
\documentclass{salt}

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\title{What projects and why%
\thanks{We are grateful to reviewers and audience members at SALT, and to the participants of the 2008 and 2009 PEPA workshops. The authors are jointly supported by collaborative NSF grants BCS-0952(862/571/497), and Beaver is further supported by  NSF grant BCS-0904913 and the NYCT TeXIT project.}
}

\author{%
\saltauthor{Mandy Simons \\ \institute{Carnegie Mellon University}} \AND
\saltauthor{Judith Tonhauser \\ \institute{The Ohio State University}} \AND
\saltauthor{David Beaver \\ \institute{The University of Texas at Austin}} \AND
\saltauthor{Craige Roberts \\ \institute{The Ohio State University}}
}


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\begin{document}


\maketitle




\section{Introduction}

The empirical phenomenon at the center of this paper is {\em
projection}, which we define (uncontroversially) as follows:

\begin{exe}
\ex \label{def}{\bf Definition of projection} \\ An implication
{\em projects} if and only if it survives as an utterance implication when
the expression that triggers the implication occurs under the
syntactic scope of an entailment-cancelling operator.
\end{exe}
Projection is observed, for example, with utterances containing
aspectual verbs like {\em stop}, as shown in (\ref{1}) and (\ref{2})
with examples from English and Paraguayan Guaran\'i (Paraguay,
Tup\'i-Guaran\'i).\footnote{The Guaran\'i examples in this paper are
 given in the standardized orthography of Guaran\'i used in Paraguay
 (\citealt{MEC}), except that all postpositions are attached to their
 host. Following the official orthography, accents are not written
 for normally accented words (stress on the final syllable); stressed
 nasal syllables are marked with a tilde.  The following glosses are
 used: 1/2/3(sg) = first/second/third person (singular), {\sc imp} =
 imperative, {\sc neg} = negation, pron = pronoun, {\sc qu} =
 question marker, {\sc rc} = relative clause.} The Guaran\'i example
in (\ref{1}) and its English translation have at least the following
implications: (i) Carla has previously smoked, and (ii) Carla stopped
smoking. The first but not the second of these implications is also
conveyed by the question version of sentence (\ref{1}), as in
(\ref{2a}), or when (\ref{1}) is embedded under entailment-cancelling
sentential operators, such as negation, as in (\ref{2b}), the
antecedent of a conditional, as in (\ref{2c}), or an epistemic modal,
as in (\ref{2d}).  Hence, by the definition in (\ref{def}), the first
but not the second implication of (\ref{1}) projects.

\begin{exe}
\ex \label{1} \gll C\'arla o-heja la jepita. \\ Carla 3-stop the smoke
\\  \glt `Carla stopped smoking.'
\ex\label{2}
\begin{xlist}
\ex\label{2a} \gll C\'arla-pa o-heja la jepita? \\ Carla{\sc -qu} 3-stop
the smoke \\ \glt `Did Carla stop smoking?'

\ex\label{2b}\gll C\'arla nd-o-hej\'a-i la jepita. \\ Carla {\sc neg-}3-stop{\sc
-neg} the smoke \\  \glt `Carla did not stop smoking.'

\ex\label{2c} \gll C\'arla o-hej\'a-ramo la jepita, a-vy'a. \\ Carla
3-stop-if the smoke 1sg-happy \\ \glt `If Carla stopped smoking, I am
happy.'

\ex\label{2d}\gll I-katu C\'arla o-heja la jepita. \\ 3-possible Carla
3-stop the smoke \\ \glt `It's possible that Carla stopped smoking.'
\end{xlist}
\end{exe}

Besides aspectual verbs, projection has been classically studied in
conjunction with the presuppositions triggered by factive verbs and
nouns, definite noun phrases, additive particles
like {\em too}, clefts and intonational backgrounding, among others
(e.g.\ \citealt{langendoen-savin71,soames:handbook,beaver97}). 
In much of the literature, it has been assumed that implications which 
project are presuppositions, and that projection is in some way a consequence 
of presuppositional status.

More recently, however, various authors have noticed that not all that
projects is a (standard classical) presupposition
(e.g.\ \citealt{ccmg90,beaver01,potts05,roberts:MS,brst09}). The
content of non-restrictive relative clauses (NRRCs), for example,
projects but is not presupposed (\citealt{ccmg90}). The NRRC in
(\ref{3a}) introduces the implication that Malena is
Juan's friend (in both the Guaran\'i and the English versions) and
this implication is also conveyed by the variant in (\ref{3b}) where
the matrix clause is negated.

\begin{exe}
\ex\label{3}
\begin{xlist}
\ex\label{3a} \gll Mal\'ena, ha'\'e-va Juan angiru, o-ho
Caaguas\'u-pe. \\ Malena 3.pron{\sc -rc} Juan friend 3-go Caagasu-to
\\ \glt `Malena, who is Juan's friend, went to Caaguasu.'
\ex\label{3b} \gll Mal\'ena, ha'\'e-va Juan angiru, nd-o-h\'o-i
Caaguas\'u-pe. \\ Malena 3.pron{\sc -rc} Juan friend {\sc
neg-}3-go{\sc -neg} Caaguasu-to \\ \glt `Malena, who is Juan's
friend, did not go to Caaguasu.
\end{xlist}
\end{exe}

