Discourse, Grammar, and At-issueness
Todor Koev
Abstract This paper explores the layered ways in which sentences convey meaning in discourse.
It takes a fresh look at the elusive notion of at-issueness, or the fact that part of the information
expressed by the sentence is felt to be more central than other sentential information (see Potts
2005; Simons et al. 2010; AnderBois et al. 2013; a.o.). I defend the view that at-issue content
interacts with the question under discussion and constitutes a proposal to update the context. My
main claim is that at-issue content is asserted content that is relatively recent in discourse. This
entails that there are both grammatical and discourse restrictions on at-issueness. The account is
implemented in an update semantics which separates the main assertion from other propositional
content and can interpret sentences without adding their descriptive content to the context.
Keywords
grammar
at-issueness, question under discussion, proposal, update semantics, discourse,
1 Introduction
When sentences are used to convey meaning in context, certain information expressed by the
sentence is often felt to be more central than other sentential information. This intuition has
motivated the view that there is a distinction to be drawn between AT-ISSUE content, or content
that carries the main point of the utterance and is open for negotiation among speech participants,
and content that is in some sense secondary (see Böer & Lycan 1976; Bach 1999; Chierchia &
McConnell-Ginet 2000; Potts 2005; Amaral et al. 2007; Roberts et al. 2009; Simons et al. 2010;
AnderBois et al. 2013; Murray 2014; Syrett & Koev 2014). For example, after hearing the
utterance in (1), the addressee is likely to treat the main clause as addressing the issue at hand
and view the appositive as adding secondary information.
(1)
Messi, who once scored a goal with his hand, won the Ballon d’Or.
This paper is devoted to explicating the properties of the elusive concept of at-issueness. I
defend a unified view according to which at-issue content interacts with the question under
discussion and constitutes a proposal to update the context. My main claim is that at-issue
content is asserted content that is relatively recent in discourse. This entails that there are both
grammatical and discourse restrictions on at-issueness. More specifically, the discussion is
centered around the following two questions:
(A)
THE GRAMMATICAL QUESTION
1
What content expressed by the sentence can be at issue?
(B)
THE DISCOURSE QUESTION
If multiple propositions that can in principle be at issue are introduced, what discourse
factors determine which of those propositions are actually at issue?
Question A asks about potential grammatical restrictions on at-issueness. For example, is it
possible that certain sentential content is conventionally encoded as at issue while other content
is conventionally encoded as not at issue? In order to answer that question, I discuss the at-issue
status of a small sample of English constructions, which includes main clauses, conjunctions,
restrictive and appositive relative clauses, factive and non-factive complements. I demonstrate
that only constructions that contribute to the main assertion – i.e. main clauses, conjunctions or
restrictive relative clauses – can be viewed as at issue content. Question B brings up the role of
discourse in determining at-issue status. Discourses are fairly complex systems and it is likely
that only certain portions are at issue at a given point. One of the major claims of the paper is
that at-issueness is tied to content that is relatively recent. Given the answers provided to
Question A and Question B, the explanation mechanism is based on both semantic composition
and recency in discourse. I implemented these ideas in an update semantics which separates the
main assertion from other propositional content and can interpret sentences without adding their
descriptive content to the context.
The structure of the paper is as follows. Section 2 discusses two related but distinct notions
of at-issueness: a discourse topic-based notion and a proposal-based notion. In Section 3, I argue
for a unified account of at-issueness that builds on those previous notions. Section 4 presents the
formal account. Section 5 is the conclusion and the Appendix briefly addresses formal issues
related to compositionality.
2 On the notion of at-issueness
The notion of at-issueness has recently generated a considerable amount of attention in the
semantics literature. Even so, the term “at-issue content” seems to have been used in closely
related but different senses by researchers. In this section, I briefly review two contrasting
conceptions of at-issueness. In Section 3, I argue for a single notion of at-issueness that slightly
modifies and unifies those two previous views.
When discussing the way the term “at-issue content” is used in previous literature, there are
several factors to consider. First, what is the informal or intuitive characterization of this term?
Second, how is the property of at-issueness empirically diagnosed? Clearly, if certain content is
claimed to be (not) at issue, there should exist appropriate diagnostics that detect such status.
Finally, one should also ask whether the theoretical explanation provided derives the pretheoretical sense in which this term is used. For example, it could be that a particular
2
construction is claimed to trigger implications with certain discourse properties but that the
theoretical account does not actually derive those properties.
Potts (2005; 2007) was among the first to use the term “at-issue” in the relevant sense. For
him, at-issue content is regular asserted content, or truth-conditional content. Potts contrasts atissue content with secondary entailments triggered by appositives or expressives. He calls such
entailments CONVENTIONAL IMPLICATURES, thus modifying Grice’s (1975) original concept along
the lines suggested in Bach (1999). The following excerpts illustrate his view of at-issueness (the
emphasis is mine):
“I use ‘at-issue entailment’ as a coverterm for regular asserted content […]. ‘At-issue
entailment’ sets up a useful contrast with CIs [=conventional implicatures], which are
secondary entailments that cooperative speakers rarely use to express controversial
propositions or carry the main themes of a discourse.” (Potts 2005: 6–7)
“[…] ‘at-issue’ […] is typically the content that speakers offer as primary and also
the content that they are most expecting to have to negotiate with their interlocutors
before it is accepted into the common ground. […] probably the most common label
for it is ‘truth conditional content’.” (Potts 2007: 666)
Potts suggests that at-issue content has two important discourse properties. First, it is primary, in
the sense that it carries the main theme or topic of discourse. This property is often expressed by
saying that at-issue content is the “main point” of the utterance. Second, at-issue content is
content that is negotiated among interlocutors before it is added to the common ground. This
second property is sometimes characterized by saying that at-issue content constitutes a
“proposal” to update the context.
Potts does not elaborate on how these discourse properties of at-issue content are empirically
diagnosed. Neither does his semantic account tell us much about the pragmatic status of at-issue
entailments. His two-dimensional semantics merely separates at-issue content from conventional
implicatures and elegantly accounts for the fact that conventional implicatures typically project.1
An illustration of Potts’ treatment of sentences with appositives is given below.
(2)
a. Lance, who was about to retire, admitted to doping.
admit.to(lance,doping) , about.to.retire(lance)
b.  
 


at-issue content
conventional implicature
The sentence in (2a) triggers two implications: the at-issue implication that Lance admitted to
doping and the conventional implicature that Lance was about to retire. However, just treating
those two implications as logically independent, as in (2b), does not make specific predictions
1
See e.g. Böer & Lycan (1976), Chierchia & McConnell-Ginet (2000), Dever (2001), AnderBois et al. (2013), Koev
(2013), and Smith & Hall (to appear) on the projection properties of appositives.
3
about the discourse properties of at-issue content (or those of conventional implicatures). The atissue proposition can be stipulated to be the main point of the utterance or to introduce an update
proposal, or both. Potts’ semantic treatment is then compatible with any broader assumptions
about what at-issue content is.
