="72" type="sub_section">
      <SectionTitle>
2.1 Observations
</SectionTitle>
      <Paragraph position="0"> Let us consider the following examples.</Paragraph>
      <Paragraph position="1">  (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).</Paragraph>
      <Paragraph position="2">  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, imperative) and the possibility of using DONC emerges from the examples.</Paragraph>
      <Paragraph position="3"> In (3-a), the second proposition appears as a consequence of the execution of the imperative, as evidenced 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.</Paragraph>
    </Section>
    <Section position="2" start_page="72" end_page="72" type="sub_section">
      <SectionTitle>
2.2 Speech acts and semantic profile
</SectionTitle>
      <Paragraph position="0"> 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 profile distinctions within theories of DRs. For instance, Sanders et al. (1992) use the primitive Source of Coherence with the two values Semantic and Pragmatic, corresponding respectively to a link between propositional contents and between illocutionary meanings (or speech acts). In Cause-Consequence or Consequence-Cause relations, the ~Such pseudo-imperatives are studied in (Clark, 1993).</Paragraph>
      <Paragraph position="1"> 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 between the propositional contents of the assertion and of the question: my watching the TV cannot influence 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 Instrument = 'the speaker asks whether p'. We could explain (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.</Paragraph>
      <Paragraph position="2"> Another variant of the same problem occurs when one tries to use commonsense DR categories like justification (Roulet et al., 1985; Mann and Thompson, 1988). DONC normally resists introducing a justification, 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).</Paragraph>
      <Paragraph position="3"> Knott (1996) proposes that semantic and pragmatic 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.</Paragraph>
      <Paragraph position="4"> 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 consistent with the impossibility of (3-b). The pragmatic intended effect is that some relation actually holds between the intended effects associated with the arguments. In (2-a), the intended effect of the assertion is that the addressee believes that the speaker did not watch TV. The intended effect of the question 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 second as one of its consequences. This seems to be the case in (2-b). Yet the linking is not natural.</Paragraph>
      <Paragraph position="5"> These hypotheses seem to suffer from calibration problems. The possible profiles they allow us to construct tend to overlicense or underlicense the observed combinations.</Paragraph>
    </Section>
    <Section position="3" start_page="72" end_page="74" type="sub_section">
      <SectionTitle>
2.3 Towards a dynamic notion of profile
</SectionTitle>
      <Paragraph position="0"> 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 situation is not real but only potential. Using accom- null 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 conclude 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.</Paragraph>
      <Paragraph position="1"> How is it that DONC seems to block accommodation in (3-b), although there is a clear Cause-Consequence relation between opening a window and getting some fresh air? Generally speaking, DONC requires that we construct an inferential bridge between the representation of the first sentence and that of the second sentence. In (3-b), obeying the command creates a potential world where the window is open. Assertions consist basi- null cally in updating a world with the information conveyed by the asserted sentence. So, they are functions from a state of some world to another state of the same world. This granted, there are several options.</Paragraph>
      <Paragraph position="2"> (i) The assertion in (3-b) is evaluated in the potential world where the window is open. There is no reason why the sentence should be odd.</Paragraph>
      <Paragraph position="3"> (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).</Paragraph>
      <Paragraph position="4"> (iii) The opening of the window and the assertion  are evaluated in different worlds. This could explain the oddness of (3-b).</Paragraph>
      <Paragraph position="5"> 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.</Paragraph>
      <Paragraph position="6"> Specifically, we make two assumptions.</Paragraph>
      <Paragraph position="7">  (i) DONC signals some consequence connection between two semantic constructs.</Paragraph>