The content of NRRCs belongs to the class that \cite{potts05} identifies as conventional implicatures. Other Pottsian CIs, including the content of epithets, honorifics and appositives, also project but are not presupposed. In (\ref{4}), the German second person politeness
morpheme {\em Sie} introduces the implication that the speaker is in a
deferential position with respect to the addressee; this implication
is conveyed although {\em Sie} occurs in the antecedent of a
conditional, an entailment-cancelling environment. The implications
introduced by the appositive in (\ref{5}), that Bill is a big
drinker, and by the expressive {\em son-of-a-bitch} in (\ref{6}), that
the speaker has a negative attitude towards Bill, likewise survive
as utterance implications in this environment.

\begin{exe}
\ex\label{4} \gll Falls Sie hungrig sind, wird mein Sohn das Essen
servieren. \\ If you(formal) hungry are will my son the food serve
\\ \glt `If you (formal) are hungry, my son will serve the food.'

\ex\label{5}If Bill, a big drinker, is here, we'll have fun.

\ex\label{6}If that son-of-a-bitch Bill left, he'd better not have
taken the flower arrangement.
\end{exe}

We hypothesize that projection is a unified phenomenon and in this
paper develop the proposal that the relevant implications of these
diverse expression types project because they share a pragmatic
property, namely {\em not-at-issueness}, introduced in detail
below. Before turning to our proposal, we review in the next section
three previous approaches to projection. Since these were developed
with only a subset of projective meanings in mind, namely
presuppositions, it is perhaps not surprising that extending these
approaches to the full range of projective meanings is problematic for
both empirical and theoretical reasons.

\section{Previous approaches to projection}

\subsection{Common ground approaches to projection}

Among the best known explanations of projection are common ground
approaches
(\citealt{stalnaker73,stalnaker74,karttunen74,lewis79,heim83}). These approaches are predicated on the assumption that utterances serve to update contexts, which are typically construed as the common ground. When a sentence has a (conventional) presupposition, context update is defined only if the relevant context entails the content of the presupposition. When the presupposition is triggered by an embedded constituent, its presuppositional requirements may be satisfied by a local extension of the context. Global projection arises when the
presuppositions triggered by an embedded constituent must be satisfied
by the initial (global) context.  In
the Guaran\'i and English versions of (\ref{9}), for example, the
possessive noun phrase {\em che-kyha} `my hammock' triggers the
presupposition that the speaker owns a hammock. Since this
presupposition is not satisfied locally, i.e.\ by the antecedent of
the conditional, it must be satisfied by the initial (global)
context, resulting in the intuition of projection.

\begin{exe}
\ex\label{9} Context: The speaker is standing next to her
hammock. \gll Nde-kaigu\'e-ramo, e-ke che-kyh\'a-pe.  \\ 2sg-lazy-if
{\sc imp}.2sg-sleep 1sg-hammock-in \\ \glt `If you're feeling lazy,
sleep in my hammock.'
\end{exe}


Common ground approaches are generally appealing for accounting for
the behavior of a subset of presuppositions, including those of pronouns and of
additive particles like {\em too}. It is not clear, however, that all
commonly recognized presupposition triggers are consistently
associated with a common ground requirement (see
e.g.\ \citealt{abbott2000pn} on definites, clefts and embedded
announcements, and \citealt{simons07} on factives). Moreover, it is
unnatural to extend this type of account to the full range
of projective meanings, many of which, as already discussed, are
explicitly distinguished from presuppositions. The content of NRRCs
and appositives, for example, is canonically intended as new
information to the addressee (\citealt{ccmg90,beaver01,potts05}); the
use of these expressions is ruled out precisely when the relevant
content is clearly common ground, as illustrated by the infelicity of
the second utterance in (\ref{sled}) as a continuation of the first.

\begin{exe}
\ex\label{sled} Bob and Carl are sledders. \#Bob, {\bf a sledder},
participated in the 2010 Winter Olympic Games.
\end{exe}

As is well known, even classic presupposition triggers can be used when the presuppositions they trigger are not already in the common ground. These cases are typically treated
within a common ground theory as involving accommodation --- a process
of ``pre-updating'' the context (common ground) with the
presuppositional information prior to carrying out the update
indicated by the sentence as a whole. Following \cite{lewis79}, accommodation is often treated as a kind of rescue strategy,
triggered by an apparent violation of a common ground
requirement.\footnote{Stalnaker (e.g. \citealt[pp.710--711]{stalnaker2002common}), however, sees accommodation as part of the normal evolution of contexts in response to incoming information, not as a rescue strategy. A formal model of accommodation as evolution of common ground is given by \citealt{beaver1992kinematics,beaver01}.} Suppose, then, that one were to extend the common ground
account to projective expressions which are clearly allowed ---
perhaps only allowed --- when their content is not in the common
ground. To do this, it would be necessary to allow that accommodation
is the default strategy for interpretation of these items. But this
seems contrary to the standard understanding of accommodation, as a
process triggered by an actual, observable, common ground constraint.