Subsequent works have put the emphasis on one of the properties of at-issueness, while
typically failing to separate it from other properties. Below, I discuss a discourse topic-based
notion and a proposal-based notion of at-issueness and show that they make different predictions
if taken in their unmodified forms. In Section 3, I demonstrate that, once certain restrictions are
introduced, those two notions are not truly distinct but rather point at a unified view of atissueness.
2.1 Q-at-issueness
Amaral et al. (2007), Roberts et al. (2009), and Simons et al. (2010) seek to explain at-issueness
in terms of a relationship to the main topic of the conversation, also called the QUESTION UNDER
DISCUSSION (or QUD). The main idea behind QUD approaches to discourse is that conversation
is hierarchically structured by questions, which introduce the topics that interlocuters address
during their interaction in conversation (see van Kuppevelt 1995; Ginzburg 1996; Roberts
1996/2012; Büring 2003). With this background in mind, Simons et al. (2010) propose the
following basic definition of at-issueness:2
“A proposition p is AT-ISSUE relative to a question Q iff […]p is relevant to Q.”
(Simons et al. 2010: 317)
The authors define relevance of a proposition to a question in terms of (partial or complete)
answerhood to that question. According to their view, a proposition is at issue if and only if it
addresses the QUD. I call this notion of at-issueness Q(UESTION)-AT-ISSUENESS and define it as
follows.
(3)
Q-AT-ISSUENESS (first version)
Semantic content is Q-AT ISSUE relative to a question iff it addresses that question.
Since Q-at-issueness is defined relative to a question, it is crucial to find ways of identifying
what the QUD is at any stage of conversation. This task is complicated by the fact that QUDs are
usually implicit. Unfortunately, the works cited above do not provide us with reliable empirical
diagnostics for identifying QUDs, which makes it hard to test the predictions of the discourse
2
Simons et al. actually allow subquestions to count as relevant to some more general question and define relevance
as a relation between two questions rather than a proposition and a question. A proposition p is at issue relative to a
question Q if and only if ?p, the yes/no question corresponding to p, has an answer that is relevant to Q. I gloss over
this subtlety here.
4
topic approach to at-issueness. In order to have a workable notion of Q-at-issueness, I will
always spell out the QUD as an explicit question that sets the stage for the upcoming utterance.
In doing so, I make the important assumption that an explicit question is identical to the current
QUD. It is in principle possible that the two diverge and that an answer further specifies or even
redefines an overt question in order to better fit the actual QUD. In fact, if something like this is
allowed, one could state that Q-at-issue content always completely resolves the QUD. For
example, if Abby asks Jared “What type of food do you like?” and receives the non-exhaustive
response “I like sushi”, one could claim that Jared completely answered the subquestion “Do you
like sushi?”, which is the immediate QUD. In what follows, I will ignore the possibility that
QUDs and explicit questions differ from one another.
This discussion and the definition in (3) above suggest the following empirical diagnostic for
Q-at-issueness (see also Tonhauser 2012).
(4)
ANSWERABILITY TEST
Let A ask a question and B address it with the semantic content expressed by some part
of a sentence. If the discourse is acceptable, then that content is Q-at issue.
The definition of Q-at-issueness and the closely related answerability test are purely
pragmatic and thus fairly liberal, in the sense that they do not impose any grammatical
restrictions on the type of semantic content that can be Q-at issue. For example, can
propositional content in general, including non-asserted content, address QUDs? I will show
below that this indeed seems possible for most types of content.
It is uncontroversial that the main assertion of an utterance can address QUDs; in fact, this is
the paradigm case of a question-answer relationship. As the examples below demonstrate,
asserted content that is QUD relevant can originate not just in the main clause, as in (5), but also
in a conjunction (6) or a restrictive relative clause (7). This suggests that conjunctions and
restrictive relative clauses contribute to the content of their host clause, in this case the main
clause.
(5)
A: Where is Jeremy?
B: He left for Vancouver.
(6)
A: What are your plans for today?
B: I will finish the paper and send in the job application.
(7)
A: What kind of guy did Svetlana end up marrying?
B: She married a guy who was born in Ukraine.
Appositive relative clauses come close to contributing asserted content. Indeed, appositive
content shares a lot of properties with regular assertions. First, there is large consensus in the
5
literature that appositives are truth-conditionally relevant, either in the sense that speakers
consider their truth value when calculating the truth value of the entire sentence (see Frege
1892/1980; Böer & Lycan 1976; Chierchia & McConnell-Ginet 2000; Schlenker 2009;
AnderBois et al. 2013; Syrett & Koev 2014) or in the sense that they project a second truth value
on top of the truth value for the main sentence (see Berckmans 1994; Bach 1999; Dever 2001;
Potts 2005). Second, appositive relative clauses routinely introduce discourse-new information.
Chierchia & McConnell-Ginet (2000) illustrate this point with the following short discourse,
where the appositive content in the second sentence is clearly novel to the hearer.
(8)
Let me tell you about Jill Jensen, a woman I met while flying from Ithaca to New York
last week. Jill, who lost something on the flight from Ithaca to New York, likes to travel
by train.
(Chierchia & McConnell-Ginet 2000: 351)
Potts (2005) makes an even stronger claim, arguing that appositives must express new
information, a condition he calls an ANTIBACKGROUNDING REQUIREMENT. For example, the
appositive in (9) repeats old information and the discourse sounds infelicitous.3
(9)
Lance Armstrong survived cancer. #When reporters interview Lance, who is a cancer
survivor, he often talks about the disease.
(Potts 2005: 34/112, slightly modified)
Given all these similarities between regular assertions and appositive content, the latter content is
expected to be able to address QUDs as well. This is indeed so. The appositive content in both
(10) and (11) provides information that partially answers the initial question.
(10)
A: What happened last night at the party?
B: Kevin, who got drunk, started pole dancing in front of everybody.
(11)
A: Why was John out of the office for so long?
B: He took care of his husband, who had prostate cancer.
(Syrett & Koev 2014: 47)
As it turns out, propositional information that goes well beyond assertions can be Q-at issue
as well. Embedded clauses are a case in point. Simons (2007) notices that certain embedding
verbs can give rise to interpretations whereby the embedded clause carries the main point of the
3
Potts’ antibackgrounding requirement is certainly not parochial to appositives but also governs the use of regular
asserted content. The discourse in (9) remains infelicitous if it is transformed in such a way that the redundant
information is contained in a main clause, as in (i).
(i)
Lance Armstrong survived cancer. #Lance is a cancer survivor and when reporters interview him, he often
talks about the disease.
A pragmatic principle which prohibits that asserted content is entailed by the context is proposed in Stalnaker (1973;
1978).
6
utterance while the main clause serves a secondary function, typically providing evidential
information about the source of the embedded proposition. Here is an example.
(12)
A: Who was Louise with last night?
B: Henry thinks / believes / said that she was with Bill.