      <Paragraph position="8"> (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.</Paragraph>
      <Paragraph position="9"> (i) is unobjectionable. One of the roles of a con- null sequence DM is to signal a consequence relation. Which notion of consequence is appropriate remains to be seen, however. From (i) we derive the observation 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 relation, the premise and the conclusion must have the same modal status (belong to the same world).</Paragraph>
      <Paragraph position="10"> Condition (i) echoes the current belief that questions 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 assertions and in contrast with questions, is evidenced by tt-,e following contrasts.</Paragraph>
      <Paragraph position="11"> (~} 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 questions 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 plausible, 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 cannot 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 presupposes 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 restriction by means o/its propositional content is essential. It distinguishes between propositional success with conditional structures is poor. See (Jayez and Rossari, 1998) for a discussion of this problem.</Paragraph>
      <Paragraph position="12"> 4Recall that we consider here the deductive use of donc. As shown in (Rossari and ,)ayez, 1997), DONC may follow questions when it hm a rephrasing use corresponding to in other ~errns (Tanaka, 1997). Deductive consequence connectives, however, are strange after questions.</Paragraph>
      <Paragraph position="13">  and pragmatic felicity. The question in (2-a) is felicitous if we assume that the speaker does not know the answer. But it is not necessarily propositionally successful 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 sensitivity constitutes the profile of DONC and of its mates ( alors and par consgquent).</Paragraph>
      <Paragraph position="14"> The difference on the left between questions and the other speech acts points to a notion of dynamicity: assertions and imperatives update information structures, questions just test them, that is, check that certain conditions are satisfied. Veltman's update logic (Veltman, 1996; Groeneveld, 1995) provides a convenient framework for studying the dynamics of information at an abstract level. Roughly, updating an information state with an expression C/ amounts to suppress all worlds where -~C/ is true. An expression Might C/ holds in an information state if the state is consistent with C/. Unfortunately, the difference between a possibility Might C/ 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 C/ (a test triggered by a question) and a dynamic update with Might C/ (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.</Paragraph>
    </Section>
    <Section position="4" start_page="74" end_page="74" type="sub_section">
      <SectionTitle>
2.4 Speech.acts and DONC
</SectionTitle>
      <Paragraph position="0"> An information state is a set of worlds (epistemic alternatives, possibilities). We consider the basic epistemic objects to be sets of information states.</Paragraph>
      <Paragraph position="1"> Information states and updates in Veltman's sense are called V-states and V-updates. Non-modal assertions (without Might) update a set of states by V-updating each member of this set (i.e. each Vstate). Imperatives have a similar effect, but they bear on a set of ideal future V-states. Might C/ assertions update states by withdrawing every V-state where Might C/ 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).</Paragraph>
      <Paragraph position="2"> However, questions, like genuine updates, are functions: applied to a state, they return this state or the absurd state (the empty set of V-states). Consider the two examples below.</Paragraph>
      <Paragraph position="3">  (6) a. It's not Paul, neither Henry, so who did it? b. This is obvious, so who would say the contrary? null  In (6-a) and (6-b), the speaker seems to be prepared to accept Nobody you might know and Nobody as appropriate 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(C/) DONC O'(C/) be the logical form of a X DONC Y construction, where O and O' are operations (updates, etc.) on C/ and C/. 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'(C/)) is predictable from the update on the left (O(C/)). DONC warns us that, for some R, R and O(C/) jointly predict that O'(C/) cannot always fail. 6 In other terms, DONC connect operations of certain kinds, not propositional contents, 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</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="74" end_page="76" type="metho">
    <SectionTitle>
D O N C-relation.