There is, moreover, evidence that true common ground constraints are
in fact not amenable to accommodation. Perhaps the most convincing
cases of expressions which robustly require some existing shared
information are anaphors, including ordinary pronouns as well as additive particles like {\em too}. These require the salience (or
familiarity) of an antecedent in the common ground: (\ref{she}) is
felicitous only if a unique woman is salient in the common ground,
thus satisfying the presupposition of the pronoun {\em she}.

\begin{exe}
\ex\label{she}If she didn't sleep in the hammock, I don't know
where she slept.
\end{exe}
The common ground requirement of anaphors is well-known to resist
accommodation
(e.g.\ \citealt{geurts-vds04,zeevat02,beaverzeevat,vonFintel08,gauker08}).
%deleted stalnaker08, vds-geurts01, abbott:where JT
Thus, in the paradigm case of a common ground constraint,
accommodation is generally ruled out. This suggests that it is conceptually problematic to treat accommodation of common ground constraints as the norm for some constructions. We conclude that common ground approaches to projection, which were
developed mainly with presuppositions in mind, cannot plausibly be
extended to capture projective behavior in general.

\subsection{Anaphoric approaches to projection}

Presuppositions are analyzed as a type of anaphor in
e.g.\ \citet{vds92} and \citet{geurts99}. The identification of an
antecedent produces the effect of projection: in e.g.\ van der Sandt's
Discourse Representation Theory model, the antecedent of the pronoun
{\em she} in (\ref{she}) would preferably be accommodated in the
global Discourse Representation Structure, thus producing the effect
of projection.

Like the common ground approaches, the anaphoric approaches were never
claimed to account for the full range of projective meanings. In fact,
it would be unnatural to so extend them as there is no evidence that
e.g.\ appositives or expressives carry anaphoric requirements. Rather,
there is evidence against such a requirement, as illustrated by
%(\ref{drink}), repeated from 
(\ref{sled}) above.
%
%\begin{exe}
%\ex\label{drink}Bob and Carl are sledders. \#Bob, {\bf a sledder},
%participated in the 2010 Winter Olympic Games.
%\end{exe}
The appositive ``a sledder'' in the second sentence of (\ref{drink}) does not have
an anaphoric requirement: if it did, we would expect the requirement to be
satisfied by the first utterance.

A second peculiarity of anaphoric approaches, at least if extended to the full
range of projective meanings, mirrors the issue discussed above for
common ground approaches: the paradigm cases of anaphoric presuppositions are precisely the cases where accommodation is highly restricted. Thus it would be peculiar to {\em explain} accommodation as the result of an anaphoric requirement.

\subsection{Multicomponent approaches to projection}

%need the \hspace here or otherwise the karttunen & peters reference does not appear as link, JT
\hspace*{0cm}\citet{karttunen-peters79} and \citet{potts05} divide meanings into
independent components (or dimensions). An utterance like
(\ref{soba}), for example, might be analyzed into the two components
in (\ref{sobb}):

\begin{exe}
\ex\label{sob}
\begin{xlist}
\ex\label{soba} Bill, the son-of-a-bitch, owes me a drink.

\ex\label{sobb} $\langle$ owes(me, bill, drink),
son-of-bitch(bill) $\rangle$
\end{xlist}
\end{exe}
In \posscitet{potts05} system, conventional implicatures are a distinguished type of meaning, which cannot interact semantically with ordinary, non-CI meanings and in particular, cannot be arguments of operators which are part of the non-CI component. This independence between meaning components is what gives rise to the effect of projection in his model.

The proposal we advance below also maintains that projection is the result of operators ``ignoring'' some of the content triggered in their scope. However, there are two reasons we do not attempt to explain projection as a result of semantic independence. First, while Potts provides empirical evidence for independence between meaning components (e.g.\ with respect to binding between
regular content and conventional implicatures), his conclusions have
been questioned by \citet{amaralrobertssmith}, who provide evidence
that there may be semantic dependencies between ordinary content and
conventional implicatures. Second, independence of meaning components could not possibly be a general explanation of all types of projection (and we must note here that Potts never claimed it could be), since presuppositions
interact with ordinary content, and e.g., can be bound. Historically, this is perhaps
the main reason why \posscitet{karttunen-peters79} two-component model was
dropped as an account of presupposition projection.


\section{Proposal: Not-at-issue content projects}

The proposal we motivate in this paper is that projection is
intimately tied to discourse structure. We claim that projection is a
consequence of the scope of sentential operators such as negation,
conditionals and modals typically being limited roughly to what is
understood as the main point, or, in the terminology we will use,
the {\em at-issue content} of the utterance. Whatever does not belong
to the main point --- the {\em not-at-issue content} --- is left out
of the scope of the operator, and hence projects. Thus, the specific
hypotheses we will defend are these:

\begin{exe}
\ex\label{hyp} {\bf Hypotheses about what projects and why}
\begin{xlist}
\ex\label{hypa} All and only those implications of (embedded) sentences which are
not-at-issue relative to the Question Under Discussion in the context
have the potential to project.