(Simons 2007: 1036)
Simons calls such uses of embedding verbs PARENTHETICAL USES and emphasizes that these are
not encoded in the semantics but rather are purely a matter of pragmatics. This is reasonable, as
none of the answers in (12B) entails that Louise is with Bill.
Finally, presupposed content often seems unable to address questions. For example, the
factive complement in (13B) has the right shape to resolve the question in (13A) but the
discourse is degraded. However, Simons (2007) notices that factive complements can sometimes
address questions, as in (14).4 It would then appear that factive complements can, at least to
some extent, carry the main point of the utterance.
(13)
A: How is your wife doing?
B: ?It’s great that she has a new job.
(14)
A: Where did Louise go last week?
B: Henry discovered / learned / found out that she had a job interview at Princeton.
(Simons 2007: 1045)
In summary, one prominent view is that at-issueness is about the relationship of semantic
content to the current QUD. I called this notion Q-at-issueness. This view does not predetermine
where in the sentence Q-at issue content originates. This is indeed in line with the data. We
found that a vast majority of semantic content can, in fact, address questions, including content
stemming from main clauses, conjunctions, restrictive and appositive relative clauses, embedded
clauses, and possibly factive complements. It should be obvious that the notion of Q-at-issueness
is very different from what Potts (2005; 2007) envisaged. According to Potts, at-issue content is
primarily reserved for the main assertion or the truth-conditional content of the sentence. In
contrast, the notion of Q-at-issueness is much more inclusive as it does not seem to be limited to
truth-conditional content at all. In the next section, I discuss another, proposal-based notion of atissueness. As we will see, this second notion is much more selective and comes close to Potts’
original intuition.
2.2 P-at-issueness
4
However, Simons also notes that factive predicates under parenthetical interpretations lose their presuppositional
properties.
7
Other authors have focused on the proposal-like nature of at-issue content. AnderBois et al.
(2013) and Murray (2014) posit a binary, grammatically-encoded distinction between at-issue vs.
not-at-issue entailments. These two types of content differ in the way they update the context:
while at-issue content updates the context indirectly, i.e. by means of constituting a proposal that
can be negotiated, not-at-issue content is directly imposed on the context without negotiation.5
To cite the authors themselves:
“We […] will take at-issue meanings to be proposals to update the input CS
[=context set] […]. In contrast, appositive content is imposed on the CS and not up
for negotiation by normal means.” (AnderBois et al. 2013: 3–4)
“This distinction between at-issue and not-at-issue content can be captured as a
distinction between information directly added to the common ground and
information proposed to be added to the common ground […].” (Murray 2014: 4)
According to these authors, main clauses conventionally introduce proposals and thus are
invariably at issue. Any content that falls outside the proposal expressed by the main clause is
not at issue. This includes not-at-issue entailments, e.g. those triggered by English appositives or
evidential markers in some languages. I will refer to this notion of at-issueness as P(ROPOSAL)AT-ISSUENESS. It can be defined as follows:
(15)
P-AT-ISSUENESS (first version)
Semantic content is P-AT ISSUE iff it is entailed by an update proposal.
The entailment requirement on the right-hand side in (15) is important. It is intended to do justice
to the intuition that if “Jenna owns a car” is at issue, then “Jenna owns a vehicle” is also at issue.
This requirement also prevents us from concluding that “Miley likes to twerk” is at issue just
because the proposal is “The magazine reported that Miley likes to twerk”. In other words, nonentailed parts of proposals, e.g. embedded propositions, are not at issue.
The main diagnostic for P-at-issueness relies on the amenability of semantic content to direct
responses. The basic idea is that content that constitutes an update proposal is negotiable and
thus is open to direct agreement or disagreement by the addressee. Other semantic content, e.g.
5
The idea that assertions constitute update proposals is already present in Stalnaker (1978; 1999) and has been
further explored in Groenendijk & Roelofsen (2009), Farkas & Bruce (2010), a.o. Consider, for example, the
following excerpts:
“An assertion can then be understood as a proposal to alter the context by adding the information that
is the content of the assertion to the body of information that defines the context […].” (Stalnaker
1999: 99)
“[…] the addressee accepts or rejects the proposal either adding the content of the assertion to the
contextual information, or leaving the context as it was […].” (Stalnaker 1999: 102)
8
presupposed content, can typically only be accessed through less direct linguistic means. I call
this diagnostic the DIRECT RESPONSE TEST and define it as follows.6
(16)
DIRECT RESPONSE TEST
Let A utter a sentence and B use a direct response to target some content expressed by
some part of a sentence. If the discourse is acceptable, then that content is P-at-issue.
This formulation employs the notion of a DIRECT RESPONSE, which needs to be explicated.
Intuitively, direct responses signal straightforward agreement or disagreement on part of the
speaker. In English, direct responses are typically expressed by “I agree”, “That’s not true”,
“Yes, she is smart”, “No, he isn’t”, etc. To be sure, it is possible for the addressee to also reject
content that is not P-at issue, though only indirectly. The mechanism of indirect rejection has a
more severe conversational effect as it disrupts the natural flow of discourse, indicating that
information that has already been accepted needs to be withdrawn. It also involves different
grammatical tools, e.g. indirect responses are typically flagged by hedges like “Actually, ...”,
“Well, ...”, “Yes, but …”, “Hey, wait a minute!”, etc.7 At the heart of the distinction between
direct vs. indirect responses lies the idea that direct responses target content that is currently
being negotiated by speech participants. There is no such requirement on indirect responses,
which can target content that is already part of the common ground or content that was never
intended to enter the common ground.
The notion of P-at-issueness turns out to be much more restrictive than the notion of Q-atissueness, discussed in the previous section. Roughly, only the main assertion can be P-at issue;
other semantic content is typically not P-at issue. First, notice that any part of the main assertion
of a sentence can be a target of a direct response, including information stemming from the main
clause (17), a clausal conjunct (18), or a restrictive relative clause (19).
(17)
A: Matthew is rich.
B: No, he isn’t.
(18)
A: Bill cheated on the exam but nobody noticed.
B: That’s not true. (He didn’t cheat. / He was reported to the Dean.)
(19)
A: The department hired a professor who was born in Japan.
B: He was born in South Korea.
6
The direct response test is known in the literature under different names and has been used to distinguish the main
assertion of the sentence from implications triggered by presupposition markers (see Strawson 1950; Shanon 1976;
Karttunen & Peters 1979; Chierchia & McConnell-Ginet 2000), epistemic modals (see Lyons 1977; Papafragou
2006; von Fintel & Gillies 2007), evidentials (see Faller 2002; Matthewson et al. 2007; Murray 2010, 2014), and
appositives (see Amaral et al. 2007; Tonhauser 2012; AnderBois et al. 2013; Koev 2013; Syrett & Koev 2014).
7
A more grammatical way to distinguish between direct and indirect responses would be to say that the latter but
not former include off-track particles or hedges like the ones just cited.
9
However, other types of content appear unable to be P-at issue. Appositive content is usually
not amenable to direct agreement or disagreement.8 In (20), for instance, the hearer can reject the
main clause content but not the appositive content.
