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DANIEL BURING

ON D-TREES, BEANS, AND B-ACCENTS

ABSTRACT. This paper presents a comprehensive pragmatic theory of contrastive topicand its relation to focus in English. In discussing various constructions involving contrastive topics, it argues that they make reference to complex, hierarchical aspects of discoursestructure. In this, it follows and spells out a proposal sketched inRoberts (1996, p. 121ff),using the formal tools found in Buring (1994, 1997b).1 It improves on existing accountsin the accuracy with which it predicts the non-occurrence of the accent patterns associated

with focus and contrastive topic, and locates the analysis of contrastive topics within abroader picture of discourse and information structure.

1. INTRODUCTION: A-ACCENT AND B-ACCENT

To introduce the phenomenon at hand, consider Jackendoff's (1972) discussion of the difference between the A-accent and the B-accent. Thetwo are phonologically distinct and, as Jackendoff points out, the choicebetween them is not free:

We presuppose ... that there were a number of people and a number of different thingsto eat, and that various people ate various things. Speaker A in the discourse is asking

questions of the form Who ate what? and Speaker B is answering. For the first intonationpattern, A is asking person by person:

( )A: Well, what about FRED? What did HE eat?

B: FRED ate the BEANS.

1 The present paper presents the key ideas of a longer manuscript (Biring, 1998), and

thoroughly revises my own earlier work. I would like to thank the audiences atMIT 1997,UCSC 1998, ESSLI, Northwestern University, Stuttgart University, Stanford 1999, UCLA,

Wuppertal 2000, and the Intonation & Meaning class at UCLA 2002, Christine Gunlogson, Line Mikkelsen, Summer Kern, and two anonymous L&P reviewers for their helpfulcomments on this material.

kLinguistics

andPhilosophy

26: 511-545, 2003.

9I' ? 2003 Kluwer Academic Publishers. Printed in theNetherlands.

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512 DANIEL BURING

For the second pattern, A is asking by foods:

(2)A: Well, what about the BEANS? Who ate THEM?

B: FRED ate the BEANS.

In each example we find the typical fall-rise of the B pitch accent and the fall of the A

accent, but in different positions: (1) has B on Fred and A on beans, and (2) is the other

way around" (Jackendoff 1972, p. 261, example numbers amended)

It is worth stressing at the outset that the choice of accent patternsfall+fall-rise (=A+B) versus fall-rise+fall (=B+A) - is context dependent:(1B) would be inappropriate in the context of (2A), and (2B) would be in

appropriate in the context of (1A). This is important, since it shows that Aand B-accents are conventionally associated with different interpretations,in particular, different appropriateness conditions. These appropriatenessconditions must predict which accent, A or B, is (im)possible on whichconstituent inwhich context.

It is useful to have a name to refer to the constituents marked by A- and

B-accents, respectively. Iwill use the terms focus to refer to a constituentmarked by the A-accent inEnglish, and contrastive topic for a constituentmarked by the B-accent. In what follows, Iwill simply mark foci and contrastive topics by subscript F and CT, respectively, the understanding beingthat all and only contrastive topics are marked by a B-accent and all foci

by an A-accent. These will be the only information structure categories

assumed.Note that I use the term contrastive topic here to refer to a linguistic cat

egory manifested by linguistic means: inEnglish, a fall-rise pitch accent. Itis distinct from more abstract notions such as topic (e.g., Reinhart (1982)),theme or (back)ground, which may but need not be formally marked byintonation or otherwise in a given sentence (see the instructive survey in

McNally (1998)). I believe, though, that some of the properties attributedto these more abstract categories are in fact properties of contrastive topicsin the narrow sense discussed here; hence the choice of term contrastivetopic.

Though Jackendoff, as many following him, has offered a characterization of the semantic/pragmatic difference between focus and contrastive

topic, no work up to today has attempted to formulate the conditions onthe occurrence of contrastive topics with the formal rigor found in therecent literature on focus (e.g., Jacobs (1991, 1992b), Rochemont (1986),Schwarzschild (1999); Selkirk (1984, 1995); von Stechow (1989) amongmany others). That is, there is no theory that predicts when the presence

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ON D-TREES, BEANS, AND B-ACCENTS 513

of a contrastive topic is obligatory, optional, or impossible. This paper setsout to develop such a theory.

2. A PREVIEW

I believe that Jackendoff's remarks, quoted above, contain all the relevantobservations to characterize when a contrastive topic is used: There is anissue about 'Who ate what?', and there are two ways of approaching theissue

(going by people,or

going by food).We can think of the

generalissue as (the meaning of) the question in (3):

(3) Who ate what?

This question is split up, as it were, into sub-questions such as 'Who atethe beans? Who ate the carrots? ...', or into sub-questions such as 'Whatdid Fred eat? What did Jonna eat? ... '.

As a first requirement, then, a representation of discourse or contextadequate tomodel these facts must provide a hierarchical structure amongquestions (and answers). Fortunately, such hierarchical models can alreadybe found for example inKlein and von Sutterheim (1987), van Kuppevelt(1991, 1995, 1996b) and Roberts (1996), and I will borrow from these

wherever possible. Following the latter, I call a question and the sub

question(s) belonging to it a strategy (see section 3 below for a precisedefinition).' As Roberts points out, such a strategy iswhat characterizes thecontext in Jackendoff's example. Regarding A- and B-accents, she writes:

... (1B) and (2B) both presuppose (3) by virtue of identical placement of prosodic focus [i.e., A- or B-accents; DB]. But the location of a L-H boundary sequence [i.e., a

B-accent; DB] ... presupposes a subquestion to the prosodically presupposed question.Because this boundary sequence is located differently in (1B) and (2B), they presupposedistinct sub-questions. The fact that for (1B), the presupposed questions (3) and (1A)form a question/sub-question strategy, means that (1B) itself presupposes such a strategy;similarly for (2B) .... Hence, ... utterances which contain both [B-accent marking and A

accent marking] ... presuppose not just a question under discussion, but a possibly complexstrategy of questions. (p. 123f, example numbers amended)

The gist of this proposal is thus that sentences containing both an A- and aB-accent are related to two contextually given questions at the same time,which form a question-sub-question strategy.

I find the notion of question-sub-question strategies to be a con

genial implementation of Jackendoff's characterization of the pertinent

1 Roughly, van Kuppevelt's discourse topics.

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514 DANIEL BURING

contexts. To express the complex relation (what Roberts calls 'presupposition') between the accent pattern (or rather: the CT/F-marking underlying

it) and the strategy that forms its discourse context, we need, as oursecond requirement, a theory of CT/F interpretation which is sufficientlyfine-grained to express the difference between, say, (iB) and (2B). Unfor

tunately, virtually all currently available approaches, including Roberts'

own, fall short of this second requirement, failing to formally implementthe distinction between contrastive topics and foci, or any two differentkinds of accents.2 Instead, accents are uniformly taken to mark foci (cf.e.g., the first sentence in the above quote), and no further reference to,say, the A/B-distinction is made in the rules relating accent placementto discourse structure. So both versions of Fred ate the beans receivethe same focus interpretation, and accordingly the same appropriatenessconditions, regardless of the choice between A- and B-accent. The onlyquestion that, e.g., Roberts' treatment actually predicts (1B) and (2B) to

presuppose is 'Who ate what?' The crucial distinction between the twodifferent sub-questionsis not formally captured.

