Aug 8, 2007 - 6See Kaufmann (2000) for a similar proposal. ..... A: He must have changed his plans then. ...... In: Faller, Martina, Stefan Kaufmann, & Pauly,.
Context Structure for Dialogues Kim B. Bruce Pomona College
Donka F. Farkas UC Santa Cruz
August 8, 2007
1
Introduction
The foundation of current work in formal pragmatics is Stalnaker (1978), where it is suggested that discourse unfolds against an ever changing background made up of a set of propositions already accepted by the discourse participants (the common ground). The essential effect of assertions on the context in which they are made, according to Stalnaker, is to add the content of the assertion to the common ground, ‘provided’, Stalnaker adds, ‘that there are no objections from the other participants in the conversation.’ Assertion, then, is a proposal to change the context by adding the propositional content of the asserted sentence to the common ground of the conversation.1 The proposal nature of assertive conversational moves, in our view, has not been given the weight it deserves. Our main goal in this paper is to remedy this shortcoming. Section 2 is devoted to developing an expanded context structure that allows us to capture the proposal nature of assertions and makes room for conversational moves that accept or reject them, and Section 3 gives the notation to be used in the rest of the paper. We then explore the consequences of this structure with respect to assertions and polar questions (Sections 4 - 6). In Section 7 we turn to the consequences of our proposals for capturing similarities and differences between moves that react to assertions and moves that react to polar questions and in Section 8 we examine some consequences for the treatment of presuppositions. Section 9 provides an extended example of the use of context states, and Section 10 concludes by summing up the main results of the paper and by looking ahead at research directions it opens. In the rest of this section we pose the questions the paper is meant to provide answers for.
1.1
Assertions and Questions
Our empirical focus is to capture similarities and differences between a series of conversational moves. First, let us consider the move of making an assertion (uttering a declarative sentence with falling intonation) and that of asking an ordinary polar question by means of uttering a polar interrogative sentence. On the similarity side, note that both types of moves allow the same reactions, as exemplified in (1) and (2): (1)
A: Sam is home. B: Yes/Yeah, he’s home./No, he isn’t home.
1 A large amount of work since Stalnaker (1978) has been devoted to the need to refine the notion of context so as to get to the level of discourse referents. The issues we are dealing with here are not relevant to these concerns and therefore they will be ignored below.
1
(2)
A: Is Sam home? B: Yes/Yeah, he’s home./No, he isn’t home.
On the differences side, note that a ‘no’ answer is more dramatic in (1) than in (2). While B may be accused of being a bit laconic and rude in (3), in (4) there seems to be something amiss with both A and B (assuming A’s utterances are made with falling intonation): (3)
A: Is Sam home now? B: No, he isn’t. A: Has Lee started dinner yet? B: No, he hasn’t. A: Is there food in the fridge? B: No, there isn’t.
(4)
A: Sam is home now. B: No, he isn’t. A: Lee has started dinner already. B: No, he hasn’t. A: There is food in the fridge. B: No, there isn’t.
The difference between negative reactions to assertions and negative reactions to questions affects their formal properties as well. Thus, there are negative answer forms that are appropriate when responding to a question but not when reacting to an assertion. In Romanian, the particle ba is possible when contradicting a positive assertion but not in a negative answer to a positive question: (5)
A: Horea e acas˘a? ‘Is Horea home?’ B: Nu, nu e./*Ba nu, nu e. ‘No, he isn’t.’
(6)
A: Horea e acas˘a. ‘Horea is home.’ B: Nu, nu e./Ba nu, nu e. ‘No, he isn’t.’
Note also that, typically, assertions do not necessarily require a reaction (though they are consistent with one), while also typically, questions do require an audience reaction.2 The formal treatment of assertions and polar questions should help capture both the overlap and the differences in possible addressee reactions. Next, note that various types of assertions have radically different effects on the conversation in which they occur. The utterances of A and B in (1) above are both assertions and yet their conversational effects are sharply different. A’s move is initiative in that it proposes the addition of a new proposition to the common ground. B’s move, on the other hand, is reactive: it is offered to signal that B accepts A’s proposal. The particles yes and no in these examples, we suggest, signal precisely this reactive nature of the move. Thus, it would be inappropriate for A to start the conversation with the utterances in (7): (7)
a. b.
Yes, Sam is at home. No, Sam is not at home.
There are two inter-related questions that have been raised so far: (i) how to account for the similarities and differences between ordinary assertions and ordinary polar questions when it comes to addressee reactions; 2
Atypical cases are assertions flagged by a special interrogative tag that requires addressee reaction, and questions specially marked making an answer optional, or rhetorical questions that do not have to be answered.
2
(ii) how to account for the similarities and differences between initiating and reactive assertions. With respect to the first issue, under the standard view, the C(ontext)C(hange)P(otential) of assertions is the addition of their propositional content to the common ground (or to their author’s commitment set, in Gunlogson 2001). As a result, assertions are taken to eliminate from the context set the worlds that are not in their denotation. The CCP of questions, on the other hand, is the partitioning of the context set into cells that correspond to full answers to the question. Under these assumptions, there is no reason to expect significant similarities in reactions to these two move types. With respect to the second issue, under standard assumptions B’s assertion in (1) is uninformative in the affirmative case, and inconsistent in the negative case. And yet, in the former instance B’s move serves a conversational purpose that differs from mere repetition. In the latter instance, although B’s move places the conversation in an inconsistent state, B herself is most likely innocent of the charge of inconsistency (unless she previously committed to the proposition that Sam is at home now). These simple examples point to the necessity of refining our theoretical tools. Below we propose an articulated context structure which allows a finer-grained characterization of the contextual effects of assertions and questions.
1.2
Special discourse states, special discourse moves
There are two further types of issues that motivate our proposals. One is the necessity of distinguishing between discourse states that can serve as natural end states of a conversation and discourse states that can not. Thus, the state of a discourse immediately after a question has been asked, but before the conversation participants have had a chance to react to the question would not be a natural end state. On the other hand, a context state that results after all the issues that have been raised up to that point have been settled or at least addressed to everybody’s satisfaction, is one where the conversation can gracefully end. The notion of conversational table that we introduce below is crucial in capturing this difference. With respect to special moves, note that until now we have talked of questions and initiating assertions raising issues and reactive moves that address the issue. Such reactive moves may lead to settling the issue to everybody’s satisfaction and thereby increasing the common ground. There are, however, more exotic conversational moves that we have to be able to model. Participants in a conversation may disagree on an issue and then decide to get out of the impasse that the disagreement creates by ‘agreeing to disagree’. Similarly, a question can be removed from the discourse table not only by settling it but also by the participants agreeing not to pursue it further. It is desirable to make room for such conversational moves, and at the same time capture in what way they differ from moves that resolve a question or accept an assertion. In the next section we propose an expanded context structure and then explore its consequences with respect to the issues mentioned above.
2 2.1
An expanded context structure Context components
We follow here Stalnaker (1978) in taking the common ground to be an essential component of context structure. The common ground of a context state K, cgK , is the set of propositions that all the participants in the conversation have publicly accepted as being true of the world in which the conversation takes place, wK . The propositions in the common ground are joint public commitments. We also follow here Stalnaker’s original insight, as developed in Gunlogson (2001), in assuming that the propositions that a participant publicly commits to during a conversation are entered on his or her commit3
ment list. In Gunlogson, the common ground is decomposed, as it were, into each participant’s commitment list, with the common ground itself being defined as an ancillary notion made up of the union of the participants’ lists. For her then, the main effect of assertions is to publicize their author’s commitment to the asserted proposition. For Stalnaker on the other hand, the main effect of assertions is to reach a context state where the asserted proposition is added to the common ground. We wish to capture both effects. We therefore separate the common ground as a special context component, while maintaining participant commitment lists as separate elements as well. A participant’s commitment list is made up of public commitments that have not (yet) become joint commitments. The common ground is made up of those propositions that have reached joint commitment status. If all that mattered was publicizing our commitments, there would be nothing strange about participants publicizing a series of mutually inconsistent commitments as long as each participant’s own commitments are consistent, as in (4) above. We therefore maintain that part of the effect of an assertion is to register the proposal of having the asserted proposition added to the common ground without in fact adding it yet to the current common ground. In order to capture the proposal nature of assertions (and that of other conversational moves), our contexts contain a special space we call the Table, where matters under discussion are entered. In this, we follow B¨uring (2003), Roberts (1996) and Ginzburg (1996), among others, who emphasize the role the question under discussion (QUD) plays in discourse. The Table is the part of the context structure that registers what is ‘at issue’. We assume that every conversational move that places an item on the Table brings with it a canonical way of removing that item from the Table. A way of removing an item from the Table counts as canonical if and only if it is a step that eventually leads to addition of information to the common ground. This, in effect, captures the Stalnakerian view that the wish to increase the common ground is one of the main engines that drives discourse. We treat as canonical reactions conversational moves whose input contexts have a nonempty Table and whose effect directs the conversation towards context states where the Table is emptied in a way that leads to an increase in the common ground. Placing an item on the Table then projects a set of future context states arrived at by performing the operations involved in the canonical removal of the relevant item from the Table. We represent them here as a set of future common grounds. Assertions project future common grounds where the asserted proposition is true. Questions project a set of priviledged future common grounds that result after possible answers to the question have been added to the common ground. We use a special context space, called the p(rojected) s(et) to record the projected common grounds that result from canonical removals of the items currently on the conversational Table. When the Table is empty, the ps contains the current common ground as its only element. When the Table is not empty, the common grounds in ps are computed based on what counts as a canonical removal of the items from the Table.3 Because canonical removals of items from the Table result in additions to the common ground, projected common grounds are supersets of the current common ground. In particular, all sets in the ps of a context structure will be supersets of that structure’s common ground. We represent the context K of a conversation between two participants A and B in diagrams of the form below: 3
Our ps is different from the projection set of Gunlogson (2001), which contains all non-empty subsets of the current context
set.
4
A DCA Common Ground cg
Table S Projected Set ps
B DCB
Figure 1 In Figure 1, DCA and DCB are the sets of propositions A and B have individually publicly committed to and which are not yet joint commitments. The cg is the set of propositions that are joint commitments of the participants. The set of public commitments of a participant A is DCA ∪ cg. If a participant is sincere, the union of her commitment list and the common ground is a subset (hopefully a proper subset) of the propositions she actually holds as true of wK .4 The contents of the Table, S, are statements and questions still under discussion, while ps is a set of common grounds that reflects canonical ways of settling the issues on the Table. Given that commitments in a conversation are propositions taken by the relevant participants to be true of wK , for each participant X, the sets DCX and DCX ∪ cg have to be consistent.