(20)
A: Edna, who is a fearless leader, started the descent.
B: No, she didn’t. / #No, she isn’t.
(cf. Amaral et al. 2007: 731)
Embedded content under non-factive predicates is not a good target of direct responses either.
(21)
A: Simon believes that Beyoncé is an amazing singer.
B: Not really. (Simon doesn’t believe that. / #Beyoncé isn’t such a great singer.)
Similarly, factive complements cannot be directly agreed or disagreed with.
(22)
A: Obama regrets that the Senate killed the bill.
B: I doubt he does. / #I doubt they did.
In short, we see that content that is not part of the main assertion is typically not open to
direct responses. The notion of P-at-issueness is then very much what Potts (2005; 2007)
conjectured at-issue content to be, i.e. asserted or truth-conditional content.
2.3 Summary
We have found evidence that the main assertion of an utterance is both Q-at issue and P-at issue.
Other semantic content, though, can be Q-at issue but is typically not P-at issue. These two
notions of at-issueness then seem to significantly differ from each other. Despite appearances, I
will propose in the following section that, once certain restrictions are applied, Q-at-issueness
and P-at-issueness can be viewed as a unified notion.
3 Towards a unified notion of at-issueness
We have discussed two notions of at-issueness, both coming from previous literature. One is
based on the relationship of semantic content to the QUD and the other is anchored in the idea
that utterances of declarative sentences introduce proposals to update the context. I called those
two notions Q-at-issueness and P-at-issueness, respectively. We observed that, as they stand,
these notions significantly differ in empirical scope: while various sorts of semantic content can
8
One exception are sentence-final appositive relative clauses, which can be a good target of direct responses (see
AnderBois et al. 2013; Koev 2013; Syrett & Koev 2014). This issue is discussed in more detail in Section 3.
10
be Q-at issue, typically only the main assertion of an utterance is P-at issue. These findings bring
up the important question of whether the two notions are in fact distinct or rather can still be
viewed as describing the same property.
I will opt for the latter position here. I will demonstrate that, once certain adjustments are
made, the two notions do not differ from each other after all. I choose to pursue this option for
several reasons, both theoretical and empirical. First, and perhaps most importantly, Q-atissueness and P-at-issueness are based on the same intuition about the layered ways in which
sentences convey meaning in context. In fact, there is a significant amount of overlap between
Q-at-issueness and P-at-issueness, e.g. when it comes to the main assertion of an utterance. Such
overlap suggests that main point and proposalhood are not independent notions but are closely
related. Second, working with two distinct notions of at-issueness would be theoretically
unparsimonious. It is much preferable to assume a single notion of at-issueness while at the same
time pay closer attention to its fine-grained properties.
One obvious aspect of the data presented in Section 2 is that P-at-issue content carves out a
subset of Q-at-issue content. We might then look for ways to limit the scope of Q-at-issueness
such that it matches P-at-issueness in empirical scope. Recall from (3) that Q-at-issueness was
defined as content that addresses the QUD. What I propose here is that content is Q-at issue not
just if it does but rather if it must address the QUD. As will become clear below, once this crucial
step in made the two notions of at-issueness become equivalent.
We saw in (5)-(7) that the main assertion of an utterance can address the QUD. What I
demonstrate here is that in fact main assertions must address the QUD. This is clear from
examples in which the main clause content does not answer the QUD while some other part of
the sentence does. In (23)-(25), only an appositive relative clause, an embedded clause or a
factive complement provides an answer to the question and the discourses are infelicitous.
(23)
A: Where did your husband grow up?
B: #Jacque, who grew up in Paris, has a great sense of humor.
(24)
A: Where is Lizzie?
B: #I dreamed that she is at her mom’s house.
(25)
A: Did Amanda quit her job?
B: #She is upset that she did.
In contrast, non-asserted content need not address the QUD. If the questions above are modified
in such a way that they are only answered by the main clause, the exchanges become acceptable.
(26)
A: What do you like most about your husband?
B: Jacque, who grew up in Paris, has a great sense of humor.
11
(27)
A: What happened last night?
B: I dreamed that Lizzie is at her mom’s house.
(28)
A: How is Amanda doing?
B: She is upset that she quit her job.
The above discussion shows that while a wide range of semantic content can address the
QUD, there are restrictions on the type of content that is required to do so. In order to
accommodate this fact, I make the following adjustments to the definitions of Q-at-issueness.
(29)
Q-AT-ISSUENESS (final version)
Semantic content is Q-AT ISSUE relative to a question iff it is required to address that
question.
Given the data in (23)-(25), this strengthened definition implicitly imposes grammatical
restrictions on the notion of Q-at-issueness by effectively limiting it to constructions that
contribute to the main assertion, i.e. main clauses, conjunctions, and restrictive relative clauses.
It thus vindicates Potts’ (2005; 2007) intuition, cited in Section 2 above, that at-issue content is
just asserted content. While non-asserted content may address the QUD as well, there is no
requirement that such content does so and thus, according to the definition in (29), non-asserted
content is not truly Q-at issue. If this analysis is on the right track, Q-at-issueness is a more
restricted notion than originally envisaged in Amaral et al. (2007), Roberts et al. (2009), and
Simons et al. (2010). Though pragmatic in nature, Q-at-issueness is also grammatically encoded,
as the origin of the proposition inside the sentence matters.
In turn, the notion of P-at-issueness, as presented in AnderBois et al. (2013) and Murray
(2014), is primarily a matter of grammar. According to that view, main clauses are
conventionally encoded as contributing proposals and thus are marked for P-at-issue status. This
is fully in line with the data discussed in (17)-(19) above. However, discourse seems to play an
important role as well. Only recent proposals are likely to be P-at issue; less recent proposals
would typically have been decided, e.g. after being explicitly negotiated or by being implicitly
accepted. This means that the order in which proposals are introduced in discourse matters, with
later proposals being more likely to be amenable to direct responses than earlier proposals.
Consider, for example, the short exchange below.
(30)
A: Matthew is rich. He recently bought an apartment in downtown Manhattan.
B: That’s not true.
The preferred interpretation of (30B) is one in which the addressee disagrees with the second and
not the first claim made by the speaker of (30A).9 This is so because the addressee did not react
9
This is confirmed by the fact that B can felicitously utter, as a reaction to A, “No, he didn’t” but not “No, he isn’t”.
12
immediately after the first sentence was uttered and thus could be taken to tacitly agree with it.
The content of the first sentence is then silently added to the context and the conversation moves
forward to negotiating the issue raised by the second sentence.