\ex\label{hypb} Operators (modals, negation, etc.) target at-issue content.
\end{xlist}
\end{exe}

Before making the notion of at-issueness more precise below, we want
to point out that the idea that projective meanings have a particular
discourse status is not entirely new but has, in fact, been advanced
under a number of related guises by previous authors about different
kinds of projective meanings. \citet[198]{stalnaker74}, among others,
describes presuppositions as ``background beliefs of the speaker'',
which are ``propositions whose truth he takes for granted, or seems to
take for granted, in making his statement'' and
\citet[553]{soames:handbook} likewise characterizes presuppositions as
having this non-central status in the set of propositions conveyed by
an utterance when he writes that ``[t]o presuppose something is to
take it for granted in a way that contrasts with asserting it''; see
also \citet[280]{ccmg90}. \citet[255]{hortonhirst} characterize a
presupposition as ``a proposition that is conveyed by a sentence or
utterance but is not part of the main point'', with ``not part of the
main point'' a notion not defined but reminiscent of Potts' general
claim that the content of conventional implicatures is not at-issue,
or not `what is said'. \citet[143f.]{abbott2000pn} likewise hints at
the relevance of the discourse status of a proposition for projection
when she writes that ``...what is asserted is what is presented as the
main point of the utterance --- what the speaker is going on record as
contributing to the discourse. [...]  Anything else will have to be
expressed in another way, typically by being presupposed''. The
remainder of this paper fleshes out more precisely what it means for
an implication to be not at-issue in a particular discourse context
and how such implications can be identified.



%``([A]n utterance of) a sentence S presupposes a proposition p if (the utterance of) S implies p and further implies that p is somehow already part of the background against which S is considered, that considering S at all involves taking p for granted.'' (Chierchia \& McConnell-Ginet 1990: 280)




\section{Defining at-issueness}

The notion of at-issueness which we will characterize draws on
\posssitet{roberts96} concept of a Question Under Discussion
(QUD). The QUD is a semantic question (i.e.\ a set of alternative
propositions) which corresponds to the current discourse topic. The
QUD may be the value of an actual question that has been asked; more
typically, it is implicit in the discourse. Once a question is under
discussion, it remains so until it has been answered or determined to
be practically unanswerable. We will say that such a question is {\em resolved}. Felicitous conversational moves must constitute
attempts to resolve the current QUD. We will say that an utterance
which constitutes such an attempt, or a speaker who produces an utterance which constitutes such an attempt, {\em addresses the QUD}. Here, we restrict attention to two types of
conversational moves: assertions and questions.

Utterances can address the QUD in a variety of ways. The simplest way
is just to answer it. Answers can be complete or partial: A complete
answer eliminates all alternatives but one; a partial one eliminates
at least one alternative. So, a complete answer to the question:
``Which students are defending this semester?''  will list all who are
defending. An answer such as ``Francesco, and maybe some others,''
constitutes only a partial answer. Assertions which constitute either
complete or partial answers to the QUD count as addressing the QUD. In
addition, a speaker may address the QUD by making an assertion whose
content merely {\em contextually entails} a (partial or complete)
answer to the QUD. For example, a speaker might answer the question
``Is Avi old enough to drink?'' by saying ``He's twenty-two.''
Assuming that the legal age for drinking in the relevant location is
common ground, then the assertion will contextually entail an answer
to the question. Another way to address the QUD is to raise another
question, perhaps initially easier to answer than the QUD itself,
which will help in ultimately resolving the QUD, in the sense that
giving an answer to the new question will provide at least a partial
answer to the QUD. So, for example, a speaker might address the
question ``What will Bill drink?'' by raising the related question
``Does Bill drink beer?''. Using these basic relations, we define a
notion of Relevance to the QUD for assertions and questions:

\begin{exe}
\ex {\bf Relevance to the QUD}
\begin{xlist}
\ex An {\bf assertion} is relevant to a QUD iff it contextually entails a partial or complete answer to the QUD.

\ex A {\bf question} is relevant to a QUD iff it has an answer which contextually entails a partial or complete answer to the QUD.
\end{xlist}
\end{exe}
Relevance to the QUD is the fundamental notion in our definition of
at-issueness.\footnote{This definition of Relevance is overly
 restrictive and should be weakened at least to allow for discourse
 moves which merely raise or lower the probability of some answer to
 the QUD being correct. Consider for example the sequence: Q: ``Is it going to rain?''  A: ``It's cloudy.''
A's utterance does not contextually entail an answer to the QUD (at
least not in Pittsburgh, PA). Intuitively, it is relevant because it
somewhat raises the probability of an affirmative answer to the
QUD. For now, we restrict attention to the simpler type of case
characterized by the definition given.}  For technical reasons, rather
than defining at-issueness directly for a proposition, we define it
via the yes/no question associated with a proposition. For any
proposition {\em p}, let {\em ?p} denote the question whether {\em p},
i.e. the partition on the set of worlds with members {\em p} and
$\neg${\em p}. Then the basic definition of at-issueness is:

\begin{exe}

\ex\label{def} A proposition {\em p} is {\bf at-issue} relative to a
question Q iff {\em ?p} is relevant to Q.