3 A dynamic model of profile
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="74" end_page="75" type="sub_section">
      <SectionTitle>
3.1 Basics
</SectionTitle>
      <Paragraph position="0"> In update semantics, information states are sets of worlds. Updating an information state with some formula C/ consists in eliminating from the information state all the worlds where C/ does not hold.</Paragraph>
      <Paragraph position="1"> 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. Members of B(P) are called expressions and axe denoted by C/, ~b,.... A world (w, w',... ) is a set of expressions. A V-state (s, s',... ) is a set of worlds.</Paragraph>
      <Paragraph position="2"> An expression C/ holds in a world w, in symbols w ~ C/, iff ~ E w. There is no expression C/ and no world w such that w ~C/andw~C/.</Paragraph>
      <Paragraph position="3"> The update of s with C/, in symbols s + C/, is defined by: s+p= {w:w esAw ~p},s+~C/= s-{w:w ~C/}, s + C/ V ~ = s + C/ U s + C/. Usual boolean equivalences hold. C/ is called the update expression.</Paragraph>
      <Paragraph position="4"> A V-state s accepts an expression C/, in symbol s If- C/ iff s / C/ = s. A V-state s tolerates an expression C/ iff  dant comes from the fact that the rules are not explicitly indicated, but are to be reconstructed via some abductive process.  Note that the empty V-state (or absurd V-state) accepts anything and tolerates nothing.</Paragraph>
      <Paragraph position="5"> This basic language is extended by considering expressions of possibility of the form Might C/. The update notion is extended as follows.</Paragraph>
      <Paragraph position="6"> Def. 2 --Update for Might expressions s + Might q~ : s if s + C/ -~ @, O otherwise.</Paragraph>
      <Paragraph position="7"> Obviously, for s C/ 0, s tolerates ~ iff s tolerates Might C/, and s accepts Might ~b iff s tolerates Might C/.</Paragraph>
    </Section>
    <Section position="2" start_page="75" end_page="75" type="sub_section">
      <SectionTitle>
3.2 Information states
</SectionTitle>
      <Paragraph position="0"> 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 C/ iff each of its V-states accepts C/.</Paragraph>
      <Paragraph position="1"> Def. 3 -- Assertive and imperative updates The update of S ~sse~t with a classical expression C/, noted S deg's~' ~q~, is the set of non-empty V-states s such that, for some s' in S ~se~t. s = s' + C/.</Paragraph>
      <Paragraph position="2"> The update of S a'~'~ with Might ~, where C/ is classical, noted S ..... ~ ~ Might C/, is the set of V-states s in S ..... * such that s tolerates ~b.</Paragraph>
      <Paragraph position="3"> The update of S ~'~p with ~b, noted S &amp;quot;~ ~C/, is defined as in the S a~'~'* case, provided that S ~mt' does not accept C/, in which case the update returns the empty set.</Paragraph>
      <Paragraph position="4"> The conditional update of S imp with C/, noted S ''~p ~ C/, returns S imp itself if S ~mp accepts ~b, and S i'~p ~ C/ otherwise. null The conditional update of S ~ is not different from the standard update: S ~ ~c C/ = S~ ~ C/.</Paragraph>
      <Paragraph position="5"> When the update of 5 with C/ is (not) the empty set, we say that the update fails (succeeds). When S ~ Might succeeds, we say that S tolerates C/. ~b is called the update expression.</Paragraph>
      <Paragraph position="6"> Assertive updates with classical expressions consist in V-updating each member of the state with the expressions. For Might C/ expressions, we keep only the V-states where C/ is not a priori excluded. Imperative updates with C/ also amount to force the realization of C/, 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 imperative states reflect assertive states: every expression 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 C/ ff it contains C/. 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 executed. 7 7See (yon Wright, 1971) on this and related topics. MustC/ expressions are considered to be classical in the context of this paper. Def, 4 -- Must ~ Might If S accepts Must C/, S ~ Might C/ succeeds.</Paragraph>
      <Paragraph position="7"> 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 C/ 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.</Paragraph>
      <Paragraph position="8"> If the sentence P consists in asserting that C/, S? .... ' $ C/ and S~ rnp = S~ rnp @c C/}.</Paragraph>
      <Paragraph position="9"> If the sentence P consists in commanding that C/, l\kul ~ ~-'1 \]1 k'-.,'l ' ~&amp;quot;'2 11 : v2 : s; ~ * C/}.</Paragraph>