One might wonder whether the preference for negotiating recent proposals is contingent on
the coherence relations between sentences. It appears that it is not. There is a sizeable amount of
coherence relations cited in the literature and various researchers have aimed to provide a viable
typology (see e.g. Hobbs 1985; Mann & Thompson 1988; Kehler 2002; Asher & Lascarides
2003). Here, I take BACKGROUND, ELABORATION, EXPLANATION, OCCASION, and RESULT as a
sample of commonly discussed coherence relations and show that they have no noticeable effect
on P-at-issueness. In (31) below, A utters a sequence of two sentences which stand in the
coherence relation as indicated. B disagrees with A by uttering a direct rejection. Importantly,
the second sentence is invariably the preferred target of B’s response. This suggests that which
proposal is currently being negotiated primarily depends on recency rather than discourse
structure.
(31)
A: Ryan stormed into the secretary’s office. He looked very upset.
A: Max had a lovely meal last night. He ate a lot of salmon.
A: Billy was in a foul mood. He recently got fired.
A: George took to the podium. He began to read off the teleprompter.
A: Sarah pushed Jeremy. He fell to the ground screaming.
B: That’s not true.
(BACKGROUND)
(ELABORATION)
(EXPLANATION)
(OCCASION)
(RESULT)
There is another piece of data that points at the importance of recency. We saw that while
appositive relative clauses are not Q-at issue (in the stronger sense specified in (29)), they share a
number of properties with asserted content (recall Section 2.1). It has previously been noticed
that their amenability to direct responses varies depending on linear position: while appositive
relative clauses are in general not open to direct responses, they can be when they occur
sentence-finally (see AnderBois et al. 2013; Koev 2013; Syrett & Koev 2014). The asymmetry in
question is illustrated below.
(32)
(33)
A: Edna, who is a fearless leader, started the descent.
B: #No, she isn’t.
(cf. Amaral et al. 2007: 731)
A: Jack followed Edna, who is a fearless leader.
B: No, she isn’t.
The above contrast can be viewed as a reflex of the general tendency of recent content to be
more easily accessible to direct responses. If we assume, quite plausibly, that the content of
sentence-final appositive relative clauses is, or can be, introduced more recently than the content
of sentence-medial relative clauses, then the contrast in (32)-(33) becomes less of a mystery.
13
What these data suggest is that proposals are normally handled in due course. I capture this
intuition by stating the following constraint on proposals in discourse.
(34)
DEFAULT ACCEPTANCE
A proposal is kept open until the addressee is given a chance to react to it. If not
explicitly addressed, a proposal is implicitly accepted.
This constraint is in line with the findings of the literature on TURN-TAKING (see e.g. Sacks et
al. 1974). Turn-taking has the goal of letting one party talk at a time, thus minimizing gaps or
overlaps and ensuring that interlocutors exchange roles in an orderly fashion. Importantly,
changes of discourse roles have been found not to be continuously distributed over the course of
a turn but rather to occur after discrete units, such as entire phrases or sentences.10 How often
such points occur will depend on the particular discourse we are in. In friendly, natural,
unregulated exchanges the addressee will have the opportunity to raise an objection after each
meaningful unit. Default Acceptance predicts for such discourses that if a sentence is not
explicitly addressed, its content is tacitly added to the common ground. Of course, we need to
also make room for the possibility that proposals remain open for longer stretches, e.g. because
the addressee has not yet been given the chance to react. This happens in discourses with more or
less explicitly set rules, such as conference talks or political debates. In such regulated
discourses, time is often strictly allocated among various speakers and thus the points of
discourse role changes are much more sparsely distributed.
Given the above discussion, we need to slightly adjust the definition of P-at-issueness in (15)
so that it only includes open proposals.
(35)
P-AT-ISSUENESS (final)
Semantic content is P-AT ISSUE iff it is entailed by an open update proposal.
We can now propose a unified notion of at-issueness. It combines P-at-issueness and Q-atissueness as two more or less equivalent characterizations of this property.
(36)
AT-ISSUENESS
Semantic content is AT-ISSUE iff it is entailed by an open update proposal and is required
to address the current QUD.
This definition implies that both discourse and grammar pull their weight in determining at-issue
status. While the question-based notion of at-issueness is generally a discourse notion, it is also
sensitive to grammar because it singles out content that is conventionally marked as addressing
10
See also de Ruiter et al. (2006) for experimental evidence that the breaking points are primarily determined by
syntactic structure, not intonation, and Stivers et al. (2009) for the claim that turn-taking is a crosslinguistically
robust phenomenon.
14
the QUD, such as main clause content. In turn, while the proposal-based notion of at-issueness is
primarily a matter of grammar, it only includes proposals that have not been decided one way or
another. These findings then answer both Question A (the “grammatical question”) and Question
B (the “discourse question”) posited in the Introduction. By combining ideas from questionbased and proposal-based models, we were able to arrive at a unified notion of at-issueness. The
next section presents a formal model that incorporates this unified view of at-issue content.
4 A formal model for at-issueness
Dynamic semantics views the meaning of sentences as their potential to modify the information
state, i.e. the shared body of knowledge (see Heim 1982; Groenendijk & Stokhof 1991; Kamp &
Reyle 1993; Veltman 1996; Beaver 2001; a.o.). Information states record two types of
information: anaphoric information and factual information. Anaphoric information, i.e.
information about available discourse referents, is standardly encoded by assignment functions.
Ever since Stalnaker (1978), factual information is referred to as the CONTEXT SET and modeled
as a set of possible worlds.11 When the speaker utters a sentence and the hearer does not object,
the worlds that are incompatible with the semantic content of the sentence are removed from the
context set. Certain discourse models also records individual discourse commitments (see
Gunlogson 2001; Groenendijk & Roelofsen 2009; Farkas & Bruce 2010). Keeping track of the
ever-changing public commitments of agents during information exchange allows us to model
the intuition that an act of assertion involves updating the commitments of its utterer without also
updating the context set. Finally, QUDs can but need not be independently represented. This is
because they can be read off the structure of the context set. After a question is asked, the context
set is partitioned into subsets that represent the possible answers to that question.
In the previous section, I argued that at-issue content encompasses two major properties: it is
inextricably linked to the current QUD and it aims to introduce fresh information in the context.
We saw that these properties single out main assertions that are relatively recent in the given
discourse. The formal account then needs to achieve several important things. It needs to be able
to separate the main assertion from other content expressed by the sentence. This separation is
guaranteed by the introduction of propositional discourse referents that encode the content of
various parts of the sentence. The semantics also needs to ensure that main assertions address the
current QUD and put forward update proposals. This is stated as restrictions on the propositional
referent that encodes the descriptive content of the sentence. More specifically, the first
restriction is that the main assertion picks out one of the alternatives associated with the QUD
and the second restriction says that the main assertion entails commitments for the speaker
without also modifying the context set. The emerging model thus requires the right interaction
between a sentence and various components of the context, i.e. the speech agents, their discourse
11
The term COMMON GROUND is used when factual information is modeled as a set of propositions, i.e. a set of sets
of possible worlds.