In thefollowing

section3,

I willpresent my

ownadaptation

of thehierarchical discourse model in Roberts (1996), particularly suited to the

purpose of the present paper. In section 4, I provide a theory of CT/F

interpretation to go along with it, which remedies the shortcomings of

existing approaches.

3. STRATEGIES AND DISCOURSE-TREES

As said above, we want a hierarchical model of discourse structure, in

particular one which comprises the idea of a strategy. The representationsused in the present paper - discourse trees - directly imports from van

Kuppevelt (1991, 1996b) and Roberts (1996) the notions of super-/sub

questions and,from the

latter,that of

strategies.I furthermore borrow the

terms Relevance and Question under Discussion, though they are defined

2 This includes Krifka (1991, 1992, 1998); Rooth (1985, 1992); Schwarzschild (1999);von Stechow (1989). Among proposals that do distinguish different categories, some,

including Ladd (1980, Chap. 5), Gussenhoven (1984, Chap. 6), and Pierrehumbert and

Hirschberg (1990), are lacking in formal detail about the pragmatic interpretation of these

altogether, while others, including Buring (1994, 1997b), Steedman (2000, p. 660), andof course Jackendoff (1972), lack a sufficiently rich discourse model to meet our first

requirement.

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slightly differently. Consider the discourse in (4), which has the moreabstract structure given in (5):

(4)a. How was the concert?

Was the sound good? No, itwas awful.

How was the audience? They were enthusiastic.

How was the band?

How was the drummer? Just fantastic.

And what about the singer? Better than ever.Did they play old songs? Not a single one.

So what did you do after the concert? ...

(5)a. question

sub-question answer

sub-questionanswer

sub-question

subsub-question answer

subsub-question answer

sub-question answer

question ...

As a perspicuous way to represent this kind of structure I propose a newnotational device, a d(iscourse)-tree as in (6), a stripped-down version ofvan Kuppevelt (1991, 1995, 1996b)'s hierarchical discourse structures:3

3 The similarity to van Kuppevelt's representations was pointed out to me by an

anonymous reviewer. Van Kuppevelt's representations are much richer than d-trees, dis

tinguishing more than just dominance and precedence, and don't determine linear orderof utterances (see e.g., van Kuppevelt (1995, p. 130, ex. (17'b)). The question whether itis desirable to change and enrich the present system so as to accommodate these morearticulate rhetorical notions is one that I am not prepared to discuss in this paper. I do

submit, though, that d-trees are more suited for the endeavor pursued here, namely to

providea

theoryof contrastive

topicand focus, an issue not at all central to van

Kuppevelt'swork.

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516 DANIEL BURING

(6) discourse

question question

subq subq subq subq

answer answer subsubq subsubq answer

I Ianswer answer

Each node in such ad-tree,

called amove(Carlson, 1983), represents

a declarative or interrogative sentence. Concretely, I assume that each move is a

syntactic phrase marker representing a sentence, excluding CT/F-marking.The d-tree encodes a total ordering of moves in it, corresponding to theirlinear order, as defined by standard tree traversal (see appendix, definition

(55)).A theory of discourse must include a generative grammar which gener

ates the set of all admissible d-trees. Whether or not, say, a question-answer

pair Q-A iswell-formed, then, is the same as asking whether there can bea d-tree which contains the constituent (7a) as a sub-part:

(7)a. Q b. Q1

A Q2

Whether or not a question-question sequence Q1-Q2 is well-formed canbe determined by asking whether there can be a d-tree inwhich Q1 imme

diately dominates Q2 as in (7b) (which makes Q1 the super-question to the

sub-question Q2).More precisely, any sequence of utterances U0, ..., Umx, where we

understand an utterance to be a phrase marker including CT/F-marking, isa wellformed discourse if these utterances map onto the moves in some

d-tree, preserving linear order. A sequence of utterances can fail to be a

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wellformed discourse if either there is no such d-tree D, or if individualutterances U fail tomap onto a particular move inD for reasons of CT/F

marking, as specified below. In the former case the set of utterances isincoherent, i.e., defective in content proper, in the latter it is incongruent,i.e., defective in (intonational) form.

Starting with coherence, what determines the set of well-formed dtrees? Since constraints on the content of discourses are not my immediateconcern in this paper Iwill only sketch two conditions here, for the sakeof illustration:

(8)a. Informativity: Don't say known things, don't ask for known

thingsb. Relevance: Stick to a question until it is sufficiently resolved

Informativity can straightforwardly be implemented using Stalnaker's

(1978) notion of a common ground, which represents the shared knowledgeof the

participants,see

appendix,definition

(59).As for Relevance, we will follow Roberts (1996) in defining it relativeto a question under discussion, QUD.4 For any move M, the question underdiscussion is the move M' immediately dominating it.5 For a move to be

relevant, itmust answer or at least address this question under discussion.I will resort to the rather vague formulation that A is an answer to Q if

A shifts the probabilistic weights among the propositions denoted by Q.6

4 QUDs are called D-topics inBiring (1994, 1997b); they are the controlling questionsof van Kuppevelt (1995, p. 128).

5 The understanding is thus that Relevance is only defined for moves immediately dominated by a question. It thus excludes any d-tree inwhich assertions occur as non-terminalnodes.

6 Stricter definitions such as inRoberts (1996, p. 104), which requires an assertive moveto entail at least a partial answer to the QUD, exclude cases like (i).

(i)Q:Will

youcome to the

party?A: Presumably.

(i) entails neither a positive nor a negative answer to Q, even though it strongly shiftsthe probability to the positive one and should certainly count as a relevant answer. To

implement my proposal, one would have to utilize Kratzer's (1981) technique of orderingone set of propositions (the propositions denoted by the QUD) using another one (e.g., thecommon ground, or some other realistic background) as an ordering source. The require

ment then is that adding an answer to the ordering source yields a different ordering on

QUD. Spelling out these definitions is beyond the scope of this paper.

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518 DANIEL BURING

Relevance can then be stated as in (9) (note that (9b) indirectly provides adefinition of sub-question):

(9) Relevance:

a. an assertion A is relevant in a d-tree DT iff A is an answer tothe QUD for A in DT

b. a question Q is relevant in a d-tree DT iff at least one answer to

Q is an answer to the QUD for Q inDT

As mentioned, Informativity and Relevance are meant as mere illustrations

of form constraints on d-trees. As they stand, they are very permissive; theycertainly do not present a restrictive theory of what is a 'reasonable discourse' (notwithstanding the question whether there can or should be sucha theory). Nor do they assign exactly one structure, let alone one possiblecontinuation, to a given sequence of utterance (which again would seemtoo strong), especially given the possibility of implicit moves introducedin section 6 below.

Ingeneral

letmeemphasize

that the above remarks are not meant to

provide a complete theory of discourse structure at the content level. Dtrees as defined here provide the bare minimum of hierarchical structureneeded for our theory of CT/F-interpretation to be developed below. Much

more refined work on the hierarchical structure of discourse can be foundelsewhere, e.g., in the aforementioned works of Jan van Kuppevelt. A full

integration of these works is a project far beyond the scope of this paper.