\end{exe}

In section \ref{section:back to def}, we'll consider some apparent
difficulties with this simple notion of at-issueness, and consider a
revision. To begin with, though, let's see how the proposed definition
works in an example, how it gives rise to the desired predictions, and
some further desirable consequences of our general approach. In example (\ref{nutri}), A's reply is our target utterance:

\begin{exe}
\ex\label{nutri} {\em Background scenario: a nutritionist has been
visiting first grade classrooms to talk to the children about
healthy eating}\\ Q: What most surprised you about the first
graders?\\ A: They didn't know that you can eat raw vegetables.
\end{exe}
To identify the implications that project (from under the matrix
clause negation) in A's utterance, we examine which implications of
the proposition embedded under negation, i.e.\ the implications of
``They knew that you can eat raw vegetables'', are (not-)at-issue. For
ease of presentation, we examine only two of the candidate
propositions. The first candidate is the factive entailment:

\begin{exe}
\ex You can eat raw vegetables.
\end{exe}
Let's call this proposition {\em p}. From {\em p}, we derive the
yes/no question {\em ?p} ``Can you eat raw vegetables?''. We then
observe that in the context given, this question has no answer which contextually entails an
answer to the QUD Q in (\ref{nutri}). That is, learning that you can
eat raw vegetables does not enable one to derive an answer to question
Q; and neither does learning that you cannot eat raw vegetables. Since
{\em ?p} is not relevant to the QUD, {\em p} is not-at-issue according
to our definition in (\ref{def}), and thus, on our account, is
predicted to project, according to hypothesis (\ref{hypa}), as
indeed it is observed to do.

Now we consider the maximal entailment of the embedded proposition:

\begin{exe}
\ex They knew that you can eat raw vegetables.
\end{exe}
Let's call this proposition {\em q}. Again, we construct from {\em q}
the associated yes/no question {\em ?q}. The question of whether the
knowledge claim holds has an answer (i.e.\ the assertion) which
contextually entails an answer to the QUD. Hence, this question is
relevant to the QUD, and hence {\em q} is at-issue. By hypothesis
(\ref{hypb}), it is because it is at-issue that it can be targeted by
negation, and hence does not project.


\section{Discussion of the hypotheses}

\subsection{Some desirable consequences}

We have proposed that projective material is not-at-issue relative to
the QUD, with at-issueness characterized as relevance to the QUD. One
important aspect of this proposal is that it provides a unified
account of projection, regardless of whether the projecting element is
a classical presupposition, a conventional implicature, or something
not easily classifiable (such as the prejacent of {\em only}).

Indeed, this proposal suggests a rather straightforward treatment of
another well known case of projection, that of intonationally
backgrounded material. There is a long standing observation that this
material projects, while focussed material ``associates'' with
operators, as illustrated by the examples in (\ref{focus1}) from
\cite{kratzer-lumps}, where the F-marked expressions are focused and
targeted by negation:

\begin{exe}
\ex \label{focus1}
\begin{xlist}
\ex Paula isn't registered in [Paris]$_{\mbox{F}}$. \\ ($\approx$ Paula
is registered somewhere, not in Paris.)

\ex \label{focus2} [Paula]$_{\mbox{F}}$ isn't registered in Paris.
\\ ($\approx$ Someone is registered in Paris, not Paula.)
\end{xlist}
\end{exe}
Other researchers have proposed special purpose rules for explaining
projection of non-focussed material, most notably \cite{geurts-vds04}
in the recent literature. For us, however, the observation is
accounted for by two independently motivated claims. First, we adopt
the rather standard assumption that focus indicates what question is
under discussion (cf.\ \citealt{jackendoff72,roberts96}). 
The QUD can, in effect, be
constructed from intonationally prominent material, while
intonationally backgrounded material is treated as independent of the
QUD, that is, as not-at-issue. Second, we claim that not-at-issue
material projects, cf.\ hypothesis (\ref{hypa}). From these two
claims, the observation about the projection of non-focussed material
follows directly. Certainly, this sketch requires further fleshing
out, but it suggests that this case of projection too can be brought
under the umbrella of our hypothesis.

There is a further very basic benefit yielded by our account. As
discussed earlier, there is a standard observation in the literature
that typically projective material is ``backgrounded'' (Stalnaker),
``non-main-point'' (Abbott) or ``not-at-issue'' (Potts). Our approach
provides a straightforward explanation of this cluster of
observations: on our account, that which projects is necessarily
not-at-issue.
%Other standard accounts do not derive this result
%directly. For one thing, all projective material has this
%backgroundedness quality. So explanations for the observation based on
%posited presuppositional properties, such as a requirement for
%presuppositions to be (treated as) part of the common ground, cannot
%explain the full range of data.


\subsection{Interaction of projection and answerhood}

Our hypothesis that material projects if and only if it is
not-at-issue predicts that if typically projective material is
rendered at-issue, it will fail to project. In this section, we will
argue that this is indeed the case; but we will also show that the
construction of examples which demonstrate this is a delicate matter.

The easiest way to test the prediction is in question/answer sequences, in which conversational structure is transparent. However, the most basic examples of this sort seem to run counter to our hypothesis. Consider for example:

\begin{exe}
\ex \label{proj&ans1}
Q1: \hspace*{.8ex} Are there any boys in your class?\\
A1: \# I (don't) like the boys in my class.

\ex \label{proj&ans2}
Q2: \hspace*{.8ex} What's the weather like?\\
A2: \# Bob realizes / doesn't realize that it's raining.
\end{exe}
According to the simple version of our definition of {\em
at-issueness} in (\ref{def}), the presuppositions of the responses
in these sequences are at-issue and hence the responses should be
given non-projective readings. But, intuitively, we interpret the
responses as a whole as (inappropriately) answering the questions;
that is, we seem to give the responses readings in which the typical
presuppositions indeed project.

%According to the simple version of our hypothesis, the responses in
%each of these sequences should be given non-projective readings,
%because in each case the typically projective material -- the
%presuppositions -- carry the answer to the question asked. But
%intuitively, we hear these as answering the question, albeit in an
%inappropriate way. That is, we seem to give the responses an
%interpretation in which the typical presupposition indeed projects.