2.2
Justification and uses of the expanded context structure
Before presenting the details of our proposals concerning assertions and polar questions in this new structure we briefly justify here its non-standard components. The separation of public commitments by participants is crucial in treating an assertion as a proposal to add the asserted proposition to the common ground. After A has asserted a sentence S with propositional content p, A is committed to p, but, until B has signaled acceptance, p is not yet in the common ground. Separating participants’ discourse commitments from the common ground is crucial in accounting for disagreements in coherent discourses. It is desirable, we suggest, to allow discourses to survive contradictions by allowing moves whereby participants agree to disagree. Assume A and B have agreed to disagree on p. The state of the discourse in this case is as in Figure 2, where s is the set of propositions in the common ground: A p Common Ground s
Table
B ¬p
Projected Set ps = {s}
Figure 2 Here then A is committed to p, B to ¬p but neither proposition is in the common ground.5 The context structure we assume allows us to define consistency at multiple levels, as in (8): (8)
a. b.
A context state K is globally consistent if and only if the propositions in cgK are consistent. A context state K is consistent relative to a participant X if and only if DCX ∪ cgK is consistent.
There are two sources of conversational crisis in this view. The first obtains when a discourse state K is 4 An important and difficult issue with which we will not deal here is what happens if participants are wrong, i.e., what happens if either commitment lists or the common ground contain propositions that are in fact false in wK . 5 The move of agreeing to disagree is defined formally in Section 4.2.2.
5
inconsistent at any of the two levels mentioned above. The second obtains when all common grounds in the projected set are inconsistent. In such a situation, one cannot empty the Table in a canonical way without reaching a globally inconsistent context state. Note that a context state can be consistent at both levels without the commitment lists of the participants being mutually consistent. In Figure 2 this is the case if s is consistent and if both p and ¬p are consistent with s. Such a discourse then is not in crisis. In order for A and B to remain consistent, A’s future commitments will have to be consistent with p, and B’s future commitments will have to be consistent with ¬p. Discourses therefore may stay globally consistent and have consistent participants even after public disagreements. This, we think, is a welcome result. Keeping commitment lists separate from the common ground allows us to capture what we take is a common conversational goal, namely increasing the store of information the conversational community has about the world in which the conversation takes place. For us, just as for Stalnaker, this amounts to increasing the common ground. As mentioned above, the Table plays a central role in capturing the proposal nature of ordinary assertions, and thus in making room for moves that accept or reject such assertions. It also plays a crucial role in characterizing the conversational move of ‘agreeing to disagree’ as well as in our account of various subtypes of assertions. We assume here that what is entered on the Table is a syntactic object. This assumption is needed because in order to develop a grammar for cross-turn conversation and ellipsis it is crucial to be able to refer to the grammatical form (and not just the propositional content) of immediately previous utterances. For instance, we will see in Section 6.3 that in Romanian ba da can only be uttered in reaction to an immediately previous utterance that places a negative sentence on the Table, while ba nu can only be uttered in reaction to a previous move that places a positive sentence on the Table: (9)
A: Horea bea bere. ‘Horea drinks beer.’ B: Ba nu, (nu bea)./*Ba da, nu bea. ‘No, he doesn’t.
(10)
A: Horea nu bea bere. ‘Horea does not drink beer.’ B: Ba da, (bea)./*Ba nu, bea. ‘Yes, he does.’
If we only had access to the propositional content of A’s utterance here we would have to assume that negative and positive propositions are distinguished, an assumption that one does not necessarily wish to make. Items on the Table form a stack.6 When the Table is not empty, the immediate goal of the conversation is to empty it, and therefore conversational moves that affect the Table must be relevant to whatever item is on the top of the stack. The stack discipline allows us to capture the tight connection between initiating conversational moves, such as an initiating assertion or question, and responding moves that address the issue an immediately preceding utterance has placed on the Table, a matter we come back to in Section 4.2 below. Finally, having the Table as a separate context structure component allows us to differentiate between context states that can be end states, i.e., states which can serve as natural endpoints of a discourse, and states that are not. The items on the Table are at issue. Therefore, as long as the Table is not empty the conversation is not in a stable state. When the Table is empty, there is no open issue and the only projected set is necessarily identical to the current common ground. Stable context states and possible end states are 6
See Kaufmann (2000) for a similar proposal. Other authors (see Ginzburg (1995)) prefer a partial order, but we have no need for the extra flexibility of redefining a partial order to reorder statements in the simple examples handled here.
6
defined below: (11)
Stable context state A context state K is stable if and only if its Table is empty.
(12)
Possible end state A context state K is a possible end state of a conversation if and only if it is stable.
We take it that a default conversational goal is to reach a stable output state whose common ground is larger than the common ground of the input state. As mentioned above, each conversational move that places an item on the Table steers the conversation towards a future state where the item is removed in such a way as to increase the common ground. We record these future states at the level of changes they bring to the common ground in the form of a set of common grounds we call the projected set. The projected set allows us to capture the intended changes to the common ground associated with a particular move. Recording these changes at the level of the projected set rather than the level of the current common ground allows us to capture the anticipatory nature of certain moves and at the same time makes room for conversational moves that react to them. The projected set assumes a central role in our treatment of conversational moves because it is at this level that the manipulative nature of these moves is captured. We need it crucially in characterizing what A’s proposal is when she makes her assertion, as well as what the questioner directs the conversation toward when he asks his question. There are, of course, many other possible choices in designing a context structure. For the matters we discuss here further additions such as the agendas of participants or public information about their private doxastic states are not necessary. As already mentioned, since we are not concerned with referential or anaphoric issues we also leave aside the question of registering discourse referents. We also note here that the information we do represent is redundant. In particular, the projected set can always be calculated from the common ground and the items on the Table stack. We nevertheless include these components in our representation for the sake of clarity and for emphasizing similarities between what we propose and earlier approaches. Maintaining the projected set as a separate component allows us to capture the fact that in our proposal the CCP of assertions and questions is essentially the same as traditionally assumed. The difference is located at the level of the context component affected. The projected set is also useful in allowing a simple characterization of the crisis the conversation reaches when a contradiction is placed on the Table. Finally, note that we are talking here in terms of removing items from the Table. Alternatively, if needed, one could opt for never removing items from the conversational Table but rather, of distinguishing between active and non-active items on the Table. Our choice is not crucial for the matters we discuss below.
3
Notation for manipulating context structures
Before turning to discussing assertions and polar questions, we define here the notation we use throughout the rest of the paper. The table T in a context structure is represented as a stack. The following notation is used to represent traditional stack operations on T : 1. push(S, T ) represents the new stack obtained by adding sentence S to the top of the stack T . 2. pop(T ) represents the stack obtained by popping off the top element of T . 3. top(T ) represents the top element of the stack T . 7
4. remove(S, T ) represents the stack obtained by removing the top-most occurrence of S from stack T . If S does not occur in T , then T is returned. Let ps = {cg1 , . . . , cgn } be a collection of sets of propositions (e.g., possible common grounds) and let p be a proposition. Then define ps ∪ p = {cg1 ∪ {p}, . . . , cgn ∪ {p}}. The operation P S(cg, T ) rebuilds the projected set ps from the current common ground cg and the contents of the Table T by iteratively performing the ps changes associated with each item on the Table. This operation is needed after a non-canonical conversational move is made, such as retracting an assertion, agreeing to disagree or withdrawing a question. The move is defined at the beginning of Section 6.
4 4.1
Assertion The C(ontext) C(hange) P(otential) of an assertion
Stalnaker’s insight on assertion is that when a speaker A asserts a sentence S with propositional content p she proposes to add p to the common ground of the input context. In making her assertion, A has not only proposed the addition of p to the input common ground but has also publicly committed herself to p. We take these effects to be characteristic of default assertions. Once we discuss all subtypes, however, it will turn out that the essential change is registering author commitment. Whether the Table, and therefore the ps are affected as well, and if so, how, depends on the details of the input context state. In what follows we will first characterize default assertions and turn to subspecies in Sections 5 and 6. Let us assume then that A asserts S with propositional content p against an input context K1 , whose common ground cg is s1 . For simplicity’s sake, let us also assume that the discourse commitment lists of the two participants, A and B, are empty, and so is the Table. The projected set of K1 then includes only s1 . The representation of K1 is as in Figure 3: A
Table
B
Projected Set ps1 = {s1 }
Common Ground s1 Figure 3: K1
In our terms, the effects of A’s move of asserting S on K1 are to add p to A’s discourse commitment list, to place S on the Table, and to project a future common ground where p is accepted, i.e., a state whose common ground is built from the current common ground by adding p to it. It will be important to what follows for the Table to record whether a sentence has been entered as an assertion or a question. We assume that both declarative and interrogative sentences have a syntactic marker, D and I, encoding their declarative and interrogative status respectively. Crucial for what follows is that the sentence radical these markers attach to be visible in the discourse and therefore we treat them as features on sentences. The context state that results after A has asserted S[D] relative to the input context K1 is given Figure 4: A p Common Ground s2 = s1
Table S[D] Projected Set ps2 = {s1 ∪ {p}}
8
B
Figure 4 K2 : A asserted S[D] relative to K1 The common ground of the output context K2 is the same as that of the input context, K1 . The change involves the author’s discourse commitment list, the Table, and, consequently, the ps. Further conversational moves must now attend to S[D] and eventually remove it from the Table in order to reach a stable state. If at the point of asserting S[D] the Table is not empty, the input projected set, psi , contains a (possibly singleton) set of projected common grounds. The impact of asserting S[D] in such a case is to add p to all the common grounds in psi . If the addition of p to a common ground in psi results in an inconsistent set, the set is removed from the output projected set, pso . Thus, pso is made up of the result of adding p to all the sets in psi and then removing those sets that are inconsistent. If the resulting projected set, pso , is the empty set, the conversation is in crisis, because then the canonical removal of S[D] from the Table results in an inconsistent common ground. We follow Krifka (2001) (see also Ginzburg (forthcoming)) in assuming that there are speech act operators that take sentences as arguments, and which are functions from input context states to output context states.7 We define the assertion operator A as a function from an input context Ki to an output context Ko , defined in (13), where S[D] is a declarative sentence with propositional content p, a is that discourse participant who is the author of the assertion, DCa,o and DCa,i are a’s input and output context discourse commitments, and To , Ti are the output and input Table respectively: (13)
A(S[D], a, Ki ) = Ko such that (i) DCa,o = DCa,i ∪ {p} (ii) To = push(S[D], Ti ) (iii) pso = psi ∪ p
Those elements of Ko that are unaffected by the move have not been listed here. We will see below that all types of assertions involve the context change potential in (i). The changes in (ii) and (iii) accompany all assertions as well except for those that simply accept a previous assertion. Varieties of assertions are defined below by imposing further constraints on the input or output context states.
4.2
Reacting to an assertion
After A has asserted S[D], S[D] is at the top of the stack on the Table. Consequently, the conversation is not in a stable state. The canonical future, reflected in the ps, is one where the assertion is accepted, i.e., its propositional content is added to the common ground. This is a canonical continuation because it leads to an increase in the information of the conversational community without resulting in inconsistency at any level. Accepting the assertion is, in fact, the only way of canonically removing the asserted sentence from the Table given that the author of the assertion is committed to its propositional content. Because of this commitment, the context state that results after an assertion is biased in favor of that assertion in Gunlogson’s terms. A non-canonical way of reacting to an assertion is partial or total denial, which does lead to crisis. We will discuss briefly both canonical and non-canonical reactions. An ordinary assertion then commits its author to the propositional content of the asserted sentence and raises an issue (places an item on the Table) while at the same time directing the conversation towards a unique resolution of that issue, namely acceptance of the assertion. 7
Given the draft status of Ginzburg (forthcoming) we do not undertake a full scale comparison of our approach and his.