4. CT-CONGRUENCE

Back to the central concern of the present paper, how things are said: Inorder for a sequence of utterances to be mapped onto the moves of a d

tree, all utterances U have to be congruent (borrowing another term from

Roberts). Congruence regards the CT/F-patterns inU, relative to the d-tree

representing the discourse.

We will distinguish two sub-conditions, a general Givenness Conditionfamiliar from the literature on focus, to be discussed in section 7, and a

specific, novel CT-Congruence Condition, to be introduced in turn; 'Con

gruence' simpliciter refers to the conjunction of these conditions, i.e., the

sub-theory which regards intonational marking.First, we define the notion of a strategy, using d-trees:

(10)a. Any sub-tree of a d-tree which is rooted in an interrogativemove is a strategy.

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We now want to be able to express the idea that CT-marking indicates

('presupposes' in Roberts' words) a strategy. What is needed is a formal

device to relate the location of CT-(and F-)marking within a sentence tothe particular strategy it occurs in. The function I Dct as defined in Biring(1997a,b) (called f[ ]I, there, see esp. 1997b, pp. 75ff) can serve exactlythis purpose. Applied to a declarative sentence a, [a]]ct yields a CT-value.

A CT-value is a set of question meanings, as illustrated in (12b) below. Forthe sake of perspicuity we can think of it as a set of questions instead, asderived by the following algorithm, which I call CT-value formation (seeappendix, definition (52)):7

(1 1)a. CT-value formation:

step 1: Replace the focus with a wh-word and front the lat

ter; if focus marks the finite verb or negation, frontthe finite verb instead.

step 2: Form a set of questions from the result of step 1 byreplacing the contrastive topic with some alternativeto it.

The output of CT-value formation for, e.g., sentence (12) is the setof questions listed in step 2 in (12a). This set corresponds to the set of

question meanings in (12b), the 'official' CT-value of FREDcT ate theBEANSF:

(12) FREDCT ate the BEANSF.a. CT-value formation:

step 1: What did Fred eat?

step 2: What did Fred eat?

What did Mary eat?What did ... eat?

b. IFREDcT ate the BEANSF]]t = {{x ate y y E De} Ix E De}

7 CT-value formation and its official semantic implementation are only defined for de

clarative sentences, and so is, consequently, the notion of 'indicating a strategy'. Indeed,I know of no instances of what should be analyzed as a CT in questions in English (or

German), and, as a reviewer points out, this seems to hold for several other languages as

well.

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520 DANIEL BURING

Regarding CT-congruence, the proposal is ...

(13) CT-Congruence:An utterance U containing a contrastive topic can map ontoa move Mu within a d-tree D only if U indicates a strategyaround Mu inD.

... where to 'indicate a strategy' is defined as in (14) below:

(14) U indicates a strategy around Mu in D iff there is a non

singleton set Q' of questions such that for each Q E Q', (i)Q is identical to or a sister of the question that immediatelydominates Mu, and (ii) I[Q]1 e [[U]Ct

The prediction of (13) is that (12) should be able to occur in a strategywhose sub-questions are drawn from the set of questions in (12b). As (15)shows, this is correct:8

(15) Who ate what?

What did Fred eat? What did Mary eat? What did ...

I I I

FREDCT te the BEANSF. MARYCT ate the EGGPLANTF.

The strategy around FREDcT ate the BEANSF in (15) is based on the setof question in the middle row, set in boldface, which are all elements of

(12b).Let us next see whether we also get the correct results when applying

CT-value formation to the twin example:

(16) FREDF ate the BEANScT

step 1: Who ate the beans?

step 2: Who ate the beans?

Who ate the eggplant?Who ate ... ?

8 Here and henceforth, I draw utterances, including CT/F-marking, into the d-trees for

expositional convenience. Strictly Speaking, only moves, without CT/F-marking are nodeswithin d-trees.

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CT-Congruence in (13) predicts that (16) can occur in a strategy thatconsists of questions as those listed in step 2 there. Again, this is the case:

(17) Who ate what?

Who ate the beans? Who ate the eggplant? Who ate ...

FREDF ate the BEANSCT. MARYF ate the EGGPLANTcT.

Finally, note that the sub-questions in (17) are not in the CT-value in (12b),and those in (15) are not in the CT-value in (16). The CT-Congruence condition in (13) thus also correctly predicts that the two intonational variantsof FRED ate the BEANS - CT+F and F+CT - cannot be exchanged.

Summing up, I have adopted the definition of a strategy given inRoberts (1996) to a framework using d-trees, and provided a formal meansto predict inwhich kinds of question+sub-question environments CTs oc

cur, and what determines their placement within the sentence. In the nextsection Iwill extend this treatment to other types of contexts.

Before doing so, letme demonstrate how the treatment just proposedimproves on previous proposals, in particular Roberts' own. As said above,the problem there is the lack of a formal distinction between A- and Baccent in the semantics. In Roberts'

system,both versions of Fred ate the

beans - (12) and (16) - receive the same focal value, namely:

(18) {xate y x,y E De}

This is themeaning of the question Who ate what? So both sentences are

predicted to 'presuppose' that question, and nothing else.9 As it stands,Roberts' theory thus predicts that both (1B/12) and (2B/16) are felicitous

in the same contexts, which is not the case, as discussed at length above.In contradistinction we now have a more complex object than just the

focal value, the CT-value. Even though the actual questions within the sets

in, say [FREDcT ate the BEANSFICt - repeated in (19a) below - are thesame as those in Roberts' (18), they are partitioned in a particular way(this iswhy the CT-value needs to be a set of sets of propositions rather

9 Two paragraphs later, Roberts (p. 124) claims" ... the answer [here (1B/12)], is con

gruent to both the immediate question under discussion, [(1B)], and the super-question[(3)]". As far as I can determine, this is not what her theory predicts.

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522 DANIEL URING

than just a set of propositions). And that partitioning is crucially differentfor the two CT/F-patterns, as demonstrated again in (19):

(19)a. IEFREDCT te the BEANSFICt = {{x ate y Iy E De} Ix E De}b. [FREDF ate the BEANScrTIC = {{x ate y I E De} Iy E De}

CT-congruence makes use of exactly that distinction, providing the neces

sary distinctions missing from Roberts' proposal.

5. PARTS OF STRATEGIES

Let us now return to Jackendoff's original example:

(20) Q: What about Fred? What did he eat?

A: FREDcT ate the BEANSF.a. I[(20A)Ict = {{x ate y Iy E De Ix De}

b. IWhat did Fred eat?, What did Mary eat?. What did Joeyeat?, ...

[(20A)]ct is a set of question meanings, sketched in (20b). By the definition in (14), CT in (20A) must indicate a strategy, which should look likethat in (21) (where Mary, of course, is thrown in for good measure):

(21) Who ate what?

What did Fred eat? What did Mary eat?

I I

FREDCT ate the BEANSF. MArycT ate...