      <Paragraph position="10"> If the sentence P is a question which respect to which @ is an answer, \[P\]~'~ = {((S ..... ~,S'~P), (S ..... *, S'mP)) : S ..... * tolerates C/}.</Paragraph>
      <Paragraph position="11"> To shorten notation, we write S ~ C/ instead of (S ..... t $ ~b, S &amp;quot;~p ~c C/) when S = (S ..... *, S&amp;quot;~P). The faithfulness condition is implemented by imposing a parallel update on S ~e~* and S i'~p in assertions. The definition separates updates and tests. Updates correspond to assertions and imperatives.</Paragraph>
      <Paragraph position="12"> 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 cannot provide a stable premise from which to draw a conclusion. This explains why consequence connectives, 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 sentences in general, but only those denotations (propositional denotations) which are 'seen' by DONC.</Paragraph>
    </Section>
    <Section position="3" start_page="75" end_page="76" type="sub_section">
      <SectionTitle>
3.3 Rules
</SectionTitle>
      <Paragraph position="0"> 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.</Paragraph>
      <Paragraph position="1">  1. A rule is an implicative structure of form C/1 A ... A C/,~ ~ C/, with its traditional semantics: ~b is true whenever C/1 ... C/n are.</Paragraph>
      <Paragraph position="2"> 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  can remedied by imposing a non-monotonic structure 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 operation (update/test) entails some other operation modulo &amp;quot;R whenever successfully executing the first entails modulo ~ that we can successfully execute the second.</Paragraph>
      <Paragraph position="3"> Def. T -- Operation entailment Let 7~ be a set of rules and O(C/) and 0'(C/) two operations of update or test with C/ and C/, we say that O(C/) T~--entails O'(C/) iff, for every global state S, applying O(C/) to S results in a state S = O(C/)\[S\] for which there exists a rule r = C/ =~X in T~ such that, if S&amp;quot; = S' ~B r is non-degenerate, O'(C/)\[S&amp;quot;\] 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 practically gives us the denotation of DONC.</Paragraph>
    </Section>
    <Section position="4" start_page="76" end_page="76" type="sub_section">
      <SectionTitle>
3.4 DONC semantic profile
</SectionTitle>
      <Paragraph position="0"> We now define the denotation of a sentence pair of form P DONC Q, where DONC has its deductive sense.</Paragraph>
      <Paragraph position="1"> It is the set of pairs of global states (S,S&amp;quot;) 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 operations 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 C/ is infelicitous if C/ already holds.</Paragraph>
      <Paragraph position="2"> However, the same command is not necessarily incompatible with the constraints on DONC.</Paragraph>
      <Paragraph position="3"> Def. 8 -- DONC semantic profile Let 7~ a set of rules, C/ and ~b two expressions. I P DONC Q\] with respect to 7~, C/, ~b is the set of pairs S, S&amp;quot;) such that: a. O(~) is the conditional version of the operation associated with P and is an update,90 ' (C/) is the conditional version of the operation associated with Q.</Paragraph>
      <Paragraph position="4"> b. There exists S' such that (S,S') E \[p\]1,~ and &lt;s', s&amp;quot;) e \[q\] c. O(C/) T~-entails O'(C/).</Paragraph>
      <Paragraph position="5"> To motivate informally this definition, consider (2-b) again. The first assertion results in updating S~ ''~t and C/irnp with an expression not watch TV. This \[C/assert oimP~ results into a state v~2 ,o 2 ; which accepts not watch TV. Let us assume that we have a rule C/, R2 = C/ ^ X ~ &amp;quot;~C/. When C/ and X are both true C/ and ~g, are both true.</Paragraph>
      <Paragraph position="6"> 9Actually, we could eliminate this condition by defining a more general notion of stability, but this would require some extra technical machinery.</Paragraph>
      <Paragraph position="7"> 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 question 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.</Paragraph>
      <Paragraph position="8"> The definition distinguishes between (i) the conditional 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.</Paragraph>
    </Section>
  </Section>
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