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4.2.1
Accepting an assertion
B’s acceptance of A’s assertion has the effect of adding p to B’s discourse commitment list. If, as a result of this addition, p becomes a joint commitment in the conversation, i.e., it is now present on the commitment lists of all participants, the following changes are triggered: • S[D] is popped off the Table stack. • p is added to the common ground of the conversation. • p is removed from the commitment lists of all participants.8 The changes just listed occur whenever all the participants in the conversation reach agreement on the issue that is at the top of the stack on the Table. Given the need to model multi-participant discourses it is convenient to introduce an auxiliary operation, M 0 , that occurs after a move M whose outcome results in agreement relative to the resolution of the issue on top of the stack on the Table. (14)
Common ground increasing operation M 0 If M contains a change of the form DCX,o = DCX,i ∪ {p}, and as a result p is now present on the commitment lists of all participants in the conversation in Ko , add the following changes to M : 1.Pop off of the top of the Table all occurrences of items that have p as an element of their denotation. 2.cgo = cgi ∪ {p}, 3.DCX,o0 = DCX,o -{p} for all participants o0 .
The common ground increasing operation M 0 turns a commitment that is shared by all participants in the discourse into an element of the common ground and cleans items sharing that propositional content from the Table, indicating that it is no longer a focus of discussion. In a move to reduce redundancy, it also deletes all instances of p from all participants’ discourse commitments lists. All the elements of the input ps to M 0 already contain p because every move that adds a proposition to a discourse commitment list also adds it to every element of the ps. After M 0 p will be an element of the output cg as well as an element of all sets in the output ps. Returning to our example, if S[D] was the only item on the Table, B’s acceptance of A’s assertion triggers M 0 , which results in an empty Table. Now the projected set contains only the new common ground, and the conversation is in a stable state. Assuming that the input context state is K2 , the output context state after B accepts A’s assertion and after M 0 applies is K3 in Figure 5. A Common Ground s3 = s2 ∪ {p}
Table
B
Projected Set ps3 = ps2 = {s3 }
Figure 5 K3 : B has accepted A’s assertion Acceptance of an assertion can be signaled by silence, by the particles yes, yeah, or ok, sure, or by saying right / correct. We suggest that these are acceptance particles signaling an acceptance move. Acceptance 8
This is a housekeeping move meant to eliminate redundancy. Recall that the participants in a conversation are taken to be publicly committed to the propositions in the common ground in addition to the propositions in their discourse commitment list.
10
of an assertion can also be performed by repeating the asserted sentence in a more or less truncated form preceded by yes or yeah.9 We treat such utterances as a special subtype of assertion signaling acceptance in Section 6. The fact that the move of accepting an assertion does not have to be overtly signaled is expected given the biasing nature of assertions that results in acceptance being the only canonical way of removing the asserted sentence from the Table. We define an operator for accepting an assertion, AA, as a function from an input context Ki to an output context Ko , defined in (15), where S[D] is a declarative sentence with propositional content p that has been asserted by some discourse participant a in a previous move and is currently at the top of the Table as well as on a’s commitment list in Ki . Let b be the participant accepting the assertion. (15)
Assertion Acceptance (AA) a. Input context conditions: (i) top(Ti ) = S[D] with propositional content p (ii) p in DCa,i , where a is a participant other than b. b. Change: AA(b, Ki ) = Ko where DCb = DCa ∪ {p}
The fact that p is an element of some discourse commitment list, required in condition (ii) above follows from S[D] being on the Table. We require the author of the acceptance to be a different participant from the author of the initial assertion because assertion acceptance by the author of the assertion is a redundant move in all respects. If b’s move results in p becoming a joint commitment in the conversation, M 0 is triggered whereby S[D] is popped off the Table, p is moved into the common ground and at the same time removed from the participants’ commitment lists. Thus, if a and b are the only participants in the conversation, b’s acceptance of an assertion S[D] with propositional content p results in an output context state where: • cgo = cgi ∪ {p} • DCa,o = DCa,i − {p} • To = pop(Ti ), where S[D] = top(Ti ) The operation AA is defined only for input contexts resulting after a sentence S[D] has been asserted. This is captured in the two input context conditions in (a) above. The effect of AA is to add the propositional content of the previously asserted sentence to the discourse commitment list of the author of the move. 4.2.2
Contradicting an assertion
Addressees don’t always acquiesce. A possible reaction to an assertion is to deny it totally or partially: (16)
A: Mary ordered chicken yesterday. B: No, she didn’t. C: No, it was beef
B’s reaction is a flat or total denial, while C’s is a partial denial. We follow van der Sandt & Maier (2003) in taking denials to be special conversational moves. In our terms, a discourse move by a participant X is a 9
There are interesting differences between various ways of signaling acceptance which we will not go into here.
11
denial if and only if X asserts S[D] with propositional content p relative to a context state Ki such that the top of the Table in Ki contains S 0 [D] with propositional content q, and q and p are inconsistent. We define total denial in (17), where S[D] denotes p and S 0 [D] denotes ¬p, and where a is the author of the denial move: (17)
Total denial a. Input context condition: S 0 [D] = top(Ti ) b. Change: T D(S[D], a, Ki ) = Ko such that (i) DCa,o = DCa,i ∪ {p} (ii) To = push(S[D], Ti ) (iii) pso = psi ∪ p
A total denial is an assertion: the changes it performs, listed under (b), make it an ordinary assertion: it registers author commitment and it adds a sentence to the Table. What is special about it are the conditions it imposes on its input context which entail that the output context, Ko , is in crisis. In contrast with assertion acceptance, we do not have here a condition requiring the author of the denial to be a different participant from the author of the assertion being denied. This is so because conversation participants may change their minds with respect to an assertion they just made. Unlike in the case of assertion acceptance, such a move is non-redundant. It does place the conversation in doulbe crisis, however, since now the discourse commitment of the author of the denial are inconsistent. Such self-denials, we assume, are accompanied by removal of the denied proposition from the author’s commitment list. Partial denials, as noted by van der Sandt and Maier, must have access to the totality of the message conveyed by the assertion they react to: its entailments, presuppositions, as well as conventional and conversational implicatures. This means that assertions have to add more than just their propositional content on the Table but we will not go into these complications here. Note also that in the case of a partial denial, the author signals acceptance of all the parts of the previous assertion that are not explicitly denied in his move. This explains why B’s second assertion below leads to self-contradiction: (18)
A: Mary ordered chicken yesterday at the restaurant. B: No, it was beef. A: It was chicken. I heard her order it. B: #Mary didn’t even go out yesterday.
We do not deal here with partial denials or with the complications an account of them would lead us to introduce. We only note that even partial denials result in an empty projected set. Total denials (or contradictions) involve rejecting the previous assertion wholesale. A conversation made up of two such consecutive moves is in crisis because the ps of the conversational state that results after B’s denial is inconsistent. The starkest form of denial is asserting the opposite of the asserted sentence on the top of the input Table stack. Such a situation is given in Figure 6, where si is the common ground of the discourse state that served as input to A’s assertion and ps4 is inconsistent:
12
A p Common Ground s4 = s1
Table S[D] ¬S[D] Projected Set ps4 = ∅
B ¬p
Figure 6 K4 : Contradiction on the Table Denials, just as acceptance moves, are reactive, i.e., they presuppose an immediately preceding conversational move, namely an assertion. They differ from acceptance, however, in that they place the conversation in crisis. The proposition the author commits to when denying a previous assertion cannot become a joint commitment without retraction on the part of another participant, and therefore the assertion cannot be removed from the Table in a canonical way. How is a stable state to be reached once there is a contradiction on the Table? There are two possibilities: (i) one of the participants retracts their assertion; (ii) the participants ‘agree to disagree’. The former move involves removing an assertion from the Table and from the commitment list of the author, thus making room for accepting the opposite proposition, which can now be added to the common ground without leading to inconsistency. If A retracts her assertion in Figure 4, the changes involved are given below: • p is removed from A’s commitment list. • S[D] is removed from the table. • The ps is recalculated based on what remains on the Table and the current common ground. We define the operator for retracting an assertion, RA, as a function from an input context Ki to an output context Ko , defined in (19), where S[D] is a declarative sentence with propositional content p, and a is the discourse participant who originally made the assertion S[D] and is now withdrawing it: (19)
Retracting an assertion (RA) RA(S, a, Ki ) = Ko such that (i) DCa,o = DCa,i − {p} (ii) To = remove(S[D], Ti ) (iii) pso = P S(cgo , To )10
A possible complication is that retracting an assertion may also lead to removing other propositions that p provided support for, such as propositions that were added as entailments of p or which were accepted on the basis of having accepted p. We do not deal with these complications here. Retraction moves are most often implicit. The author of the retraction usually signals it by asserting a sentence that signals the acceptance of the denial and the retraction of the previous assertion: (20)
10
A: Sam has left town this morning. B: Oh, no, he hasn’t. I ran into him five minutes ago in the coffee shop. A: He must have changed his plans then./He hasn’t left then after all./Something must have come up then.
The PS operator for reconstructing the projected set from the common ground and Table is defined in Section 6.
13
Dealing with such mechanisms that appear to soften retractions is an interesting issue that we have to leave open at present. The move of ‘agreeing to disagree’ involves removing both S[D] and S 0 [D] from the table without removing either p or q from the relevant commitment lists. Each participant remains publicly committed to the propositional content of whatever they asserted, but neither p nor q are added to the common ground. The state of the conversation after the move of agreeing to disagree has been carried out in our example is as in Figure 7: A p Common Ground s5 = s4
Table
B ¬p
Projected Set ps5 = {s5 }
Figure 7 K5 : A and B have agreed to disagree relative to K4 The common ground in K5 is identical to the common ground in Ki , the context state that served as input to the move in which A asserted S[D]. Under the assumption that that common ground was consistent and that it was consistent with both p and ¬p, the context state K5 is consistent at every level and therefore the conversation is no longer in crisis even though the commitment lists of the two participants in K5 are mutually inconsistent. Separating commitment lists from the common ground is crucial in capturing the fact that after a move of agreeing to disagree the conversation is not in crisis. In future context states, however, in order for A to stay consistent, her public commitments have to be consistent with p, while in order for B to be consistent, his public commitments have to be consistent with ¬p. Informally, the move of agreeing to disagree results in the following changes: • S[D] and S 0 [D] are removed from the Table. • The ps is recalculated from the Table and common ground. We define the operator for agreeing to disagree, AD, as a function from an input context Ki to an output context Ko , defined in (21), where S[D] and S 0 [D] have inconsistent propositional contents, and To , Ti are the output and input Table respectively: (21)
Agreeing to disagree AD(Ki ) = Ko such that a. Input context conditions (i) S[D] and S 0 [D] are on the top of the Table. (ii) p is in DCA and q is in DCB , where A and B are different participants. b. Change (i) To = remove(S[D], remove(S 0 [D], Ti )) (ii) pso = P S(cg, To )
The move of agreeing to disagree is carried out in actual conversations by a participant proposing it by uttering an imperative such as Let’s agree to disagree/Let’s not pursue this further and the other participant agreeing to comply with the imperative. The imperative in this case is special in that compliance with it involves a change in the context state of the conversation.