15
commitments, the context set, and the QUD. In the formal system presented below, all these
notions are modeled as components of the UTTERANCE CONTEXT. The formal system thus merges
the Stalnakerian notion of a context as agreed-upon information with the Kaplanian notion of a
context as representing the speech situation (see Stalnaker 1978; Kaplan 1989). More
specifically, I model speech contexts as quintuples that consist of two individuals and three sets
of worlds, representing the speaker, the hearer, their individual discourse commitments, and the
context set (respectively).12
(37)
c  c SP , c HR , c DC .SP , c DC .HR , c CS 
In the first part of this section, I present an update semantics which incorporates the notion of
a speech context just outlined. The second part of the section offers an account of at-issueness
and its interactions with grammar and discourse. The Appendix outlines a way to recast the
dynamic parts of the semantics in static type-theoretic terms and thus enjoy full compositionality.
4.1 An update semantics with speech contexts
I assume the following basic logical types: e for individuals,  for possible worlds, s for
assignment functions, and t for truth values. Among the more important complex types are  t
(the type of propositions, i.e. sets of words), e  e   t   t   t (the type of speech contexts, i.e.
quintuples consisting of two individuals and three propositions), st (the type of information
states, i.e. sets of assignment functions), and ( st ) st (the type of updates, i.e. functions from
information states to information states).
Models M consist of non-empty and pairwise disjoint sets of individuals DM, possible worlds
WM, assignment functions GM, and truth values {T,F} , as well as the basic interpretation function
IM.13 Domains for objects of complex types are recursively built from these sets. As is standard,
assignment functions interpret variables and the basic interpretation function interprets the
constants of the language. Both functions respect typing, i.e. they assign to each term of some
type an element of the domain of the same type.
Information states are sets of assignment functions, i.e.   G , for any information state  .
As already mentioned, factual information is part of the utterance context. Since the utterance
context figures into the semantics as a discourse referent (see e.g. Partee 1989; Condoravdi &
Gawron 1996; Zeevat 1999; Maier 2009; Bittner 2012; Hunter 2013), its interpretation will
depend on the assignment functions in the information state.
12
One could call the first two coordinates the KAPLANIAN COORDINATES and the last three coordinates the
STALNAKERIAN COORDINATES. Additional (Kaplanian) coordinates for the world/time/location of the utterance can
be added as needed.
13
In what follows, I drop reference to models as non-essential.
16
There are two sorts of terms: functional terms and dynamic terms. The interpretation rules for
functional terms are stated below.14
(38)
FUNCTIONAL TERMS
a. sp(c )g  proj1 ( c g ) ,
hr ( c )g  proj2 (c g ) ,
dc.sp(c )g  proj3 ( c g ) ,
dc.hr ( c )g  proj4 ( c g ) ,
cs( c )g  proj5 (c g )
b.  p max   {w  p g | g   }
c.  p qud   { p g | g   and there is no g '   :  p g   p g ' }
d.  p alt  ( p max  ) ( D   p max  ) ,
( p, x )alt  
 { p 
g
| g   and d   x g }
d De
The five terms in (38a) refer to the different coordinates of a speech context, accessed
through projection functions. Where c is a speech context variable, sp(c ) , hr (c ) , dc.sp( c ) ,
dc.hr ( c ) , cs(c ) stand for the speaker, the hearer, the discourse commitments of the speaker, the
discourse commitments of the hearer, and the context set of c (respectively).
The term p max in (38b), the maximized value of the propositional term p , represents the set
of worlds that are contained in any of p’s values in the given information state. For example, if
  {g1 , g2 , g3} and p is a propositional variable such that g1 ( p )  {} , g2 ( p )  {w1} , and
g3 ( p )  {w2 } , then  p max   {w1 , w2 } . Maximized values thus represent the full proposition
expressed by a propositional term.
The term p qud in (38c) is interpreted as the set of maximal values of p in the given
information state and will be used to encode the structure of the context set after a question is
uttered. Where k represents the utterance context, cs( k )qud stands for the inquisitive value of the
context set, i.e. the different ways in which the context can be settled. Imagine, for example, that
the assignment functions in  map cs( k ) to the following sets of worlds: {w1 , w2 } , {w1 , w3 } ,
{w1} , {w2 } , and {w3 } . If so, cs( k )qud   {{w1 , w2 },{w1 , w3},{w2 }} .
The two terms in (38d) refer to question alternatives. The term p alt stands for the set of
alternatives triggered by the polar question “?p” and is interpreted as the set consisting of the
14
Strictly speaking, functional terms are interpreted with respect to two parameters: an assignment function g and an
information state σ. In practice though, only one of those is needed. I will only mark the parameter that is actually
required to interpret the given expression.
17
maximized value of
p , its complement, and all of their subsets. For example, let
D  {w1 , w2 , w3} and  p max   {w1 , w2 } . Then, the first set in the union is the power set
{{w1 , w2 },{w1},{w2 },{}} and the second set is the power set {{w3 },{}} . What p alt then amounts
to is the union of those two sets, i.e. {{w1 , w2 },{w1},{w2 },{w3 },{}} . Assuming that the question is
“Did Gabe win?”, the two maximal sets {w1 , w2 } and {w3 } represent the “Yes” and the “No”
answers to that question, respectively. Notice that the set  palt  is downward closed under the
subset relation.
The term ( p, x )alt stands for the set of alternatives triggered by p for x, or the answer set for
the content question “ ? x p( x ) ”. In order to understand its interpretation, note first that
{ p g | g   and d   x g } is the set of values for p produced by any assignment function in 
which also maps x to d. If we now take the union of such sets per individuals in the domain, we
arrive at the interpretation of ( p, x )alt . To illustrate, let D  {w1 , w2 , w3 , w4 } , De  {a , b} , and let
there be eight assignments in  which assign values to p for x as specified below.

g1
p
x
{w1 , w2 } a
g2
{w1}
a
g3
g4
{w2 }
a
{}
a
g5 {w3 , w4 } b
{w3}
b
g6
g7
g8
{w4 }
b
{}
b
Table 1 A hypothetical information state
Given
that,
{ p g | g   and a   x g }
is
{{w1 , w2 },{w1},{w2 },{}}
and
{ p g | g   and b   x g } is {{w3 , w4 },{w3 },{w4 },{}} , so ( p, u )alt is interpreted as the union
{{w1 , w2 },{w1},{w2 },{w3 , w4 },{w3 },{w4 },{}} . For example, if the question is “Who won?” and
there are only two people under consideration, {w1 , w2 } and {w3 , w4 } express the proposition that
one or the other won. As above, the set of alternatives is downward closed under set inclusion.
Dynamic terms (intuitively, statements) express updates, i.e. functions from information
states to information states.
(39)
DYNAMIC TERMS
18
a.   R p (t1 ,..., tn )  {g   | for all w   p g , :  w,t1 g , ,..., tn g ,    R g , }
b.  t1  t2   {g   | t1 g , t2 g , } , where  is , , or 
c.          
d.  v   {g ' | there is a g   such that for all u : if u  v then g '(u )  g (u )}
if CS (  )  CS ( )
  
e.     
 undefined otherwise
Atomic dynamic terms describing lexical relations, as in (39a), are relativized to sets of
worlds which encode the propositional information expressed (see Stone 1999; Stone & Hardt
1999). For example, the interpretation of slothp ( x ) will only keep those assignments g which
verify that g ( x ) is a sloth throughout the worlds in g ( p ) . Subscripting lexical predicates with
propositional variables is crucial for keeping apart the various propositions expressed by the
sentence. Dynamic terms for logical relations, as in (39b), do not carry propositional subscripts.