Is there such a strategy in (20)? No All there is in (20) is thematerial

corresponding to the left branch of the strategy in (21). Remember, however, what I said above; namely that for a question-answer sequence Q-Ato be well-formed, there must be one d-tree containing Q-A as a sub-tree.

And this is the case for (20), which again, is the left branch of (21).This might look like a rather technical maneuver, but it is not. While

(20) is certainly a well-formed question-answer sequence on its own,native speakers will typically attribute to the answer FREDCT ate the

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BEANSF some sort of indication that other people ate other things (notethat Jackendoff's characterization of the context, as well as his choice of

the question What about Fred? What did he eat?, rather than just Whatdid Fred eat?, hint at this, too). I submit that it is exactly the presence ofamore complex discourse structure, containing questions likeWhat did Xeat?, that people infer upon hearing sentence (20) with a contrastive topicin it. The answer FREDCT ate the BEANSF thus contrasts with the equallyadequate Fred ate the BEANSF, which lacks any such indication. Thus theformulation that a question-answer pair iswell-formed as long as there issome well-formed d-tree containing it is not just a trick to neutralize contrastive topic effects in simple sequences. Even in such cases the sentence

with a contrastive topic conveys additional, discourse-related meaning.How do we get from 'there are other questions of the form What did

X eat?' (which iswhat contrastive topic, according to (14), conventionallyexpresses) to 'other people ate different things'? I claim that this is a standard conversational implicature: First, given that we just heard what Fred

ate, the question will be about someone other than him (Informativity).

Second,if the

speakerknew that someone else ate

beans, too, theycould

have been briefer and more informative if they had said 'Fred and Y atethe beans' instead. We therefore conclude that the speaker is aware of other

people having eaten, and is not aware that any of them ate beans. From this,the stronger statement that the speaker is aware that they did not eat beansis derived in the way familiar from, e.g., generalized quantity implicatures(cf. Gazdar (1979)). So while it is part of the conventional meaning of

(20A) that there are other questions in a local strategy, it is merely a

(cancelable) conversational implicature that other people ate other things.Indeed, it is perfectly fine to follow up on (20A) by saying ... but I don'tknow what the others ate or ... and maybe Mary ate beans, too (amoredetailed discussion can be found inBuiring (1997b)).

In previous work I called these cases purely implicational topics, stress

ing the fact that the presence of a contrastive topic is understood as arhetorical device here, as e.g., in (22) (Roberts 1996, p. 122 discusses a

parallel example):

(22) Q: Where were you (at the time of the murder)?A: IcT was at HOMEF.

As before, choice of the CT-marked structure over a plain Iwas at HOMEFserves to indicate the presence of amore complex strategy which could berooted in a question likeWhere was everyone (at the time of themurder)?

The speaker might use it to suggests that another sub-question of that

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524 DANIEL BURING

strategy should be discussed, that is, that other people might not have as

waterproof an alibi.

How can we think of this in terms of discourse dynamics? Does thequestioner in (22) already have a more complex d-tree in mind, when

they ask the question, or do they have to accommodate it upon hearingthe answer? Who makes up d-trees in the course of the conversation, and

when? The present proposal is actually rather neutral with regard to these

questions. Recall that we said that a sequence of utterances Uo, ..., Ukmust be mapped onto the moves in some d-tree. There can be more thanone d-tree that 'fits' a given sequence, and nothing guarantees that all

participants in the discourse have the same d-tree 'inmind' while conduct

ing the conversation. It is of course a reasonable, though not necessary,assumption that speakers have a particular idea about the structure of thediscourse up until the present point, and perhaps even beyond that, which

corresponds to a particular class of d-trees.A's answer in (22) requires that the d-tree representing the discourse in

(22) contains a particular implicit super-question toWhere were you?, and

at least one more sub-question following Where were you? 'coming up'.The present proposal remains uncommitted with regard to the questionwhether this means that the questioner Q has assumed the discourse tohave such a structure prior to A's utterance or not. It only demands thatafter A's utterance, the structure of the discourse assumed must correspondto a d-tree with the properties described.

In sum, this section showed how discourses consisting of only one

question and one answer can be treated in the current framework. A contrastive topic indicates that the sequence is part of a larger discourse which- since it is not part of the actual example - the competent speaker can

only guess at, using the information provided by the location of contrastive

topic and focus in the sentence. Given this assumption, implicature-effectsfound with contrastive topics turn out to follow straightforwardly from thetreatment developed so far.

6. IMPLICIT MOVES

Consider now another sort of question-answer pairs; (23a) is a slight variation of Jackendoff's earlier example, (23b) is the English counterpart of

Btiring's (1994) partial topic example:

(23)a. Who ate what? - FREDCT ate the BEANSF.

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b. What did the pop stars wear? - The FEMALECT pop stars woreCAFTANSF.

Do these examples meet our definition of CT-congruence? No again TheCT-values are given in (24a) and (24b), respectively:10

(24)a. B(23a)ict = {{x ate y Iy E De} I E Det What did x eat?

b. I(23b)]ct = {{ the P stars wore x Ix De} IP E Det}' What did the P pop stars wear?

The meanings of the overt wh-questions in (23) are not elements of theCT-values in (24). Note though that the questions in the CT-values are

potential sub-questions to the actual questions in (23a/b). Put differently,an example like (23b) could be mapped onto the underlined moves in adiscourse tree like (25):

(25) What did the pop stars wear?

What did the female pop stars wear? What did the male pop stars wear?

I IThe FEMALEcT pop stars wore CAFTANSF

So far we assumed that a question followed by an answer in a discourse

needs to be mapped onto a question-move immediately dominating theanswer-move in a well-formed d-tree. Let us assume instead that a mapping as indicated in (25) is possible, too.We will say that the sub-question'What did the female pop stars wear?' is an implicit (as opposed to ex

plicit) question in the d-tree. The claim is thus that examples like (23a)and (23b) must be mapped onto d-trees which contain an implicit, i.e.,

unpronounced, move in between those present in the examples. In (26) I

give amore general definition incorporating this assumption (cf. appendix,definitions (62) and (63)):

(26) A sequence of utterances (Uo, ..., U)n constitutes a wellformed discourse iff there is a well formed d-tree DT such that

(Uo, ..., Un) can be mapped onto the explicit moves of some

(possibly improper) part of DT.10

(23a) would be predicted fine under a theory which treats contrastive topics as foci,such as Roberts (1996). But (23b) would presuppose the question 'Which pop stars wore

what?'; so no general solution along these lines seems tenable.

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526 DANIEL BURING

Implicit moves - in particular implicit questions - are assumed by manyauthors (see e.g., van Kuppevelt (1991, 1995, 1996a,b) and the references

therein). I am not aware, however, of any proposal which addresses howthe implicit/explicit distinction interacts with CT/F-marking. This will bedone in the next section.

7. GIVENNESS

As a starting point, notice that the CT-marking on Fred in (23a) andfemalein (23b) is obligatory. Contrast, e.g., (27a) (=(23b)), with (27b) (implicit

moves are marked by parentheses and italics):


(What did the female pop stars wear?)a. The FEMALEcT pop stars wore CAFTANSF.b. #The female pop stars wore CAFTANSF.