14
4.3
Conclusion
In this section we have put to use the context structure proposed in Section 2 in order to capture the proposal nature of assertions. The enlarged context structure makes room for capturing reactions to assertions (both acceptance and denial) and allows us to characterize the non-canonical conversational moves of agreeing to disagree and of retracting an assertion. The old insights concerning the CCP of assertive moves are preserved, but distributed among the various context components we are working with. The conversational moves are characterized by the change in the input context they bring about as well as by possible conditions they impose on various components of the input state. We are thus able to characterize what is common to the two assertive moves we have discussed so far, default assertions and denials: they add their propositional content on the author’s commitment list, place the asserted sentence on the Table, and affect the projected set by adding the propositional content of the asserted sentence to all members of the input ps. Denials are special in that their propositional content is inconsistent with the propositional content of a sentence asserted in the immediately previous move and therefore they place the context in crisis.
5
Polar questions
In this section we consider the CCP of polar interrogative sentences illustrated in (22): (22)
Is it raining?
We refer to a question speech act performed by a polar interrogative as a polar question. Polar interrogatives are closest in form, and, as we will see, in CCP, to the corresponding declarative sentence. Our aim is to capture the similarities and differences between making an assertion and asking a polar question. We focus here on polar interrogatives but some aspects of the analysis generalize directly to constituent questions as well, and those will be formulated in general terms. The special issues posed by constituent questions remain outside the scope of this paper.
5.1
The CCP of interrogative sentences
We assume, following standard wisdom, that the denotation of an interrogative sentence is the set of its possible complete answers. Assuming then that the propositional content of It is raining is p, the propositional content of (22) is {p, ¬p}. Syntactically, polar questions are made up of a question operator and a sentence radical S denoting a proposition p. We represent such sentences as S[I] and assume that S and its denotation are available for discourse manipulation. The denotation of the polar interrogative sentence S[I] is {p, ¬p}. The effect of A asking the question in (22) in a context K is to place the issue of whether it is raining on the Table without registering any absolute commitment relative to p or ¬p. In Gunlogson’s terms, posing a polar question S[I] (or any other sort of question) does not lead to an absolute bias in favor of the denotation of S.11 In our terms, asking a polar question S[I] results in adding S[I] to the top of the stack of the Table without the concomitant addition of p to the author’s commitment list. Placing a question on the Table steers the conversation towards a state in which the question is settled. For us, this means that the effect of asking a question on the ps is to take each projected common ground in it and replace it by new ones, each obtained by adding a proposition in the denotation of the question to the projected common ground. This is equivalent to the Groenendijk and Stokhof CCP of questions obtained 11 We do not, of course, exclude cases where the context was already biased, which, arguably, is what happens in rhetorical questions.
15
by partitioning context sets. In the case of a polar question S[I], each common ground cg 0 in the input ps is replaced by two sets, cg 0 ∪ {p} and cg 0 ∪ {¬p}. Polar interrogative sentences can be positive or negative. In English, negation can be ‘internal’, as in (23-a) or ‘external’, as in (23-b). (23)
a. b.
Is it not raining? Isn’t it raining?
The common wisdom on negative questions of the type in (23-a) is that they involve some sort of bias in favor of the proposition in the scope of the negative operator, i.e., in this case, in favor of it being, in fact, raining. There are languages, such as Hungarian or Romanian, where there is no parallel syntactic difference. The only way of asking the corresponding negative question is as in (24): (24)
a. b.
Nu plou˘a? (R) ‘Not rains?’ Nem esik? (H) ‘Not rains?’
Biasing effects are associated in these languages with various intonation contours or the use of special particles. The issue of question bias is much debated in the literature (see, for instance, van Rooij & Safarova (2003), Romero & Han (2004) and references therein). We cannot add anything substantive to this debate. We only note that the bias a negative polar question brings about is never quite as radical as that of an assertion. Neither a positive nor a negative answer to a polar question brings the conversation to a crisis, the way a contradictory reaction to an assertion does. In our view this is mirrored by the fact that assertions project acceptance only, while polar questions, even if biasing, project a future for each answer. Our approach is consistent with van Rooij & Safarova (2003), where it is argued that the bias associated with a negative question is a pragmatic phenomenon. A way to register questioner bias towards one or the other of the possible ways of settling a polar question would be to encode a preference for one or the other cell in the partition. In our terms, this would mean registering a preference for certain future common grounds in the output ps over others. This preference can be rooted either in the author’s own bias in favor of one of the alternatives or in the author’s guess as to the preference of the addressee toward one or the other of the answers. This type of bias, then, has to do with whether the author thinks one or the other of the two conversational futures projected by the question is more likely to become the actual future or is a preferable alternative. It is different in kind from the type of bias assertions introduce. In our view, just as in Gunlogson (2001), this difference is rooted in the fact that assertions register author commitment while questions do not. We first present the effect of asking a polar question on a context state informally and then turn to defining a question speech act operator Q. Assuming that both the Table and the participants’ discourse commitment lists are empty, the context state after asking a polar interrogative sentence S[I] is as in Figure 8: A Common Ground s8
Table B S[I] Projected Set ps8 = {s8 ∪ {p}, s8 ∪ {¬p}}
16
Figure 8 K8 : S[I] was asked relative to some input context Ki In the concrete case of a polar question such as Is it raining?, we assume that the denotation of S is p and the denotation of S[I] is {p, ¬p}. A crucial difference between questions and assertions is that in the case of the former, the commitment sets remain unchanged, while in the case of the latter, this is not the case. The nature of the change on the ps is the same for both questions and assertions: the projected common grounds in the input ps are replaced by sets obtained by adding each of the denotations of the item placed on the Table. The difference resides in the fact that the denotation of an interrogative sentence is a set of propositions while that of a declarative sentence is a single proposition.12 The overall effect of asking a polar interrogative S[I] on a context state K is given below. • Add S[I] to the top of the stack on the Table. • Replace each projected common ground in the input ps by two sets, one in which p is added to the projected common ground and one in which ¬p is added to it. Eliminate inconsistent sets. More formally now, we define the polar question operator PQ as in (25), where S[I] is a polar interrogative sentence, and where P is the set of propositions {p, ¬p} that form the denotation of the interrogative sentence: (25)
Polar question operator (PQ) PQ(S[I], Ki ) = Ko such that (i) To = push(S[I], Ti ) (ii) pso = {s ∪ {p} | p ∈ P, s ∈ psi } − {s0 | s0 is inconsistent} S = ( p∈P psi ∪p) − {s0 | s0 is inconsistent}.
Constituent questions, we assume, have the same effect on the projected set as polar questions: pso is the result of augmenting each s in psi with each proposition in the denotation of the question. The major difference is that the sentence radical in their case is not a closed sentence. Returning to polar questions and assertions, the two sentences It is raining and Is it raining? share a sentence radical and differ in the [D] and [I] feature associated with it. Questions (whether polar or constituent questions) are like ordinary assertions in that they place the conversation in an unstable state by placing an item on the Table. The resulting state in the case of questions is different, however, because the ps now includes separate projections for each of the possible answers to the question. We call such a context state inquisitive. The default way in which an inquisitive context is returned to a stable state is by the addressee providing a complete answer to the question and the questioner accepting it. There are, however, special questions that indicate that the author does not, in fact, expect the addressee to settle the issue immediately. In Romanian, for instance, the particle oare in a question signals that the author does not necessarily expect an answer: (26)
Oare Petru a sosit deja? oare Peter has arrived already Has Peter arrived already?
In our framework questions marked by oare widen the ps by including not only projected common grounds in which the question is settled but also a copy of the elements of the input ps thereby indicating that not 12
Our discourse structures do not keep track of who placed a particular item on the Table because nothing we discuss here is sensitive to this aspect. Adding such a mechanism would not cause any problems we are aware of.
17
answering the question is one of the canonical discourse futures. These questions therefore are special in that for them removal from the Table without change in the current cg is a canonical option. Oare in Romanian is among the morphemes associated with free choice. This connection is not surprising under the suggested account since adding oare to a question widens the domain of alternative projected sets and free choice is commonly associated with a widened domain of alternatives. We now consider some of the consequences of this approach to (polar) questions. First, note that having the uttered sentence entered on the Table allows us to differentiate between positive and negative polar questions while at the same time assigning them the same denotation. A negative polar question such as: (27)
Is it not raining?
has the same effect on the ps as its positive counterpart. It differs from it, however, in that it places a negative rather than a positive sentence on the Table. Pragmatic differences between positive and negative polar questions as well as differences in the way they can be answered are connected in our view to the difference in the contribution the two types of questions make to the Table without having to give up the uniform account of the denotation of questions.13 Let us now turn to comparing an assertion using a declarative sentence S[D] and a polar question using the polar interrogative S[I], exemplified below. (28)
a. b.
It is raining. Is it raining?
The two speech acts are similar in that they both raise an issue, namely the issue of whether it is raining, and direct the conversation towards a state where the issue is resolved. The fact that the two utterances raise the same issue is captured in our view by the fact that they add the same sentence radical to the Table, namely it is raining. The fact that they direct the conversation toward a state in which the issue is resolved is captured by the fact that once each of these utterances has been processed, each projected common ground in ps in the output context state is such that either it contains the proposition that it is raining or its negation. In both cases the propositional content of the sentence being processed is decided relative to each projected common ground in the output ps. We define when a proposition p is decided relative to a common ground cg and a conversational state in (29): (29)
a. b. c.
A proposition p is decided relative to a common ground cg if and only if either cg implies p or it implies its negation. If a proposition p is decided relative to the common ground cgK of a conversational state K, p is decided in K. If the denotation of a sentence is decided relative to a common ground cg, the sentence is decided relative to cg.
Given this definition, an interrogative sentence is decided relative to a common ground cg if and only if each proposition in its denotation is decided relative to cg. If an assertion is informative and if a question is non-redundant, their denotation is not (yet) decided relative to the cg in their input context state. We follow Gunlogson (2001) in placing the crucial difference between assertions and questions at the level of their effect on the discourse commitments of participants. Assertions of all types commit their author to the propositional content of the asserted sentence, while questions, of all types, do not add any of 13
As mentioned above, we leave open the important issue of the difference between ‘inner negation’ questions such as (27) and ‘outer negation’ questions, such as Isn’t it raining?