Examples such these demonstrate, unsurprisingly, that attempts to answer questions using presuppositions or conventional implicatures are typically infelicitous.\footnote{Common
 ground approaches don't give satisfying accounts of the answerhood
 constraint even for standard cases of presupposition since they must
 allow for {\em transparent accommodation}: a presuppositional expression
 is used although it is transparent to speaker and addressee that the
 relevant proposition was not part of the pre-utterance common
 ground. But if this is allowable, then why shouldn't this sort of
 accommodation be utilized to provide an answer to a question? To
 explain this within a common ground approach, some additional
 principle would need to be invoked. But this cannot be a principle
 along the lines of ``Don't pretend that material is common ground
 when it obviously isn't.'', because it would be violated by every
 case of transparent accommodation.} They appear, at first blush, to
be counterexamples to our proposal because they allow projection (of
the presuppositions), even though this content is at-issue relative to
the QUD. Observe, though, that readings of the responses in
(\ref{proj&ans1}) and (\ref{proj&ans2}) where the presuppositions do
not project would fail to give even partial answers to the QUD. For
example, on its non-projective reading, utterance of the negated
version of A2 in (\ref{proj&ans2}) is equivalent to ``Either it is not
raining, or it is raining and Bob doesn't realize that it is,''. This
fails to answer Q2, the question of what the weather is like, while
also introducing a completely irrelevant proposition regarding Bob's
knowledge state. A listener is thus faced with a choice between two
infelicitous readings: one reading where negation has maximal scope
(and the presupposition does not project), which produces irrelevance
to the QUD; and another (where the presupposition projects) which
provides an answer to the QUD, but requires a mis-match between
projection and at-issueness. We conclude, then, that the strong
infelicity of these sequences reflects the fact that neither the
projective nor the non-projective interpretations are conversationally
appropriate. The apparent preference for a projective reading may be
due to the fact that this reading, although infelicitous, is still
better than the alternative non-projective reading; or may be due to
the fact that, given that both readings are bad, the default
projective reading is prominent. (We return to the issue of defaults
below.)

Interestingly, identical or at least very similar examples to the ones
we have just looked at can be rendered quite acceptable given some
additional background:

\begin{exe}
\ex \label{proj&ans3}
{\em Context: My daughter Chloe is writing invitations to her birthday party to kids in her class. I notice that all of the invitations are to girls.}\\
Mom: Are there any boys in your class?\\
Chloe: I don't like the boys in my class.

\ex \label{proj&ans4}
{\em Context: Quentin, Ann and Bob have just eaten dinner at a restaurant where the tip is usually incorporated into the bill. Bob handed Quentin what he said was his share of the bill, then left the table. Quentin is confused by the amount of money Bob has handed him:}\\
Quentin: Are we supposed to leave a tip?\\
Ann: Bob doesn't realize that the tip is included in the price.
\end{exe}
These sequences appear to be counterexamples to the standard claim
noted above, that the answer to a question may not felicitously be
given by presuppositional content. They also appear to be
counterexamples to our hypothesis, for the content which projects is
at-issue relative to the question asked.

But these sequences require a closer look. We need to
consider why added contextual information makes the sequences
felicitous, when, absent that information, they seemed
extremely odd. It appears that the effect of the added information is
to allow us to make inferences about the broader conversational goals
of the questioner (as perceived by the responder), and thus to
identify implicit questions under discussion. Consider first example
(\ref{proj&ans3}). In responding to my question, Chloe not only
answers the direct question actually asked, but also an implicit
question along the lines of ``Why aren't you inviting any boys to your
party?''. The asserted content of her response contains an answer to
that question, while the existence implication is backgrounded (but
can also be construed as at-issue, as we discuss below.)  What renders
 this sequence felicitous is precisely that it is possible to
 reconstruct this higher question which is answered by the
 non-projective part of the response. Sequence (\ref{proj&ans4}) is
 similar: Ann construes Quentin's question as aimed at answering a
 larger question, namely, ``Why did Bob give me this amount of
 money?''.

Again, on a non-projecting reading, the responses in both cases would
be irrelevant to the discourse topic. In order to find a felicitous
interpretation for the response, it is necessary to construct the
higher question relative to which the typically projective material is
not-at-issue. What differentiates between the contextualized examples
and the non-contextualized ones is simply the availability of
information which allows for the construction of this implicit
question. Once the implicit question is identified, the projective
reading becomes consistent with our hypothesis.

If our hypothesis is correct, we would expect to find {\em some}
question/answer sequences where the at-issueness status of content
affects projection.  Here are two:

\begin{exe}
\ex \label{proj&ans5}Q3: Does France have a king?\\
A3: Well, the king of France didn't attend the opening of Parliament.

\ex \label{proj&ans6}Q4: Is Harry dating Sally?\\
A4: Bill doesn't know that he is.

\end{exe}
Let's work through what is going on with these sequences. A's answer
in (\ref{proj&ans5}) receives an interpretation in which the existence
implication of the definite does not project over negation, an
interpretation paraphrasable as ``There was no king of France
attending the opening of Parliament.'' Making sense of this response
requires accommodating an assumption that if there were a king of
France, he would attend the opening of Parliament. Given this
assumption, the response can be read as providing evidence that there
may well not be a king of France. The felicity of the response
improves with a special intonation contour (c.f. the Uncertainty Contour of \citealt{wardhirschberg1985}). We take the intonation and the discourse particle {\em well} to signal a less-than-maximally coherent
discourse move (see \citealt{schiffrin87} for {\em well}). 