Why is this? One might suspect that CT is obligatory because there is a

strategy here. The rule would thus be that strategies must be indicated byCTs. This, however, is not the case, as (28) shows. If the sub-question is

explicit, CT is genuinely optional; it is up to the speaker tomark or notmark the strategy, as is particularly clear if the pertinent constituent is inaddition pronominalized, as in (28c):


What did the female pop stars wear?

a. The FEMALECT pop stars wore CAFTANSF.

b. The female pop stars wore CAFTANSF.c. They wore CAFTANSF.

The contrast between (27) and (28) suggests that CT-marking is obligatoryonly with implicit sub-questions. Intuitively, this is not surprising: A newelement like the adjective female must bear an accent when first used inthe discourse. This is done in the explicit sub-question in (28) (which, notabene, requires an accent on female), but only in the answer in (27).

This reasoning, however, rests on two crucial premises: First that CT/F

marking has something to do with the given/new distinction, and secondthat implicit moves, though crucial for Relevance and the CT-condition,cannot serve to introduce a new element and make it count as 'given' for

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moves to follow. But so far we haven't been assuming so.1 To remedythis, let us follow Schwarzschild (1999) in assuming that (29) holds:

(29) Givenness:

Every constituent which is not Given needs to be marked.

For the purposes at hand, think of Given (with a capital G) as 'previously mentioned' (or Rochemont's (1986) c-construable); more in detail,a constituent is Given if there is a previously uttered constituent whichis identical (female-female), an instance or hyponym (Slaughterhouse5/novel-book), coreferent (a man-the man/he), but also if its semanticallyvacuous (something). A precise and comprehensive definition of Givenness in this technical sense is provided in Schwarzschild (1999), towhichthe reader is referred.

Crucially for our purposes, Givenness will only 'see' explicit moves.

Implicit moves, just like any kind of hierarchical relation such as questionunder discussion or strategy are irrelevant for it. If we understand 'marked'

in (29) tomean 'F- or CT- marked', the accurate prediction results: CT cannot be omitted if the element it marks has not been mentioned previously,or in an implicit question only.12

It is worth pointing out that the addition of (29) introduces an inter

esting factorization into the present theory. CT-marking now is subject to a

general appropriateness condition qua being an accent, namely (29), which

indiscriminately regards F- and CT-marking, and regards explicit moves

only. In addition it is subject to other, more specific appropriateness con

ditions qua being a CT-accent (as opposed to an F-accent), namely thosestated in the CT-condition, which do not discriminate between implicit and

explicit moves, as shown in the previous section.Note furthermore that (29) also takes care of an aspect that we have

ignored so far: Accenting inCT-less clauses. It predicts, for example, that

1 And in fact, the two frameworks this theory is built on- Roberts (1996) and Biring

(1994, 1997b) - don't. They both assume that F- (and in the case of Biiring, CT-) placementis determined with respect to the QUD, and neither of them makes the relevant distinctionbetween implicit and explicit moves.

12 This is not to say that every non-Given constituent must be accented. As is welldocumented in the literature, a single accent on a word can license F-marking on morethan just that word, as formally modelled through the horizontal part of the focus projection rules of Selkirk (1984, 1995) and Rochemont (1986), the accent domain rules ofGussenhoven (1983,1999), or the integration process of Jacobs (1992, 1999), among others. I assume that the same holds for CT-marking (cf. Bring (1997b, 3.1.3)); the examplesdiscussed here do not involve such cases, so there is no need to commit to or explicate here,

any one of these approaches. Whether, as an anonymous reviewer suggests, other markingsthan CT and F can mark non-Given constituents, too, is a topic for future research.

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528 DANIEL BURING

F will be on caftans in (28b) and (28c) above, rather than on, say, wore. Italso carries over to focus in questions, predicting e.g., that the explicit sub

question What did the female pop stars wear? in (28) will have an accenton female.13 For a more general exposition of this theory of F-marking, Irefer again to the seminal Schwarzschild (1999).

At this point our account is by and large complete. We have developeda theory of d-trees which supports a theory of CT/F-interpretation. Dtrees consist of explicit and implicit moves which are ordered linearlyand hierarchically. For a d-tree to be well-formed, each move has to

obey principles such as Informativity and Relevance, which regard onlythe (truth-conditional) content (the 'ordinary semantic value' in terms of

Rooth (1992)) of moves. For a sequence of utterances to be a wellformed

discourse, each utterance must map onto a move in a d-tree, subject toCon

gruence, which governs the CT/F-patterns, and, ultimately, the accenting.We have isolated two sub-principles of Congruence, spelled out in (30),

the presently crucial and new one of which is explicated in (30c):

(30)a. Givenness Condition:

An utterance U can map onto a move Mu within a d-tree D

only if every constituent C in U which is not Given is CT- orF-marked.

b. CT-Congruence:An utterance U containing a contrastive topic can map ontoa move Mu within a d-tree D only if U indicates a strategyaround Mu inD.

c. U indicates a strategy around Mu in D iff there is a non

singleton set Q' of questions such that for each Q E Q', (i)Q is identical to or a sister of the question that immediatelydominates Mu, and (ii) [[QD0 E I[U]t.

I have demonstrated how these conditions capture various examples in

volving B-accents, among them Jackendoff's original cases as well asanswers to

multiple wh-questions,and various cases of isolated

questionanswer sequences, parallel to the German cases discussed inmy earlierwork. The remaining sections discuss some extensions and refinements ofthis basic approach.

13With the same goal inmind, Roberts (1996, p. 112) defines the focus alternative setsfor questions and requires that they equal the local question under discussion. For What didthe FemaleF pop stars wear? this set is {the q pop stars wore x Ix E De, q E Det }, i.e.,the meaning of the question 'Which pop stars wore what?' Although this is one possible

super-question,it is not the

onlyone, as (28) shows. I conclude that the treatment in terms

of Givenness ismore general.

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8. FANDCT

In the last section we established under which circumstances CT- or F

marking is obligatory, namely if an element is not Given. Restricting ourattention to sentences with two such elements, we end up with four logicalpossibilities: CT+CT, F+F, CT+F and F+CT. What determines the choice?

First of all, there must be a strategy for CT to occur at all. Otherwise,CT-Congruence in (13) is violated. Two cases inwhich it is predicted tobe violated are (31) and (32) ((31) courtesy of an anonymous reviewer; seeJacobs

(1997, p. 100) fora

parallelGerman

example):

(31) B: It looks like someone already ate from the buffet -

A: Yes, JOHNF ate the BEANSF.

A':# Yes, JOHNcT ate the BEANSF.

A":# Yes, JOHNF ate the BEANScT.

(32) Q: Did Knut break up with Allessa?

A: No, ALLESSAF broke up with KNUTF.

A':# No, ALLESSAcT broke up with KNUTF.

A":# No, ALLESSAF broke up with KNUTcT.