18
the propositions in their denotation to the commitment list of their author.14
5.2
Responding to a polar question
The canonical way of removing a polar question from the Table is to settle it. If a participant asserts an answer, the context changes in the ways in which ordinary assertions affect the input context state, namely, the asserted answer is added to the Table, the propositional content is added to each common ground in the projected set, and the propositional content of the asserted sentence is added to the author’s commitment list. Let us assume that A has asked a polar question S[I] with propositional content {p, ¬p} putting the context in the state given in Figure 8. If B now responds by asserting answer S[D], with propositional content p, the context is changed to the state in Figure 9, where S[D] is now on top of the stack on the Table, p is on B’s commitment list, and the projected set has been modified by adding p to each set in ps and then removing all context sets in the input projected set that contained ¬p (because they are now inconsistent): A
Common Ground s9 = s8
Table S[I] S[D] Projected Set ps9 = {s8 ∪ {p}}
B p
Figure 9 K9 : B has answered the question raised in K8 B’s answer affects the Table, the projected set, and B’s commitment list. Crucially, reacting to a question differs from reacting to an assertion because in the latter case the input context is categorically biased in favor of the denotation of the sentence on top of the Table stack. Since the question did not commit its author to either proposition in the denotation of the question, the asserted answer will not be a joint commitment. Thus, if A asks S[I] and B answers by asserting S[D], the propositional content of the sentence radical S is in DCb,o but is not in DCa,o and therefore the auxiliary operation M 0 cannot apply. Note also that answering a question negatively does not lead to conversational crisis while reacting negatively to an assertion does. The similarity between B’s asserting S[D] ‘out of the blue’ and his asserting S[D] against the input context in K8 , which is inquisitive with respect to p, comes from the assertive CCP of the two moves: in both cases S[D] is added to the Table, the propositional content of S is added to the author’s discourse commitment list, and the output ps is obtained by adding p to each set in the input ps. The difference between asserting ‘out of the blue’ and asserting as a reaction to a question concerns the input context state. In the case of an answer, the input context state is inquisitive. As we will see below, this difference matters to the form the asserted sentence can take.
5.3
Accepting the response to a question
If A accepts B’s response S[D] to the question whether S, which is the canonical reaction, p is added to A’s commitment list exactly as in the case in which an ordinary assertion is accepted, using the AA operator. Note that in ordinary cases this is the most canonical reaction of all since in canonical cases the questioner 14
Questions do, however, commit their author to whatever presuppositions are associated with the interrogative sentence. See section 8 for further discussion.
19
is assumed not to know the answer to her question while the addressee is assumed to know it. If accepting the answer results in p becoming a joint commitment, M 0 applies as before with the only difference that now both S[I] and S[D] are removed from the stack. The resulting state of the context is as in Figure 10: A Common Ground s10 = s9 ∪ p
Table
B
Projected Set ps10 = {s10 }
Figure 10: A has accepted B’s answer Had B answered A’s question by asserting the negation of S, ¬S, and had A accepted that answer, the context change moves would have been the same except that the addition to the common ground had been ¬p. But in that case too, both S[I], the sentence the questioner placed on the Table, and ¬S[D], the negative answer, are removed from the Table once the answer has been accepted. Sometimes the answer to a question is provided by answers to a series of subquestions or via the accumulated effect of assertions made in response to the question. A question is fully answered in a context state K if and only if it is decided relative to cgK , the common ground of K. We make here the simplifying assumption that a question may be removed from the Table when its propositional content is decided in the common ground. This means that rhetorical questions may be removed without an explicit answer, which we think is the right result. Getting to a more realistic account of when questions count as answered and how and when they are removed from the conversational table would require a separate paper. The moves that followed A’s question in our example were canonical in that they eventually led to enlarging the common ground by settling the issue the question raised. In the view we have given here then, making an assertion and asking a polar question are parallel in that the issue of the acceptance or rejection of a proposition (the denotation of the sentence radical) is raised. The assertion raises the issue and simultaneously offers a way of settling it, namely accepting the proposition expressed by the sentence placed on the Table. The polar question raises the issue but leaves its resolution open (even in the case of biased questions that favor more or less strongly one resolution over the other). The CCP of a sequence of conversational moves made up of asking S[I], answering it positively and accepting the answer is, by the end of the sequence, the same as if someone had asserted S[D] and the interlocutors had accepted the assertion. Just as agreeing to disagree is a non-canonical way of removing an assertion from the table, one can agree not to pursue a question if there is no agreement on an answer, thereby removing it from the Table without having resolved it. Such a move is non-canonical because the question is popped off the stack without any concomitant enrichment of the common ground. Once the question is removed, the projection set must be recalculated. Such moves may be prompted by participants declaring their inability to provide information that would lead to answering the question. Agreeing not to pursue a question is similar to retracting an assertion except that the commitment list of participants is not affected. The changes involved are given below: • Q is removed from the table. • The projected set is recalculated from the Table and common ground. We define the operator for retracting a question, RQ, as a function from an input context Ki to an output context Ko , defined in (30), where Q is a question (polar or not), and To , Ti are the output and input Table respectively: 20
(30)
Retracting a question (RQ) RQ(Q, Ki ) = Ko such that (i) To = remove(Q, Ti ) (iii) pso = P S(cgo , To )
Here pso must be recalculated because retracting a question is a non-canonical move.
5.4
Conclusion
What we have said in this section only scratches the surface of the many complex issues that are raised when one considers the CCP of questions and their answers. We have concentrated here on asserting a sentence and asking the corresponding polar question, and we have located the similarity in the sentence radical that is placed on the Table. In both cases, the propositional content of the sentence radical is added to each element of the input projected set. Since the denotation of declarative sentences differs from the denotation of interrogatives, the addition operation yields different results in the two cases. Another crucial difference concerns the presence of author commitment in the case of assertions and its lack in the case of questions. Important issues we leave open, on the question side, involve question bias as well as the issue of the details of generalizing the approach to constituent questions. On the answer side, there is the issue of differentiating partial answers from answers that resolve the question. On the more global side, there is the question of dealing with superquestions and subquestions. These issues can stay open while we pursue our limited aim, namely that of capturing the essential differences and similarities between asking a polar question and making an assertion and between reacting to an assertion and reacting to a polar question.
6
Reconstructing the projected set
As indicated earlier, if a conversation reaches a crisis and then is resolved by retracting a statement or question then we must recalculate the projected set from the common ground and the contents of the Table. Let T = {T1 , . . . , Tm } be the contents of the Table and let cg be the common ground. We build the projected set iteratively as follows: 1. ps0 = {cg}. 2. If Ti is of the form Si [D] with propositional content p then let ps0i = {cg ∪ {p} | cg ∈ psi−1 }. The set psi is obtained by throwing away all inconsistent sets in ps0i . 3. If Ti is of the form Si [I] with propositional content q then let ps0i = {cg∪{p}, cg∪{¬p} | cg ∈ psi−1 }. The set psi is obtained by throwing away all inconsistent sets in ps0i . The new projected set ps is simply psm . This algorithm starts from the common ground of the conversation and calculates the current projected set by performing on the common ground the ps changes associated with every item on the stack in turn. Such a recalculation is needed whenever items are removed from the Table in a non-canonical way, that is, without concomitant addition to the common ground of the conversation.
7
Responding assertions
Discourse moves can be differentiated not only with respect to how they affect the input context state but also with respect to what the properties of the input context state are. In this section we exploit this fact 21
in order to capture in more detail the similarities and differences between ‘out of the blue’ assertions and assertions that react to a previously made assertion or to a previously posed polar question. We want to capture the reacting nature of the latter while at the same time maintaining the differences drawn above between answering a question and accepting or rejecting an assertion. There are many ways in which an assertion may be seen to be reacting to an immediately preceding discourse move. In what follows, we restrict our attention to a subtype of reactive moves we call responding assertions, which will be defined shortly. First, however, consider the dialogue in (31): (31)
A: It’s raining. B: Yes, it’s raining. A: It’s raining.
Here, all three discourse contributions are, essentially, assertions sharing a propositional content, and yet the third assertion is superfluous while the first two are not. Our account allows us to capture this difference. At the linguistic level, the difference between ‘out of the blue’ assertions and responding assertions is crucial in understanding the grammar of cross-turn discourse. As mentioned already, discourse particles such as yes and no in utterances such as that of B above, signal that the sentence they precede functions as a response. The use of these particles in ‘out of the blue’ assertions results in ungrammaticality. Let us now turn to the issue of responding assertions to questions and responding assertions to previous assertions, exemplified in (32): (32)
a. b.
A: Sam’s home. B: Yes, indeed, he’s home./No, in fact, he isn’t home.
(33)
a. b.
A: Is Sam home? B: Yes, he’s home./No, he isn’t home.
The (b) assertions in both examples are responding. In (32), however, the negative response places the discourse in crisis while in (33) it does not. This difference has linguistic reflexes in intonation and particle usage. Note also that while the positive response in (32) settles the issue of whether Sam is at home or not, and therefore no further acceptance of B’s assertion is called for, in (33) this is not so. After B offers her answer, the question is considered settled only if A accepts B’s answer. In what follows we first define a class of discourse moves we call responding assertions. This will make it possible to capture what the (b) assertions in (32) and (33) share, and what distinguishes them from the assertion in (32-a). We then turn to drawing a typology of responding assertions in terms of what they respond to and what their relation is to what is on the Table in the input context state. This will allow us to differentiate between the (b) reactions in (32) and (33), as well as between the two reactions within each response.
7.1
Initiating and responding assertions
Intuitively, the crucial distinction between ‘out of the blue’ assertions and assertions made in response to a previous assertion or as an answer to a previous question is that in the latter case the input context state is necessarily unstable. In addition, we are concentrating here on a subset of reactive assertions we call responding, defined in in (34), where S stands for a (positive or negative) sentence radical: (34)
Responding assertions An assertion move is responding if and only if: 22
(i) top(Ti ) = S with propositional content p (ii) The assertive move commits its author to p or ¬p. An assertion is responding if and only if there is a sentence radical on the top of the input Table, and the assertion commits its author to the propositional content of that sentence radical or its opposite. Thus, uttering a declarative sentence S[D] with propositional content p is a responding assertion if and only if the input context state had on the top of its Table an interrogative or declarative sentence whose sentence radical has the propositional content p or ¬p. In our little dialogues in (32) and (33) the utterances in (b) are responding assertions. We call initiating those assertions whose propositional content is not directly related to the item on the top of the stack on the input Table. We will not try to define this notion formally here since doing so would take us beyond assertions and polar questions, which constitute our focus. Intuitively then, the utterances in (32) and (33) are initiating assuming that they are made relative to an empty input Table. The particles yes and no are appropriate in responding assertions but not in initiating ones. Responding assertions have been defined in a narrow way so that answers to constituent questions do not count as responding assertions. In their case, the denotation of the sentence radical is not a simple proposition and therefore an assertion cannot have the same or the opposite propositional content as that of the sentence radical in a constituent question. Obviously, a wider notion of response is needed to capture what is common between assertions that answer polar questions and assertions that answer constituent questions. The narrow notion we defined above, however, is needed to capture that subclass of responses that allows the particles yes and no in English. Crucially, these particles are appropriate in narrow responses as defined here, whether to assertions or polar questions, but not in answers to constituent questions: (35)
a. b.
A: Who is here? B: *Yes, Sam is here.
(36)
a. b.
A: Is Sam here? B: Yes, he’s here.
The particles yes and no mark the responding assertion as being the same as or the opposite of a sentence radical S on the top of the input Table. Answers to constituent questions are not responding assertions in this narrow sense, and therefore they cannot be preceded by the particles yes or no.15 Our assumption that an assertion and its corresponding polar question place the same sentence radical on the Table is crucial in accounting for the fact that responses to both assertions and polar questions may be preceded by yes and no.