The existence implication of the definite is here clearly at-issue by
our current definition; and it does not project, as predicted by our
hypothesis (\ref{hypa}). Unlike examples (\ref{proj&ans1}) and
(\ref{proj&ans2}), the non-projecting reading is relevant to the QUD
(given accommodation of the necessary assumption) and hence
felicitous. Hence, in this example, we can finally see the effect we
wanted to demonstrate: projection is suppressed where the relevant
content is at-issue --- but only where the resulting non-projecting
interpretation is itself relevant to the QUD.

Example (\ref{proj&ans6}) has a similar structure. The response A4
requires intonation marking uncertainty. Given this intonation, it receives a
non-projecting reading ``It is not the case that Bill knows that Harry
is dating Sally.'' Making sense of the sequence again requires the
accommodation of a particular assumption, in this case the assumption
that if Harry were dating Sally, Bill would know about it. Given this
assumption, the non-projecting reading of A4 is conversationally
felicitous.



\section{Back to the definition of at-issueness}\label{section:back to def}

So far, we have worked with a rather simple definition of at-issueness, and a simple characterization of the relationship between at-issueness and projection. In this section, we discuss some complications and open questions.

The first issue in need of discussion is the role of
convention. At-issueness, as we have defined it in (\ref{def}), is
determined solely by conversational structure. Whether or not a
particular (propositional) implication of an utterance is at-issue
depends only on what the current QUD is. If the implication (or its
negation) is a potential answer to the QUD, the proposition is
at-issue; otherwise, it is not.

But this runs counter to intuitions and observations that linguistic
form is, at the very least, a strong indicator of projective status
--- hence the widely accepted view that presuppositions are
conventional parts of lexical content. Now, it is also the case that
linguistic form is a strong indicator of at-issueness status. The use
of a definite, for example, is a good indicator that the question of
existence of the relevant entity is not under
discussion. As we've seen, we can force the existential implication of
a definite to be at-issue, but this is not the norm. It is precisely
such observations which led us to our hypothesis connecting projection
to at-issueness in the first place.

There is thus a natural way to connect at-issueness to conventional
marking. We posit that at least some constructions or lexical items
conventionally mark their content as not-at-issue.
%\footnote{We assume
%that content can be conventionally marked as not-at-issue, but is
%never marked as at-issue. Thus, material unmarked as not-at-issue
%might be either at-issue or not-at-issue.} 
%
% DIB: I removed the above footnote on the basis that focus and clefts might be examples of marking of at-issueness.
%
The infelicity of
examples like (\ref{proj&ans1}) and (\ref{proj&ans2}) can then be
explained in terms of a mismatch between conventional marking and
actual at-issueness status: the material marked as not-at-issue is
what carries the answer to the question (hence is in fact at-issue);
while the unmarked material which should be the candidate for at-issue
content is not relevant to the QUD.

We remain agnostic as to which expressions
conventionally mark at-issue status. In some cases where
content introduced by an expression is typically not-at-issue, an
account in terms of general pragmatic principles may be available.  We
note also that expressions which mark not-at-issueness apparently do
so defeasibly. For example, if definites are treated as
indicators of the not-at-issue status of an existence
implication, it must be allowed that some uses are not so understood,
given that definites can sometimes be used felicitously to introduce
at-issue content.  Allowing that at-issueness status is sometimes
linguistically marked does not change the predictions of our account
as currently framed. Our hypothesis claims that material projects if
and only if it is {\em actually} not-at-issue. Since (by assumption) conventional marking at most indicates
a default expectation of not-at-issue status, such marking is of very limited significance in the version of our theory considered so far.

This takes us to the second issue in need of discussion. Sometimes,
more than one proposition conveyed by an utterance turns out to be
at-issue, according to our current definition; and sometimes, these
additional at-issue propositions are projective. Consider the
following case, a slight modification of example (\ref{proj&ans1})
above:

\begin{exe}
\ex \label{invite2}Q:  Why aren't you inviting any boys from your class to the party?\\
A: I don't like the boys in my class.
\end{exe}
As discussed above, the definite in A's response gives rise to the
implication that there are boys in her class. But this proposition is
at-issue relative to the QUD since the question of whether or not
there are boys in the class has an answer (namely the negative) which
would answer the QUD. We easily recognize that this is {\em not}
intended as (part of) the answer in part because of the form used. In
light of these observations, we propose a more complex (and admittedly
less clear-cut) characterization of at-issueness that takes into
account the intention of the speaker.

\begin{exe}
\ex {\bf Revised definition of at-issueness}

\begin{xlist}
\ex A proposition {\em p} is at-issue iff the speaker intends to address the QUD via {\em ?p}.
\ex An intention to address the QUD via {\em ?p} is {\bf felicitous} only if:
 \begin{enumerate}
 \item {\em ?p} is relevant to the QUD, and
 \item the speaker can reasonably expect the addressee to recognize this intention.
 \end{enumerate}
\end{xlist}
\end{exe}
On this definition, speaker intention determines at-issueness. But
speaker intention is constrained by relevance to the QUD, and by the
requirement that the intention be identifiable by the addressee. This
is how linguistic marking of at-issueness status comes to affect
projection: if some proposition is linguistically marked as
not-at-issue, then, as long as the resulting interpretation is
felicitous in other respects, the addressee will take it that the
speaker does not intend to address the QUD via that proposition. This
allows us to deal with cases like (\ref{invite2}): As the existence
implication is indicated to be not-at-issue, the addressee can safely
treat it as such, and hence as projective, taking the remaining
content as the target of negation.