The strategies indicated by (31A'/A") would involve questions of the form'What did X eat?', and 'Who ate X?', respectively, pertaining to a superquestion like 'Who ate what?'. But B's utterance makes it clear that no such

strategy is of interest here, since John ate the beans completely answersthe question at hand. Similarly, no strategy involving questions of the form'Who did X break up with?' or 'Who broke up with X?' will be helpful,

or indeed possible in answering (32Q) after the utterance of Allessa broke

up with Knut, which in the pertinent context provides a complete answer

to the question. Therefore the precondition for using CT - the presence ofa strategy - is not met and only F is predicted to be possible, correctly, it

appears.14To move to the other extreme, sometimes more than one strategy is

possible. An explicit sub-question will indicate which one the speakerchooses; with an implicit sub-question, only the CT/F-pattern of the an

14 As to why Allessa and Knut can and must be F-marked, despite being Given, the

reader is referred again to Schwarzschild (1999).

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530 DANIEL BURING

swer will tell. The result is interchangeability of CT+F and F+CT with

respect to a given question:

(33)a. Who ate what?/What did people eat?

(Who ate the beans?) FREDF ate the BEANScT.b. Who ate what?/What did people eat?

(What did Fred eat?) FREDCT ate the BEANSF.

Depending on what the speaker regards as the more promising strategy, she

might choose to go dish-by-dish as in (33a) (making the dishes the 'sortalkey', or as Jackendoff calls it the 'independent variable'), or person-byperson as in (33b).

In between these two cases (no strategy or multiple strategies) we findthose inwhich only one strategy is feasible. This is the case in the pop star

example:

(34)a. What did the pop stars wear?

(What did the female pop stars wear?)The FEMALECT pop stars wore CAFTANSF.

b. What did the pop stars wear?

# (Which pop stars wore caftans?)# The FEMALEF pop stars wore CAFTANSCT.

Thesub-question

and answer in (24b) are odd, and hence marked by #.As far as Congruence goes, however, there is nothing wrong with them.

Nonetheless, the present account offers an explanation for the oddness:

By the CT-condition, the answer in (34b) indicates a strategy which asks

by pieces of clothing, rather than by (groups of) pop stars. At this point,grammar ends and world knowledge takes over: since this is a pointlessand ineffective strategy to approach answering the super-question 'Whatdid the pop stars wear?', we perceive of it as pragmatically odd. Resonant

with this line of argument, note that (34b) indeed turns into a happy answerto (34), if one imagines a context inwhich there is only a limited numberof different costumes towear.

In a case where there are plausible strategies, does one have to use oneof them? Take (34) once more. We've established that both female and

caftans are in need of marking (they are not Given), and that female, butnot caftans qualifies for CT-marking. Together this predicts that the patternCT + F will be possible (and F + CT will not). But is F + F possible, too?

Speakers seem inclined to judge (35A) as anomalous, if not unacceptable:

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(35) Q: What did the pop stars wear?

A:# The FEMALEF pop stars wore CAFTANSF.

It seems as though the option of using CT + F blocks using F + F (thoughthe latter is in principle possible, cf. (31/32) above). So far, nothing accounts for this, since F does not impose any requirements on the elementsitmarks and should therefore be possible wherever CT is. The oddity of

(35) then suggests a principle like (36):

(36) If a constituent needs to be marked due to Givenness, CT

marking is preferred over F-marking, where possible.

Perhaps (36) is derivable, namely from the assumption that F is generallyavoided where not strictly speaking necessary (cf. Schwarzschild's (1999)principle Avoid F); F is barred not only on Given constituents, but alsoon non-Given ones which could alternatively be CT-marked (see Biiring(1998) for an implementation of this). I leave investigation of this matter

to further research, and assume (36) for the time being.Arguably, (36) also accounts for the following contrast:

(37) Do any of your students work on a Finno-Ugric language?a. Well, let's see. RUFUScr works on CALAUTEANF.

b. Well, let's see. RUFUSF works on CALAUTEANF.

Answer(37a) implies

that Calautean is not aFinno-Ugric language.

The

CT-marking indicates a strategy of the type 'Which language does studentX work on?', and at least some of these questions lead to answers whichanswer question (37) (e.g., Sabina works on Hungarian). (37b) on the otherhand implies that Calautean is a Finno-Ugric language. If so, it is a directand complete answer to the question. Hence, there is no strategy and CT

marking is impossible.While the latter fact explains that (37a) is inappropriate ifCalautean is

Finno-Ugric (provided that complete answers cannot be part of a strategy,cf. section 9), nothing seems to prevent (37b) from being used if it isn't.Just because there is a strategy it doesn't need to be marked. And the factthat Rufus is not Given could be taken care of by marking it F, as in (37b).

The preference principle in (36) provides a solution to this puzzle: DoubleF as in (37b) marking will be chosen only if there is no strategy available;otherwise, CT+F is preferred, as in (37a).

Another way of conceiving of (36) is thus to think of it as a means to

avoid ambiguity: If there is a strategy, indicate itby using contrastive topic,

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532 DANIEL BURING

so that multiple-F is used unambiguously in strategy-less context. The factthat CT may be omitted in cases like (28b) above would be explained by

assuming that here the explicit sub-question serves tomake the strategyvisible already. Again, Iwon't speculate further on the issue here.

To sum up, the theory at this point predicts that F+F is possible only inthe absence of a strategy. Otherwise, CT+F or F+CT will be chosen. Thechoice between the latter two depends on the choice of strategy, which

may or may not be determinate given a particular main question. Apparentoptionality between CT+F and F+CT reflects a discourse which - up to theutterance in question - is compatible with two different d-trees.

The question we haven't addressed yet iswhether we also find CT+CT

patterns. In Biiring (1997b) I pointed out that a contrastive topic in German must be followed by at least one focus. Accordingly, CT+CT doesn't

exist, just as little as F+CT or sole CT. In English the situation is differentin that we do find sole B-accents, which should be indicative of a solecontrastive topic. I do not at this point have a complete account of theseto offer. A cursory glance suggests that they indicate strategies made upof

polar questions;the

following exampleis taken from O'Connor and

Arnold (1973, p. 173):

(38) Can Jack and Bill come to tea? - BILLCT can.

The implicit subquestion here is 'Can Bill come to tea?', the obvious othermember being 'Can Jack come to tea?'. Would such a strategy be indicated

by the answer in (38)? It would if we assumed the meaning of a polarquestion to be the singleton set containing its literal meaning, as in (39):

(39)a. [Can Jack come to tea?]? = {Jack can come to tea}b. [Can Bill come to tea?]] = {Bill can come to tea}c. [BillcT can ]ct = {{x can come to tea} I E De}

On such an account, CT-Congruence is obeyed in (38). This then wouldlead us to predict that CT+CT patterns should be possible in English, too.I leave it to further research to (dis)confirm this prediction.

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9. ATTACHMENT

Consider (40):

(40) Q: How many (of the 74) abstracts got accepted?

SQI: Did any abstracts get accepted?Al: (Yes,) SOMECT abstracts DIDF get accepted.

SQ2: Did most abstracts get accepted?A2: (Yes,) MOSTCT abstracts DIDF

get accepted.

I take it that this discourse is acceptable (though perhaps the focus accentsin the answers can and are even preferred to be omitted, cf. the previoussection). Assuming that focus on the finite verb can signal so-called verum

focus, the CT-values of Al and A2 are (41):

(41) I[(40A1)]jC = [[(40A2)]Jc = {{Q abstracts got accepted} IQ E

Det,t } Did X abstract get accepted?