7.2
Responding Assertion Typology
Responding assertions can be differentiated based on three criteria: (a) whether they respond to an assertion or a polar question; (b) whether they commit the author to the propositional content of the sentence radical on the top of the input Table or its opposite; (c) whether they assert a positive or a negative sentence radical. The third criterion becomes crucial only when we turn to polarity particles in the next subsection. The first criterion concerns the status of the input context. In case of responses to assertions, the top of the Table contains S[D] and the propositional content of the sentence radical, p, is present at least on the DC list of the participant who asserted S[D]. Furthermore, the projected common grounds in the input 15
The problem in (35) may be connected to Topic/Focus articulation. The particles yes and no place the focus on the polarity of the sentence they attach to. In answers to ‘wh’ questions on the other hand, the focus must be on the item that replaces the wh constituent. The characterization we give of these particles is consistent with such an approach, given that in the case of responding assertions an alternative with the same polarity as the assertion or its opposite is present in the input context.
23
ps all contain p (unless the conversation is already in crisis, a circumstance we leave out of the discussion for now). In the case of responses to polar questions, the top of the stack of the input table contains S[I], entered as a result of a participant having asked a polar question, and therefore p is not on that participant’s discourse commitment list. As a result of the context change brought about when S[I] was entered, the input ps contains both context sets that contain p and context sets that contain ¬p. The second criterion concerns the relationship between the proposition the assertion commits its author to and the propositional content of the sentence radical on the top of the input Table. There are two possibilities: (i) the response commits its author to the same proposition, or (ii) the response commits its author to the opposite proposition. In the first case the assertion will be accepting, while in the second, it will be reversing. We assume accepting assertions have the feature [same] and reversing assertions have the feature [reverse], defined in (37). (37)
a. b.
A responding assertion has the feature [same] if and only if it commits its author to the same proposition as the denotation of the sentence radical on the top of the input Table. A responding assertion has the feature [reverse] if and only if it commits its author to the complement of the denotation of the sentence radical on the top of the input Table.
Combining the two criteria, we get [same] and [reverse] responses to assertions and [same] and [reverse] responses to polar questions. In the case of responses to assertions, a [same] response accepts the sentence radical on the top of the input Table, the most canonical reaction to an assertion. A [reverse] response, on the other hand, has the effect of a contradiction. It is the least canonical response since it places the conversation in a crisis. In the case of responses to polar questions, neither [same] nor [reverse] responses lead to crisis. They each require acceptance by the other participant(s) before the initial question and its answer can be removed from the Table. Since [same] responses are simpler, however, they count as more canonical than [reverse] responses even in answers to polar questions. Let us look first at a [same] response to an assertion, repeated in (38): (38)
A: Sam’s at home. B: Yes/yeah/yep, he’s at home.
Here the effect of B’s assertion is equivalent to accepting an assertion, namely AA. A’s assertion places S[D] on the Table and adds p to DCa creating a ps that contains only common grounds that contain p and are consistent. S is therefore positively decided in all the common grounds in the input ps to B’s assertion. We are also assuming that there had been no earlier shared commitment to p. The effect of B’s assertion is to add p to DCb , where p is the propositional content of the sentence on the top of the input Table. This change turns p into a shared commitment for a two person dialogue. At this point then the auxiliary move M 0 applies, moving p into the common ground of the conversation, and changing the Table and the commitment sets of the participants. The context changes that B’s move triggers are the same as if B had said OK, Aha, Fine or had nodded.16 The case of a [same] assertion in response to an assertion is the only case in which the propositional content of an assertion is not added to the Table. Adding the propositional content of the assertion to the Table in this case would be an unnecessary complication since the sentence has already been asserted and therefore the change to the Table and the ps would be redundant. The move itself, however, is non-redundant since it gets p on the author’s commitment list and thereby gets the context one step closer to 16
Repeating an assertion to signal acceptance is different from indicating acceptance by the means just mentioned in that the author of the assertion assumes authority over the sentence she asserts in a way that non-assertive acceptances do not. We are grateful to Christine Gunlogson for insightful comments and discussion on this issue. Here we leave the question of how to characterize this difference open.
24
turning p into a joint commitment. Common to all assertions then is the fact that they add their propositional content to the discourse commitment list of their author. The asserted sentence is added to the Table as well unless this addition would be redundant, i.e., unless we have a [same] assertion responding to an assertion. Let us now consider the case of a [reverse] response to an assertion, the situation in (39): (39)
A: Sam’s at home. B: No, in fact/actually, he isn’t.
This is the case of a contradiction discussed in Section 4.2.2 above. B’s assertion commits her to a proposition that is the opposite of the proposition on the top of the Table. This is not an acceptance and therefore B’s sentence is added to the Table. Because this is a response to an assertion, A is committed to the propositional content of the sentence on the Table and the input ps contains only common grounds that contain p. The context after B’s assertion is in crisis, as discussed before.17 Turning now to responses to polar questions. In the dialogue in (40) (40)
A: Is Sam home? B: Yes, he is.
the input context state to B’s assertion contains S[I] on the Table but no commitment to p on the part of A. B’s assertion commits her to p but since this commitment is not (yet) joint commitment, S is added to the Table and the input ps is changed so as to add p to each of its sets. Since there is no joint commitment to p, the common ground increasing operation M 0 does not apply. The Table therefore is not cleared and nothing is yet added to cgo . Once A accepts B’s assertion, these operations apply, resulting in the addition of p to the common ground of the conversation and the removal of A and B’s contributions from the Table. Had B answered negatively, by asserting No, he isn’t, no contradiction would have resulted. In her next move, A would have been free to accept B’s negative answer without danger of becoming inconsistent. Let us now go back to the dialogue in (31), repeated below. (41)
A: It’s raining. B: Yes, it’s raining. A: It’s raining.
Here A’s first assertion is initiating; it raises an issue and projects a single resolution. B’s assertion accepts A’s resolution and thereby settles the question in the way A has projected. The propositional content of A’s first assertion is now a joint commitment and the Table is cleared. A’s second assertion raises an issue that has just been settled, projecting a resolution that has just been reached, and thereby achieves nothing. In absurd dialogues made up of a series of assertion/contradiction pairs (exemplified in (4) in Section 1), the trouble consists in the participants ignoring the crisis caused by the contradictions, and thereby getting deeper and deeper into a conversation that cannot reach a stable end state. 17 Most often, contradictions involve the assertion of a proposition that is inconsistent with the previous assertion rather than being its opposite. Such moves still qualify as [reverse] since they commit their author to the opposite of the propositional content of the previous assertion though in this case indirectly. However, they are not responding assertions in the narrow sense in which we use the term here.
25
7.3
Responding particles
In this section we take a closer look at the particles signaling responding assertions and the parameters they are sensitive to. So far we have established that in dialogues such as (42), (42)
A: Is Sam home?/Sam is home. B: Yes, he’s home./No, he isn’t home.
B’s utterances are responding assertions. The first answer is a [same] responding assertion, and the second is a [reverse] assertion. In the case in which these assertions respond to a previous assertion, the first amounts to acceptance, the second to flat denial. The particles yes and no placed at the left edge of a declarative sentence signal the responding nature of the assertion. We treat them as presupposing the responding nature of the assertive move. They are therefore inappropriate in assertions made relative to an input context state whose Table does not contain, on the top of its stack, an item the assertion could be interpreted as a response to. The choice between yes and no is influenced by whether the responding assertion is [same] or [reverse], as well as by the polarity of the sentence asserted in the responding assertion move. Note now that a [reverse] assertion in reaction to a polar question answers the question negatively but does not lead to any crisis. Such a move in reaction to an assertion, on the other hand, leads to conversational crisis since it creates an empty pso . We call [reverse] assertions that react to an assertion contradictions and [reverse] assertions that react to a polar question, negative answers. Contradictions and negative answers share the [reverse] feature but are distinguished with respect to both the input context state and the output context state. Contradictions lead to conversational crisis and therefore are non-canonical conversational moves while negative answers do not lead to crisis and in fact, are canonical in that they may lead to an increase in the common ground without involving retraction.18 The similarities in form between B’s moves in the first two sample dialogues above are due to the fact that they are both responding assertions with relative polarity [same] in the case of the yes reaction, and with relative polarity [reverse] in the case of the no reaction. The difference in the conversational state that results after B made her response is due to the differences in the input context state in the two cases. The importance of distinguishing between [same] and [reverse] responding assertions becomes evident once we consider the inventories of polarity particles across languages. We cannot go here into the detailed study of polarity particles within a language or cross-linguistically. We will, however, give a general characterization in order to show connections between particle usage and the context architecture proposed here. As discussed in Pope (1976), there are languages that use polarity particles to signal relative polarity, i.e., [same] and [reverse], such as Japanese, while others have polarity particles meant to primarily signal the negative/positive polarity of the asserted sentence in responding assertions. There are also languages that use a combination of particles. As mentioned in Section 1, Romanian has three polarity particles, da, roughly the same as yes, nu, roughly the same as no/not, and ba, whose function is to signal [reverse]. We call particles like da and nu absolute polarity particles. Their use is primarily sensitive to the third criterion responding assertions can be classified by, namely the polarity of the sentence they assert. We assume here that sentence radicals are either positive or negative, a fact encoded in their form. The positive 18 Note that we are not committed to a completely symmetric treatment of [same] and [reverse] responses to polar questions. As already noted, the [same] answer will always be a simpler move than the [reverse] one, which is a point of differentiation. This distinction is useful in accounting for the difference between positive and negative answers to polar questions.
26
polarity particle da in Romanian is associated with responding assertions where the polarity of the asserted sentence is positive; the negative polarity particle nu is associated with responding assertions where the polarity of that asserted sentence is negative: (43)
A: Ana a plecat. ‘Ana left.’ B: Da. / Da, a plecat. ‘Yes./Yes, she left.’
(44)
A: Ana nu a plecat. ‘Ana didn’t leave.’ B: Nu, n-a plecat. ‘No, she hasn’t.’
(45)
A: Ana a plecat? ‘Did Ana leave?’ B: Da. / Da, a plecat. / Nu. / Nu, n-a plecat. ‘Yes./Yes, she left. /No, she hasn’t left.’
The absolute polarity particles may occur on their own or immediately followed by a ‘sentence echo’ which is the asserted sentence. We are interested here in the third particle, ba, which, we claim, signals that the responding assertion has the relative polarity feature [reverse]. We exemplify its use below: (46)
A: Ana a plecat. ‘Ana left.’ B: Ba nu, n-a plecat. ‘No, she didn’t.’
(47)
A: Ana a plecat? ‘Has Ana left?” B: Nu. / Nu, n-a plecat. /*Ba nu. /*Ba nu, n-a plecat. ‘No, she hasn’t.’
(48)
A: Ana nu a plecat. ‘Ana didn’t leave.’ B: Ba da. / Ba a plecat. /Ba da, a plecat. ‘You are wrong, she did.’