This approach also helps with cases of apparently at-issue NRRCs:

\begin{exe}
\ex \label{NRRC}
\begin{xlist}
\exi{Q:}  Who's coming to the dinner tonight?
\exi{A:}  Well, I haven't talked to Charles, who probably won't be able to come, but I did talk to Sally, who is coming.
\end{xlist}
\end{exe}
Here, the (partial) answer to the overt question is contained in the
NRRCs, but these nonetheless project. (For further discussion and
data, see \citealt{PottsHbk}.) The following example,  offered by Chris Barker (p.c.) involves an
epithet:

\begin{exe}
\ex \label{SOB}
\begin{xlist}
\exi{Q:} What do you think of Bill?
\exi{A:} I've never met the son-of-a-bitch.
\end{xlist}
\end{exe}
In example (\ref{NRRC}), we seem to find the at-issue content in the
projecting NRRC, while the main clause content is apparently
irrelevant. However, the utterance is obviously an appropriate
response to the question. We suggest that this is again a case where
an implicit question must be reconstructed.


Rather than directly answering
the overt question, A instead answers the question of who she has
talked to about the dinner, but includes answers to the overt
question in the NRRCs. As a discourse strategy, this is
reasonable since ultimately it provides more
relevant information than a direct answer would have
given. What makes this strategy easily retrievable is the fact that
the content of NRRCs is by default not-at-issue. Something similar can
be said about Barker's example (\ref{SOB}). Here it seems that, superficially at least, A is refusing to answer the question explicitly posed. Instead, A gives a negative answer to the unasked question of whether A has met Bill, thus
challenging Q's presupposition that A is in a position to offer an opinion about Bill. Since A's negative attitude to Bill is not relevant to this question, it survives as an utterance implication.

The characterization of at-issueness in terms of speaker intention
gives us leeway to resolve some difficulties that arise with the previous
characterization in (\ref{def}). However, it makes some simple cases
more difficult. Consider our treatment of (\ref{proj&ans5}): We
argued there that the existence implication of the definite was
at-issue, by virtue of the fact that it constitutes an answer to the
QUD. According to the revised definition, this implication is at-issue
iff the speaker intends to address the QUD via the question of whether
there is a king of France. But it is more intuitive here to say that
the speaker addresses the QUD via the question of whether the king of
France was at the opening of Parliament. It thus appears that in this
case, the simpler notion of at-issueness serves us better. We leave
this as a topic for further investigation.


\section{Conclusion}

The proposal we have presented here would benefit from both development, and further empirical work. For example, although the Guaran\'i data in section 1 provides suggestive evidence for the cross-linguistic relevance of the issues we have discussed, it remains open to what extent projective meaning is a locus of cross-linguistic variation.\footnote{Another empirical issue relates to experimental results of \cite{jayez2009}, a response to an earlier version of our proposal. For reasons of space, we cannot discuss those results here.} However,
there are three central planks to the theory we are constructing for
which we hope to have made a good case.

%\vspace*{-.41cm}
%\begin{itemize}

First, projection is a unified phenomenon, and therefore cannot be
   given an account relying on specific properties of particular
   types of meanings (such as presupposition or conventional
   implicature).% \vspace*{-.23cm}

 Second, the common property of projective meanings can be
   characterized in terms of some notion of at-issueness utilizing
   the concept of relevance to a QUD. Projection itself is
   intimately related to the structuring of information in
   discourse. It is a consequence of the fact that in the totality
   of information conveyed by an utterance, some is central to the
   speaker's conversational goals, and some is peripheral. The
   peripheral projects. %\vspace*{-.23cm}

 And finally, projection is not a matter of elements of content
   ``escaping'' the scope of an operator, but rather of elements
   being ``ignored'' by operators. Speakers use operators to target content which is
   central to their conversational goals.
%\end{itemize}

\bibliography{salt20}

\begin{addresses}
\begin{address}
  Mandy Simons\\
Baker Hall 135, Carnegie Mellon University \\
Pittsburgh, PA 15213-3890 \\
  \email{simons@andrew.cmu.edu}
\end{address}
\begin{address}
Judith Tonhauser \\
222 Oxley Hall, 1712 Neil Ave \\
Columbus, OH 43210-1298 \\
  \email{judith@ling.osu.edu}
\end{address}
\begin{address}
  David Beaver \\
Calhoun Hall 414, 1 University Station B5100 \\
Austin, TX 78712-0198 USA \\
  \email{dib@mail.utexas.edu}
\end{address}
\begin{address}
  Craige Roberts \\
222 Oxley Hall, 1712 Neil Ave \\
Columbus, OH 43210-1298 \\
  \email{croberts@ling.osu.edu}
\end{address}
\end{addresses}
\end{document}