Since themeanings of SQ1 - {some abstracts got accepted} - and SQ2 -{most abstracts got accepted - are both members of (41), (40) is predictedto be fine.15 But now consider the following continuations of (40):

(42) SQ3: Did all the abstracts get accepted?A3-1:# (Yes,) ALLcT the abstracts DIDF get accepted.A3-2: (Yes,) ALLF the abstracts got accepted.A3-3: (No, exactly) ONECT abstract was REJECTEDF.

A3-1, with CT + F, is downright bad. Why? It cannot be because A3-1concludes the strategy (the main question Q is completely answered), for

so does A3-3. It cannotbe because of the

propositionalcontent of

A3-1,for that is the same as that of A3-2. The only thing that teases A3-1 apartfrom all of Al, A2, and A3-3 is that A3-1 is by itself a complete answerto the main question Q, in (40). Apparently, an answer which doesn't justend a strategy, but completely subsumes it, cannot be marked to indicate

15 I've stuck to the assumption (made in the previous section) that polar questions are

represented by singleton sets. Nothing would change ifwe assumed them (and themembersof the CT-values of sentences with verum focus) to denote two-membered sets of the form

{p,W-p} instead.

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534 DANIEL BURING

that strategy, propose to implement this by forcing (40) + (42-A3-2) to be

represented as in (44) rather than in (43):

(43) Q

SQ1 SQ2 SQ3

I I I

not: Al A2 A3-2

(44) Q

SQ1 SQ2 SQ3 A3-2

I . I

but: Al A2

According to (44), A3-2 is not in a position to indicate the strategy rootedinQ. Therefore it cannot contain CT-marking as in A3-1 in (42). To block

(43) we need to invoke an additional principle which requires 'highestattachment':

(45) Principle of highest attachment:

IfM is a complete answer to Q, Q immediately dominates M.

I can see no particular reason why (45) holds, but the data clearly tell us inthis case.16

16Perhaps more striking are the German scope inversion data (i), discussed in Buiring

(1997a), and (ii):

Q: How many politicians are corrupt?/Are all politicians corrupt?

(i) ALLECT Politiker sind NICHTF corrupt.all politicians are not corrupt

(ii) ALLECT Politiker SINDF corrupt.all politicians are corrupt

Both sentences indicate a strategy including questions like 'Are X politicians corrupt?'.(ii), however, answers the very super-question 'How many politicians are corrupt?' and

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10. ACCENTING

While it is not thegoal

of thispaper

toprovide

acomprehensive theory ofthe prosodic realization of CT and F where they mark larger constituents,

I would like to close with some speculations about the issue (see Steedman (2000) for a recent, elegant, and somewhat radical proposal whichis largely compatible with the pragmatics devised in this paper'7). Above

we assumed that both CT- and F-marking can serve tomark a non-Givenelement. While this is in fact the only function of F, it is something CTdoes 'along the way'. Its primary function is to indicate a strategy. It is

tempting to try and separate out these two functions. The idea is that thenon-Givenness marking function of CT is really the effect of an F-marking,while CT exclusively marks the strategy. What we used to refer to as CT isthus a combination of an F-mark and a CT-mark, the latter dominating theformer. (46) illustrates this idea:

(46) Q: Who ate what?

A: [[FRED]FlCT ate the BEANSF.

If this idea could be sustained, the resulting picture would be very simple:F marks non-Givenness and non-Givenness is marked by F; CT marks

strategies. There are two suggestive pieces of evidence for this view.First, it iswell-known that within a larger focus, sub-constituents must

remain unstressed if they are Given. This phenomenon is generally referredto as deaccenting and can be accounted for by assuming that F is licit only

on non-Given constituents.'8 Strikingly, we find the same phenomenonwith contrastive topics:

is therefore unacceptable with CT. (i) does the same on a reading where it means 'all

politicians are non-corrupt', but not on one where itmeans 'not all politicians are corrupt'.It therefore only has the latter reading with CT, even though it is ambiguous without.

17 Here's how: The feature CT corresponds to the 'theme' part of the theme-rhemedistinction in Steedman (2000), and F, on the proposal to be introduced in this section,to his 'focus' (both within the theme and within the rheme) (but see note 19 below);Steedman's 'rheme' is just the complement of the CT, which doesn't have a semantic objectcorresponding to it in the present theory, though. A detailed comparison of the pragmaticside of both proposals, to the extent that they are worked out, is not within the scope of this

paper.18 The truth is more complicated, as discussed perspicuously in Schwarzschild (1999);

his treatment in terms of theAvoid F principle is fully compatible with the story told here.

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536 DANIEL BORING

(47) Q: Where will the guests at Ivan and Theona's wedding beseated?

(SQ1: Where will friends and relatives of the couple sit?)Al: [FRIENDS and RELATIVES of the couple]cr will sit

[at the TABLE]F.

(SQ2: Where will reporters sit?)A2: [REPORTERS]cr have to sit [in the BACK]F.

The crucial move here is Al: The CT inAl is clearly the entire subject NP;

note that the strategy consists of questions of the form 'Where will X sit?',not 'Where will X of the couple sit?', which wouldn't be instantiated by'Where will reporters sit?'. But since the couple is given (through mention

ing of Ivan and Theona inQ), it is deaccented, and it has to be: Friends andrelatives of the COUPLE will sit at the TABLE would clearly be infelicitousin this example (though itmight be okay in a different strategy, which

would go on talking about friends and relatives of someone else).Pursuing the idea that the actual accent placement within a CT is a

function of F-marking within the CT, we can explain this straightforwardly.The choice is between (48a) and (48b):

(48) [FRIENDSF and RELATIVESF of the COUPLEF]CT

b. [FRIENDSF and RELATIVESF of the couple]cr

The noun couple, though Given, is nonetheless (and thus wrongly) F

marked in (48a); in (48b) on the other hand, it is (correctly) unmarked,hence unaccented.19

As for the second piece of evidence, let us look at the actual phonological realization of the two accents. In the tradition of Pierrehumbert

(1980), the contour realizing focus is analyzed as a plain high pitch accent,H* (the falling contour is the result of that accent being followed by a

(default) L-phrase tone). The fall-rise that comes with the contrastive topic,on the other hand, is characterized as a combination of a pitch accent plusa high boundary tone, H%. The pitch accent in this 'tune' is variously described as a plain high tone, H*, or a rise, L+H*; combined with the default

19 Note that this effect cannot be achieved through a general condition against superfluous CT-marking, since, as we have seen in section 7, CT-marking is generally possible ifthere is a strategy, regardless of Givenness.

This example also argues against the proposal in Steedman (2000) that the CT-value (histheme alternative set) should abstract over the focus within the CT (his theme) only, forthat would wrongly yield 'Where will X of the couple sit?' as the theme alternatives, as

pointed out in the main text.