(49)
A: Ana nu a plecat? ‘Didn’t Ana leave?’ B: Ba da. / Ba a plecat. / Ba da, a plecat.’ ‘Yes, she did.’
In the standard dialect, ba cannot occur on its own. It must be followed by one of the absolute polarity particles or by a ‘sentence echo’. The full complex details of particle use in responding assertions in Romanian and beyond must be left for another occasion. We only want to note here that in the above examples, ba functions as a signal of the feature [reverse]. The particle or sentence echo following ba encodes the absolute polarity of the asserted sentence. Note that in Romanian ba can be used to return a negative assertion when the input context presented a positive sentence, in which case ba is followed by nu or a negative sentence echo, as well as to return a positive sentence when the input context presented a negative one, in which case the absolute polarity signal will be positive (da and/or a positive sentence echo). As noted at the outset, the use of ba is sensitive to whether the move is a reaction to an assertion or a reaction to a question, as the contrast between (46) and (47) shows. In [reverse] moves that react to a negative input sentence, however, this contrast disappears, as shown in (48) and (49). These data point to the fact that whether [reverse] is marked or not in a responding assertion is sensitive to the absolute polarity of the input sentence as well as to whether the move is a contradiction or not. The tentative generalizations that emerge are given in (50): (50)
(i) [reverse] in contradictions tends to be more marked than in answers to questions (ii) [reverse] tends to be more marked when it reacts to a negative input sentence than when it reacts to a positive one.
Justifying and accounting for these generalizations is the task of future work. We end by noting, in support of (ii), that in French and German the particles si and doch are used as [reverse] particles specialized to moves that return a positive sentence when presented with a negative one. Thus, the French or German 27
‘third’ particles are close in function to the Romanian ba da: (51)
A: Anne n’est pas partie. ‘Anne didn’t leave.’ B: Mais si. ‘You are wrong, she did.’
(52)
A: Anne n’est pas partie? ‘Didn’t Anne leave?” B: Mais si. ‘Yes, she did.’
(53)
A: Anna kommt mit ins Kino nicht. ‘Anna isn’t coming along to the movies.’ B: Doch! Sie kommt schon. ‘You are wrong. She’s coming.’
(54)
A: Sie wollen diesen Job nicht? ‘Don’t you want this job?’ B: Doch! Ich brauche das Geld. ‘But I do. I need the money.’
The features of responding assertions discussed here are crucial to understanding the details of the use and function of [reverse] particles. Defining these features relied on the notion of responding assertion, which, in turn, was based on the essentials of the context structure we proposed in Section 2, as well as on the view of assertions and polar questions presented in Section 3. The existence of these particles therefore lends support to the proposals made above.
8
Presuppositions
We present here a brief outline of how our view of context structure handles presuppositions and presupposition accommodation. We assume that common to the family of phenomena known in the literature as ‘presuppositions of an utterance U ’ is the fact that they are conditions that the input context state Ki must meet in order for Ki + U to be defined, where + ranges over the functions associated with speech act operators. Various types of presuppositions differ with respect to what triggers them and what part of the input context state they constrain. In the discourse model we proposed above, there are multiple layers where presupposition triggers may be located and there are multiple context components that these triggers may affect. The innermost layer where presupposition triggers may be found is the sentence that constitutes the argument of the speech act operator. We exemplify such triggers with the lexical presupposition of the predicate stop. Another source for presuppositions in this larger sense involves linguistic markers that signal the type of speech act the utterance is meant to perform. Particles, intonation contours, and syntactic forms that mark a particular type of speech act then are presupposition triggers in the sense that the context change potential of the utterance they occur in is defined only if the input context state meets the conditions imposed by the speech act these elements signal.19 Various types and subtypes of speech acts impose more or less specific requirements on their input context state argument. Linguistic elements that mark these speech acts function as presupposition triggers, imposing on the input context the specific requirements associated with the speech act they mark. We exemplify this type of presupposition trigger with the particle ba in Romanian, used to mark [reverse] assertions. 19
See Zeevat (2004) for a view of particles as speech act markers which is in the same vein as the proposals we make here.
28
8.1
Lexical presuppositions
Let us consider a classical lexical presupposition trigger, namely stop.20 It is the lexical meaning of such presupposition triggering verbs that is responsible for the presence of the presupposition. Let us assume then that as part of knowing the meaning of stop we know that the first sentence in (55) presupposes the second. (55)
a. b.
Bob stopped smoking. Bob used to smoke.
Let us also assume that the proposition expressed by the first sentence is p, and that expressed by the second is q. We suggest that presuppositions of this sort constrain whatever common ground the sentence radical containing their trigger is to be added to. Therefore, if Bob stopped smoking is the argument of a speech act operator such as the assertion operator A or the question operator Q, the speech act is defined only for input context states in which the common grounds in the input ps, psi , contain q. In embedded contexts, exemplified in (56), (56)
Sam thinks that Bob stopped smoking.
p has to be added to the set of propositions Es that form Sam’s epistemic base. In this case then, it is Es that has to meet the presuppositions of the complement clause. It is the task of the semantics of propositional attitudes to explain the parallelism between asserting, questioning, commanding and being the complement of a predicate such as believe, say, think, wonder or order, request, command, a task we do not attempt to carry out here. In what follows we restrict our attention to matrix sentences. We consider now what happens in case such a lexical presupposition is not met in the input context state. We assume that there are two options then: • Take issue with the presupposition, e.g., “Did Bob use to smoke?” or “I didn’t know Bob used to smoke”, or even denial of the presupposition as in “What do you mean? Bob never smoked”. • ‘Accommodate’ the presupposition by adding it to the common ground. The context model we have presented here can handle both options. Suppose speaker A asserts (55-a) relative to an input context state K. If q follows from all the sets in psK , (55-a) is added to the Table, p is added to DCA , and p is added to the sets in psK as usual. Now if q does not, in fact, follow from all the sets in psK (55-a) cannot be added to K because the special requirement p imposes on the common grounds to which it is to be added is not met. The accommodation route involves an implicit step that minimally changes the input context in such a way as to make it meet the presupposition of A’s assertion. It is the context state created by this implicit step that is then treated as the input to A’s assertion. The implicit step creates the context state K 0 which is just like K except q is now taken as having been accepted in the common ground. This means that cgK 0 = cgK ∪ {q} and psK 0 = psK ∪ q. K 0 is the context state one would obtain had A asserted q relative to K 0 and had B accepted that assertion. 20
Whether the presuppositions of definite DPs should be treated on a par with the lexical presuppositions associated with factive predicates or verbs like stop is an open question we do not address here. A full discussion of the issue of the typology of presuppositions is well beyond the scope of our paper.
29
The presupposition in this case targets the common ground alone and is accommodated by the addition of the presupposed material to it.21 Invitation to accommodation amounts to requesting the addition of the presupposed proposition to the common ground of the conversation bypassing its addition to the Table and therefore skipping the stage where the addressee could object to this addition. Such an invitation then amounts to presenting the presupposition as ‘uncontroversial’, i.e., as a proposition whose assertion the addressee would accept as a matter of course. Propositions inconsistent with cgK or with the addressee’s discourse commitments will not be accommodatable. The less likely B is to object to A asserting q, the more accommodatable q is. If B is willing to accommodate, K 0 is created and thereby she implicitly accepts the presupposition. The conversation then has moved implicitly from K to K 0 and now A’s assertion is made relative to the input context K 0 . B’s next move involves acceptance or rejection of the claim that Bob stopped smoking. If, on the other hand, B is not willing to accommodate she is unwilling to accept q. She would then stop the fast forwarding process that leads from K to K 0 . She can do this by rejecting the presupposition outright or by forcing A to explicitly assert it relative to K and therefore to make room for discussion and debate. If A and B come to an agreement and B accepts the presupposition, the context reaches a state relative to which the initial, presupposing sentence can be added. A’s public commitment to q once he has publicly committed to p follows if p entails q, as is usually the case. It also follows from the assumption that speakers are committed to additions to the common ground rendered necessary by their conversational moves. The account of the presuppositions of questions or any other speech act types that involve adding the proposition expressed by a sentence containing a lexical presupposition trigger of this sort to a projected common ground is parallel to what we sketched here for assertions.
8.2
Speech act presuppositions
Given our richer context structure, we are led to expect that particular utterances may place conditions on the input context state that do not involve only the input common ground and projected set. Such ‘nonclassical’ presuppositions do in fact exist, encoded in sentence particles as well as in intonation. Zeevat (2004) suggests that presuppositional particles, such as too, doch, instead, are, in fact, particular speech act type markers rather than lexical presuppositions. We can add to these actually, signaling [reverse] assertions and absolutely, signaling [same] reactive moves. In our terms, these items mark a particular speech act type that is defined only for input contexts meeting certain requirements.22 A particular subvariety of speech acts we discussed above are responding assertions. They are defined only for input contexts that have, at the top of the input Table, an assertion or question of a certain form. Utterances that are to be processed as responding assertions can, and sometimes must, be marked by particular polarity particles or special intonation contours. In Romanian, utterances involving the particle ba followed by the positive or negative particles da or nu must be interpreted as [reverse] assertions: (57)
a. b.
Ba da, a plecat. ‘But yes, he/she left.’ Ba nu, n-a plecat. ‘But no, he/she did not leave.’
21
Throughout this paper we have abstracted away from the important matter of discourse referents and their role and place. Context structures have to of course be further complicated to make room for such ‘micro’ context issues as well as for salience distinctions of both discourse referents and propositional information. 22 We cannot deal here with the distinction between ‘strong’ triggers, whose presuppositions must be met by the main context, and weak triggers, whose presuppositions, apparently, can also be met by certain embedded contexts. The particle too in English belongs to the latter group, while the particle ba in Romanian belongs to the former. See, again, Zeevat (2004) and references cited therein for an interesting discussion.
30
The first example above presupposes that the input context state has a sentence radical equivalent to ’X did not leave’, on the top of the Table, while the second example requires the input state to have ’X left’ on the top of the Table entered as a result of an assertion, where X is the referent of the null subject of the two sentences. In our view then, the use of ba encodes requirements concerning details of the state of the Table of the input context. This is a different type of condition than what we saw with lexical presuppositions because it does not involve implicit agreement on a particular issue but rather, the assumption that a particular issue has been raised and is under discussion and therefore present on the top of the stack on the Table. Presuppositions triggered by these particles are similar to the lexical presuppositions we looked at above in that in both cases we have linguistic expressions (stop and particles) that contribute specific conditions that the input context state must meet in order for the utterance to effect its intended context change. But the way these conditions work is quite different. In the case of the presupposition of stop, the condition involves the presence of a piece of information in the common ground. If the presupposition is not met, its accommodation involves implicit agreement on a piece of information assumed to be uncontroversial. Implicit agreement on various uncontroversial facts is an unavoidable accompaniment of linguistic communication. We are assuming a large pool of shared knowledge that, thankfully, we can draw upon without having to raise each such piece of knowledge as an issue, i.e., without having to place it on the conversational Table and have it accepted by our interlocutors. In the case of the particle ba, the condition it imposes is specific to the nature of the speech act performed and it targets the state of the conversation immediately prior to the utterance in question. Accommodating such a presupposition would involve changing the history of the conversation and assuming that a particular conversational move has occurred when in fact we both know it hasn’t. This is a much more complicated issue then simply assuming that a particular uncontroversial fact is part of shared knowledge. Meeting speech act presuppositions does not require implicit or explicit agreement on an issue. Unsurprisingly, accommodating such speech act presuppositions is close to impossible. One might conclude that the only conversational moves that might be implicit are assertions and assertion acceptances. This would be too hasty, however, since implicit raising of questions is not, in fact, impossible. Plausible candidates for this type of accommodation are the implicit questions required in B¨uring (2003) to account for the effect of B-accents. In the cases dealt with in B¨uring, a particular intonation contour on the answer to an actual question raised in the discourse may trigger the step of implicitly raising another question. An interesting property of these moves, however, which renders them similar to ‘bridging’ accommodation, is that the implicit questions raised are always connected to an explicitly raised question. Our discussion of presupposition has, we know, raised more issues than it answered. The aim of this section was merely to illustrate concretely how lexical and speech act presuppositions would be handled in our system, and to point to some of the distinctions and parallels the proposed view of context structure lends itself to.