As is standard, conjunction is defined as sequential update first with the left and then with the
right conjunct (39c). The rule in (39d) assigns a random value to a variable v by introducing into
the information state any assignment g' that differs from some old assignment g at most with
respect to the value g' assigns to v. (39e) tells us that presupposed terms, set out by an
underlining, are interpreted as regular updates if they do not modify the context set. (This last
condition is expressed in terms of the CS predicate, defined in (40b) below.) Otherwise,
presupposed terms cannot be interpreted.15
In the remaining part of this section, I discuss speech contexts in more detail and define some
auxiliary concepts. First, a quintuple of two individuals and three propositions would not count
as a speech context unless certain dependencies hold between its coordinates. For any speech
context c, we have to require that the speaker and the hearer of c are publicly committed to their
discourse commitments. In turn, all individual discourse commitments need to be included in the
context set, thus guaranteeing that the context set is shared among all discourse participants.
A second issue arises from the fact that a speech context is represented as discourse referent
and thus different assignments in the information state could assign to it different values. We
then need to ensure that, at any point of conversation, there is a unique speaker and a unique
hearer across the entire information state. This can be achieved by defining a concept of a
DISCOURSE-INITIAL INFORMATION STATE that is anchored to a given speaker and hearer, and by
assuming that discourse roles are flipped as interlocutors take turns. From now on, I will use the
distinguished variable k to represent the utterance context. A discourse-initial information state
15
Notice that, whenever defined,    is not just  as  might introduce new discourse referents and change the
information state. This is the case in “John majored in psychology but now he regrets that he studied a social
science”, where the indefinite “a social science” inside the factive complement introduces a fresh discourse referent.
19
anchored

a ,b
to
a
speaker
a
and
a
hearer
b
can
then
be
defined
as
: {g | a  proj1 ( g ( k )) and b  proj2 ( g ( k ))} .
A related problem concerns possible non-maximal values of the last three coordinates of
speech contexts. Assignments could assign to k , the utterance context variable, values in which
a context set candidate cs( k ) represents a proper subset of the actual context set. In an
information state like   {g1 , g2 , g3 , g 4 } we could for example have cs( k )g1  {w1 , w2 } ,
cs( k )g2  {w1} , cs( k )g3  {w2 } , and cs( k )g4  {} , where only the first assignment encodes
the entire context set. We can extract the full discourse commitment sets or the full context set in
a state  as shown below. The question under discussion in  can be defined as the collection
of all maximal values of cs( k ) .
(40)
a. DC.SP( ) : dc.sp( k )max  ,
DC.HR( ) : dc.hr ( k )max 
b. CS ( ) : cs( k )max 
c. QUD( ) : cs( k )qud 
There are several relationships that hold between the sets defined in (40). As stated above,
each discourse commitment value is included in the respective context set value, i.e.
dc.sp( k )max g  cs( k )max g and dc.hr ( k )max g  cs( k )max g , for any assignment g. It then
follows that for any information state  , DC.SP( )  CS ( ) and DC.HR( )  CS ( ) . It also
follows that QUD ( )  CS ( ) : since QUD ( ) is set of all maximal values of cs( k ) ,
QUD ( ) is the set of all worlds in any value of cs( k ) in  , which is equivalent to CS ( ) . In
other words, CS ( ) is the informative content of QUD ( ) . Notice also that QUD ( ) contains
all the maximal answers to the question under discussion, or else -- if the most recent question
under discussion has been resolved -- it would be the singleton set {CS ( )} . We can then say
that CS ( ) is SETTLED if and only if CS ( )  QUD( ) ; otherwise CS ( ) is INQUISITIVE.16 For
example, the context set in the state  illustrated in Table 1 above is inquisitive because
CS ( )  {w1 , w2 , w3 , w4 } is not a member of QUD( )  {{w1 , w2 },{w3 , w4 }} .
This concludes the presentation of the semantics.
4.2 Explaining at-issueness
16
This terminology follows work in inquisitive semantics (see Groenendijk 2007; Groenendijk & Roelofsen 2009;
Ciardelli et al. 2013).
20
Recall from Section 3 that the main assertion of a sentence is its at-issue content, in the sense
that it necessarily addresses the QUD and constitutes an update proposal. A simple sentence as in
(41a) can then be logically represented as in (41b).
(41)
a. Matt is rich.

 x  x  matt  richp ( x ) 
b.
p


introduce proposal
descriptive content of proposal
p  cs( k )qud

proposal addresses the QUD

dc.sp( k )  p



speaker is committed to proposal
The different parts of the formula have the effects on the information state as indicated. The first
conjunct introduces the proposal proposition. The next three conjuncts specify the descriptive
content of the proposal by requiring that Matt is rich in all of its worlds. The penultimate
conjunct says that the proposal is one of the possible answers to the current QUD. The final
conjunct states that the speaker’s discourse commitments are included in the proposal
proposition. Overall, uttering a declarative sentence amounts to introducing a proposal that
addresses the QUD and that the speaker is publicly committed to. This means that the descriptive
content of declarative sentences is conventionally encoded as being at issue.
The logical representation in (41b) can be compositionally derived as follows. We first let
smart   x p.smart p ( x )
Jack x   P p.x  x  jack  P( x )( p )
and
compose
to
 p.x  x  jack  smart p ( x ) .17 I assume that declarative sentences own their illocutionary
force to the presence of a declarative operator that sits on top of the structure and that has the
following lexical translation: DECLp   P.p  P( p )  p  cs( k )qud  dc.sp( k )  p . To
improve readability, I introduce the abbreviation in (42), which captures the import of the
declarative operator, so that DECLp   P.decl p ( P( p )) . The sentence in (41) can then be
represented more succinctly as in (43).18
(42)
decl p ( ) : p    p  cs( k )qud  dc.sp( k )  p
(43)
decl p (x  x  matt  richp ( x ))
As for conjunctions and restrictive relative clauses, we know from the examples in (6)-(7)
and (18)-(19) that they impose restrictions on the proposal proposition.19 This can be ensured by
17
The formal system presented in Section 4.1 does not have lambda terms in it. The Appendix demonstrates how the
dynamic parts of the semantics can be emulated in a static type logic with lambda terms.
18
I use superscripted variables to indicate the introduction of discourse referents and subscripted variables to signal
anaphoric dependencies (see Barwise 1987).
19
This is actually only true for conjunctions and restrictive relative clauses placed in main clauses. If embedded
under an operator, these constructions will restrict the proposition introduced by the embedding operator. The
declarative operator discussed above already gives a hint on how propositional operators are modeled in the logic.