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L-phrase accent; both variants will result in a fall-rise pattern, either H* LH% or L+H* L-H%. In an example like (47A1)/(48b), the pitch accent is

realized on (the lexical stress syllables of) friends and relatives, while theboundary tone is realized on the last syllable of couple (capitals indicatemain stress syllables in accented words):

( (L+)H* (L+)H*L- H% H* L-L%

[FRIENDS and RElatives of the couple ]CT will sit [at the TAble]F

(49) suggests a very simple relation between CT/F-marking and accents,

essentiallythat assumed in Steedman

(2000): CT-markingis realized

bya

boundary tone on the constituents so marked, F-marking is realized by a

pitch accent on the constituents so marked (if the B-accent contains reallyjust an H* pitch accent, this is even the same one in both environments). Ifthe two of them coincide, we get a complex accent:

H* L-H%

(50) [[FRED]F ]CT

11. SUMMARY

The aim of this paper was to outline a theory of CT- and F-marking. Two

assumptions I hope to have motivated are:

* The theory needs to include both F- and CT-marking; neither isreducible to the other.

* CT/F-theory needs to make reference to a complex model of discourse,in particular one that allows to define inherently hierarchical notionslike strategy in addition to question under discussion and common

ground.

I have shown that, given these assumptions, a variety of phenomena can begiven a uniform treatment.

Since the present model assumes a tripartite structure (CT, F, and

neither), it is formally, though not pragmatically, comparable to the linkfocus-tail structures in the work of Enric Vallduvi and his colleagues(Vallduvi 1990, 1993; Vallduvi and Engdahl 1996, a.o.), suggesting thatthe cross-linguistic phenomena discussed in these works might be amenable to a treatment in terms of the pragmatics proposed here. Initial

applications of the present framework toHungarian, Japanese, Korean and

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Comment or Rheme-Theme have a role to play in the explanation of other

phenomena, but for those discussed here, I submit, they are irrelevant (seeagain McNally (1998) for a similar point of view).

12. APPENDIX: FORMAL DEFINITIONS

12.1. CT-Value

We presuppose a function I[A]]? hich delivers meanings in the domain of

A in the usual way (I ignore worlds and assignments):

(51) For all A, B, let + abbreviate the composition rule applied in

determining the ordinary meaning of a complex expression [AB], i.e., I[ABI = I[A1O I[B]D.

In addition, we assume a function I[A]C, which delivers meanings in the

power set of the power set ofDtype(A);

his is the function called |[D in

Biiring (1997b), a conservative extension of [lf from Rooth (1992) (whichdelivers meanings in the power set of Dtype(A)).

(52) [[AIc equalsa. Dtype(A)1, fA is F marked, otherwise

b. {{ca I E Dtype(A)), fA is CT-marked, otherwise

c. {{I[A]]?}}, ifA is a terminal, otherwise

d. I[Bcft, ifA = [B], otherwise

e. { I3b, c[b E [B]Jct &c E I[C]c & P = Ia I3b', c'[b' E b &

c' E c & a = + c']}]}, if A = [B C]

12.2. D-Trees

12.2.1. MainDefinitionsWe assume a set D* of all well-formed discourses (Roberts' (1996)

information structures), such that

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540 DANIEL BURING

(53) (ICG,D,EXPLICIT) E D* iff

a. ICG is a set of propositions (the initial common ground of the

participants)b. Dis a tree

c. EXPLICIT is a function from nodes in D to {O, 1

d. nodes inD, called moves, are syntactic phrase markers (withoutCT/F-marking)

e. all moves in D are Informativef. all moves in D are Relevant

g. all moves inD meet the Minimality Condition

(54) Minimality Condition:

IfM is a complete answer to Q (i.e., if IM]? logically entails

p orW-p for every p E I[Q]?), Q immediately dominates M

12.2.2. Ancillary Definitions(55) Precedence:

For any Moves M1 and M2, M1 precedes M2 in D if

a. M1 dominates M2, or

b. there areMoves M3 and M4 which are sisters in D, M3 is to theleft of M4, and M3 dominates or equals Ml and M4 dominates

or equals M2

(56) Predecessor:

Let PREDD(M) be that function which assigns to any move Mthe smallest set of moves M' such that

a. M' precedes M in D

b. EXPLICIT(M') = 1

(57) Common Ground:

Let CGD(M) be a function from moves M in a d-tree D in

(ICG,D,EXPLICIT) to sets S of propositions such that for anyMove M inD, S is the smallest set such that

a. ICGc S

b. I[M']] E S iffM' is an assertive move inD and M'precedes

MinD

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(58) Immediate Question under Discussion:

Let IQUDD(M) be a function from moves M in a d-tree D to

sets of propositions, such that IQUDD(M) = I[QI where Q isthe node immediately dominating M in D

12.2.3. Conditions on Propositional Content

(59) Informativity: A move M in D is informative iff

a. M is an assertion and CGD(M) does neither entail I[M]] norW-I[M1?, or

b. M is a question and for at least some element p in I[M0?,

CGD(M) does neither entail p norW-p

(60) Relevance: A move M in D is relevant iff

a. M is assertive and [M?0 answers IQUDD(M), or

b. M is interrogative and at least one answer to I[M]D answers

IQUDD(M).

(61) Answer:A proposition p answers a set of propositions Q ifp contextuallyentails a change in probabilistic weight for at least some q E Q.

12.3. Wellformed Discourse

We now come to the core, the definition of wellformed sequences of utter

ances, including CT/F-marking. Generally, U refers to an utterance, i.e.,a phrase marker with CT/F, while M refers to a (corresponding) move

(phrase marker without CT/F-marking) in a d-tree D.

(62) A sequence (Uo, ... Umax) of phrase markers including CT/F

marking is d-wellformed iff there is a d-tree D such that for each

Un, 0 < n < max, Un has a congruent map Map(Un) amongthe moves in D, and for all m, if m < n, then Map(Um) E

PREDD (Map(U,)).

(63) Mu inD is a congruent map for U iff

a. EXPLICIT(M) = 1

b. Mu = U, except for CT/F-marking (remember thatmoves don'tinclude CT/F-marking)

c. the mapping respects Givenness

d. themapping respects CT-Congruence

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542 DANIEL BURING

Derivatively, Um is appropriate with respect to (U0, ..., Uk) iff (UO, ...

Uk, Um) is d-wellformed.

12.4. Congruence

(64) Givenness Condition:

An utterance U can map onto a move Mu within a d-tree D onlyif every constituent C inU is either

a. Given, i.e., C, or an expression synonymous with C, or a

hyponym of C, occurs in some move M' E PREDD(MU) (cf.Schwarzschild (1999, p. 151) for a much refined and uniformdefinition), or

b. CT- or F-marked

If the remarks in section 10 are adopted, the reference to CT-marking canbe dropped from (64).

(65) CT-Congruence:An utterance U containing a contrastive topic can map onto amove Mu within a d-tree D only ifU indicates a strategy around

Mu in D.

(66) U indicates a strategy around Mu in D iff there is a non

singleton set Q' of questions such that for each Q E Q', (i)Q is identical to or a sister of the question that immediatelydominates Mu, and (ii) I[QD?E I[U]Ct

(67) Preference Principle:If a constituent a needs to be marked due to Givenness, CT

marking is preferred over F-marking, where possible.

Again, ifCT always dominates F, (67) must be changed to:

(68) Preference Principle, revised:

An F dominated by CT is preferred to a bare F.

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