9
An example illustrating context states
In this section we provide a series of examples showing how context states evolve during a conversation. We look at a relatively simple scenario to see how the context state changes as a conversation progresses. Our conversation will involve an assertion S1 and two questions S2 ? and S3 ?, where the propositional content of each Si is pi . For simplicity, we assume that at the beginning the common ground is empty. Suppose the conversation proceeds as follows, where we mark utterances with D or I to indicate whether 31
A: p
B: OK
B: q?
A: q'?
A: q
B: ¬q'
B: OK
A: OK
Table 1: Tree representing sample dialogue. they are assertions or questions: (58)
A: We should eat out tonight. S1 [D] B: Should we go to Sabieng Thai? S2 [I]? A: Would you rather go somewhere else? S3 [I]? B: No, I wouldn’t. ¬S3 [D] A: OK (accepting ¬S3 [D]) A: So we should go to Sabieng Thai then. S2 [D] B: OK (accepting S2 [D]) B: OK (accepting S1 [D])
In this sample conversation, we have inserted “OK” to mark places where one participant accepts an assertion of the other. A strictly linear presentation of a conversation is less helpful than a structured one that helps focus what topics are under discussion. The presentation in Table 1 represents the dialogue as a dialogue-tree, where each direct response to a question or assertion is listed as a daughter of the question or assertion. Notice that the listing of the conversation given above corresponds to a preorder traversal of the dialogue tree.23 We will have more to say about this later. Let us now trace what happens with our context representation as the conversation progresses. Initially 23
A preorder traversal of a tree is accomplished by first visiting the root and then performing a preorder traversal of each of its subtrees, processed from left to right. For example a preorder traversal of the tree in Figure 1 would result in first visiting the root: “A: S1 [D]”, performing a preorder traversal of the subtree headed by “B: S2 [I]?”, and then performing a preorder traversal of the subtree of the root headed by “B: OK” (which is trivial, just visit its root “B: OK”).
32
neither participant has any public commitments, the common ground consists of the set cg0 = ∅, and the projected set ps0 is {cg0 } = {∅}. A Common Ground cg0 = ∅
Table
B
Projected Set ps0 = {∅}
Figure 1: Initial context To begin, A asserts S1 [D]. The common ground stays the same, but A’s list of discourse commitments changes to include p1 and the projected set changes to reflect the assertion p1 . Notice that ps1 still contains a single set, but that set now projects the acceptance of p1 . A p1 Common Ground cg1 = ∅
Table S1 [D] Projected Set ps1 = {{p1 }}
B
Figure 2: Context after A asserts S1 [D] B does not immediately accept A’s assertion but rather asks S2 [I]?. The context set stays the same as before. However the projected set changes to reflect the possible responses to the question: p2 and ¬p2 . The projected set now contains two sets, corresponding to the two possible responses to B’s question. A p1 Common Ground cg2 = ∅
Table B S1 [D] S2 [I] Projected Set ps2 = {{p1 , p2 }, {p1 , ¬p2 }}
Figure 3: Context after B asks S2 [I]? A responds by asking S3 [I]? before venturing an answer to B’s question. The common ground remains unchanged. The projected set changes again to reflect the two possible responses to the question S3 [I]: p3 or ¬p3 . The projected set now contains four sets, each corresponding to one of the possible pairs of responses to the questions (and all assuming that p1 will be accepted).
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A p1
Table B S1 [D] S2 [I] S3 [I] Projected Set ps3 = {{p1 , p2 , p3 }, {p1 , p2 , ¬p3 }, {p1 , ¬p2 , p3 }, {p1 , ¬p2 , ¬p3 }}
Common Ground cg3 = ∅
Figure 4: Context after A asks S3 [I]? Next, B settles A’s question by asserting ¬S3 [D]. The context set has still not changed. The projected set changes to anticipate ¬S3 [D] being accepted: ps4 = {{p1 , p2 , ¬p3 }, {p1 , ¬p2 , ¬p3 }}. The projected set now only contains two sets, as we threw away the inconsistent sets containing both p3 and ¬p3 . A p1
Table B S1 [D] ¬p3 S2 [I] S3 [I] ¬S3 [D] Projected Set ps4 = {{p1 , p2 , ¬p3 }, {p1 , ¬p2 , ¬p3 }}
Common Ground cg4 = ∅
Figure 5: Context after B asserts ¬S3 [D] Now A accepts B’s answer, namely ¬S3 [D]. Using the common ground increasing operation M 0 , both ¬S3 [D] and S3 [I] are popped off of the table, the proposition ¬p3 is removed from B’s discourse commitments, and ¬p3 is added to the common ground. The projected set remains unchanged. Notice that each element of the projected set is always a superset of the context set. A p1 Common Ground cg5 = {¬p3 }
Table B S1 [D] S2 [I] Projected Set ps5 = {{p1 , p2 , ¬p3 }, {p1 , ¬p2 , ¬p3 }}
Figure 6: Context after A accepts ¬S3 [D] Next A replies S2 [D] to B’s earlier question. What changes is the projected set, anticipating acceptance, and B’s discourse list. The new projected set is ps6 = {{p1 , p2 , ¬p3 }} because p2 is inconsistent with the second set in ps5 . Notice that at this point there is only one expected outcome. We anticipate the common ground when the table is empty to be {p1 , p2 , ¬p3 }, assuming that no other issues are raised and placed on the table.
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A p1 p2 Common Ground cg6 = {¬p3 }
Table S1 [D] S2 [I] S2 [D] Projected Set ps6 = {{p1 , p2 , ¬p3 }}
B
Figure 7: Context after A asserts S2 [D] B accepts the answer S2 [D]. By the operation M 0 , p2 is moved from A’s commitment list to the common ground, while both S2 [I] and S2 [D] are removed from the table. The projected set remains unchanged. A p1 Common Ground cg7 = {p2 , ¬p3 }
Table S1 [D] Projected Set ps7 = {{p1 , p2 , ¬p3 }}
B
Figure 8: Context after B accepts S2 [D] Now if B accepts the assertion S1 [D], p1 is moved from A’s commitment list to the common ground, S1 [D] is removed from the table, and the projected set is unchanged. At this point the table is empty and ps8 = {cg8 }, as expected. A
Table
Common Ground cg8 = {p1 , p2 , ¬p3 }
B
Projected Set ps8 = {{p1 , p2 , ¬p3 }}
Figure 9: Context after B accepts S1 [D] If there is disagreement at any point then the projected set becomes empty. For example, suppose after stage 4, A denies the answer ¬S3 [D] by asserting S3 [D]. Then ps5 is formed by first attempting to add p3 to every set in ps4 , but all of those sets are inconsistent because they already contain ¬p3 . As a result, ps5 = ∅, signaling that the conversation is in crisis. The same thing would happen at this point if B asserted ¬p1 since that is also inconsistent with all the sets in ps4 .
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A p1 , p 3
Common Ground cg50 = ∅
Table S1 [D] S2 [I] S3 [I] ¬S3 [D] S3 [D] Projected Set ps05 = ∅
B ¬p3
Figure 10: Context in crisis after A asserts S3 [D] We noted earlier that a preorder traversal of the tree in Figure 1 corresponds to the listing of the items of the conversation in the order in which they occur. While a “recursive” description of a preorder traversal, such as that given in footnote 23, is the simplest way of describing a preorder traversal, it is also possible to write as iterative (and hence, non-recursive) algorithm to express this traversal. Writing such an algorithm requires the use of a stack to save information as to where one is in the tree. Readers familiar with the iterative algorithm for performing a preorder traversal will recognize that our Table performs the role of the stack in traversing the tree. In particular, at each point in the conversation in which either speaker makes an assertion or question, the Table records the path from the root of the tree to that utterance. In the case where the last action has been an acceptance of an assertion, that assertion (and the question it settles, if any) are removed from the stack, and the stack now corresponds to a path from the root to the most recent unsettled item on the table. Figure 6 corresponds to the context in which ¬S3 [D] has just been accepted as the answer to S3 [I]?. The stack in that figure corresponds to the path in Figure 1 from the root “A: S1 [D]” to its left child “B: S2 [D]?”. The nodes in its left subtree (headed by “A:S3 [I]?”) have now been completely settled and hence no longer need to be retained on the stack. The nodes in the right subtree represent future parts of the conversation that will eventually be processed. Of course the other components of the context – the common ground and projected set – have no corresponding components in a simple preorder traversal of a tree. However, the correspondence of the Table with the stack data structure for performing a preorder traversal of a d-tree helps explain why this is a necessary component of a context structure for modeling a dialog. Because the d-tree is constructed “on-the-fly”, the Table is essential for keeping track of whether the conversation has progressed to a point where it could represent a complete dialogue tree.
10
Conclusion
The expanded context structure we propose in this paper allows us to treat assertions as proposals to change the context in a particular way. This is a welcome result because it makes room for conversational moves that accept or reject an assertion, while at the same time making it possible to capture what is common as well as what is different between assertions and polar questions. Under the approach developed above, it is not surprising that reactions to polar questions and reactions to assertions can overlap in significant ways. Neither is it surprising that the overlap is not total, especially when it comes to [reverse] reactions. The proposals made here open the door towards a systematic study of responding assertions. The above proposals are exploratory and as such they leave many questions open. One of the largest
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is the extension of what we have said here about polar questions to questions in general. A salient issue in the formal pragmatics of questions that we have not addressed above is the nature of the bias introduced by ‘conducive’ questions (in Bolinger’s term) and the role of negation in these questions. Drawing a typology of questions (including rhetorical questions) is, obviously, an open matter. Dealing with it will, we suspect, lead to considerable additions to what we said above about polar questions. Finally, while we have dealt with some exotic discourse moves, there are many others that need to be addressed. Some urgent questions concern the context change potential of the other main sentence types, imperatives and exclamatives, as well as other discourse moves such as making a supposition. We suspect that the proposals we made here will change as these issues are addressed but we also hope that they will prove useful in furthering our understanding of them.
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