See below for definitions of interrogative operators, a comma operator, and attitude operators.
21
assuming
who 
the
and 
translations
 PQ p.Q( p )  P( p )
and
 PQ x p.Q( x )( p )  P( x )( p ) , where the former lexical item combines two clausal
meanings (functions from propositions to updates) while the latter item combines two predicate
meanings (functions from individuals and propositions to updates). Assuming that
Edna x is a fearless leader   p.x  x  edna  fearless.leaderp ( x ) is derived as in (41) above
and that she x started the descent 
 p.start.descent p ( x ) , where she x 
x , we get for (44a) the
translation in (44b). Similarly, if a x   PQ p.x  P( x )( p )  Q( x )( p ) and “woman”, “spoke
Sherpa”, and “started the descent” have predicative meanings similar to “smart” in (41), (45a)
receives the representation in (45b).
(44)
a. Edna is a fearless leader and she started the descent.
b. decl p (x  x  edna  fearless.leaderp ( x )  start.descent p ( x ))
(45)
a. A woman who spoke Sherpa started the descent.
b. decl p (x  woman p ( x )  speak .sherpa p ( x )  start.descent p ( x ))
In short, conjunctions and restrictive relative clauses do not introduce propositional discourse
referents on their own. Rather, they place restrictions on the proposition associated with the host
clause. Since in main clauses this proposition is the proposal, the semantic content contributed by
those constructions is correctly predicted to be able to be at issue.
Next, I discuss how QUDs are established and resolved in discourse. While assertions incur
commitments for their utterers and update the context set only if accepted, questions have an
immediate effect on the context set. When an interrogative sentence is uttered, the context set is
partitioned into alternatives that express the possible answers to the question at hand.20 For
simplicity, I assume that those are the complete answers, i.e. the answers that fully resolve the
issue raised. For polar questions, the choice is between the positive and the negative answer. For
content questions, there will be one alternative per answer. Interrogative sentences can then be
logically represented as shown below.
(46)
a. Did Gabe win?
b. p  x  x  gabe  win p ( x )  cs( k )  p alt
(47)
a. Who won?
b. p  x  win p ( x )  cs( k )  ( p, x )alt
20
This idea broadly follows the proposition set approach to the semantics of questions, which originated in Hamblin
(1973), Karttunen (1977), and Groenendjik & Stokhof (1984).
22
The representation of the polar question in (46) introduces the proposition that Gabe won and
requires that any context set candidate is included in it (the “Yes” answer) or its complement (the
“No” answer). This follows from the fact that p alt denotes the set consisting of the maximized
value of p, its complement, and all of their subsets (recall Section 4.1). The restriction
cs( k )  p alt then says that each value of cs( k ) only has worlds in which Gabe won or worlds in
which Gabe did not win; that is, each value decides between the positive and the negative answer
to (46a). Similarly, the representation of the content question in (47) introduces a proposition and
an individual, and states that any context set candidate is included in some of the possible
answers, e.g. “Jeff won”, “Kate won”, etc. This is because of the way the term ( p, x )alt is
interpreted. As discussed in Section 4.1, this term denotes the set of alternatives and their
subsets. So cs( k )  ( p, x )alt amounts to saying that each value of cs( k ) only has worlds in it in
which one of the competitors won.
The representations in (46)-(47) can be compositionally derived if we let wh-words have the
indefinite-like translation of who x   P p.x  P( x )( p ) . Parallel to the declarative case, I
postulate that polar or content interrogative sentences are headed by the interrogative operators
INT p   P.p  P( p )  cs( k )  p alt or INTxp   P.p  P( p )  cs( k )  ( p, x )alt , respectively. If
we abbreviate the predictable parts of their contribution as in (48), we can write the logical
representations in (46b) and (47b) as in (49a) and (49b), respectively.
(48)
a. int p ( ) : p    cs( k )  p alt
b. int xp ( ) : p    cs( k )  ( p, x )alt ,
where x is the variable introduced by the wh-word in 
(49)
a. int p (x  x  gabe  win p ( x ))
b. int xp (x  win p ( x ))
We now have a good grasp of the effect questions have on the context set and can understand
how proposals interact with the QUD. As an illustration, consider the following short exchange.
(50)
a. A: Is Matt rich?
 p  x  x  matt  richp ( x )  cs( k )  p alt
b. B: He is (rich).
 q  x  richq ( x )  q  cs( k )qud  dc.sp( k )  q
c. A: OK.
 cs( k )  q
Due to the last conjunct in (50a), cs( k )  p alt , the question structures the context set in such a
way that the value of each cs( k ) either has worlds in which Matt is rich or worlds in which Matt
is not rich. This means that the context set is represented by two disjunctive and complementing
23
sets of worlds and all of their subsets. That is, the context set is inquisitive, since there is no
maximum element among the different candidates (recall the definition in Section 4.1 above).
The utterance in (50b) introduces the proposal that Matt is rich. The penultimate conjunct
q  cs( k )qud requires that the proposal be one of the two alternative answers to the question in
(50a). That is, proposals necessarily address the current QUD, or else they produce the empty
information state. Proposals also entail commitments for the speaker, expressed in (50b) as
dc.sp( k )  q . If the proposal is accepted, e.g. because the addressee voices agreement as in
(50c), the context set is reduced to worlds included in the proposal proposition by means of
cs( k )  q . Since the proposal proposition was one of the answers to the question in (50a), the
context set of the output information state is settled.
The just described development of the context set is illustrated below for the following toy
model. There are three worlds in the domain: w1 , w2 , and w3 ; the context set in the input
information state  has two worlds in it: w1 and w2 ; Matt is rich in w1 and w3 but not in w2 .

g1
g2
g3
g4
cs( k )
 ' cs( k )
 '' cs( k )
{w1 , w2 }
A: Is Matt rich?
B: He is rich. А: ОК.
{w1} 
g2 {w1}
 g2 {w1} 
{w2 }
g3 {w2 }
{}
g4
{}
g4
{}
CS ( )  {w1 , w2 }
CS ( ')  {w1 , w2 }
CS ( '')  {w1}
QUD( )  {{w1 , w2 }}
QUD( ')  {{w1},{w2 }}
QUD( '')  {{w1}}
Table 2 A representation of the context set development in (50)
In order to be able to fully represent the discourse in (50), we need to model the fact that the
speaker and the hearer exchange discourse roles. Such changes are metalinguistic and typically
not marked by overt lexical material, yet they have an effect on interpretation. I thus introduce
the term cdr ( k ) to mark a change of discourse roles in k and view it as abbreviating the
following sequence of conjuncts.
(51)
cdr ( k ) : c  sp
( k )
 hr (c)  hr
( k )
 sp( c)  dc.sp
( k )
 dc.hr ( c) 



speaker becomes hearer
hearer becomes speaker
speaker's DCs become
hearer's DCs
dc.hr
( k )
 dc.sp( c)  cs
( k )
 cs(c)  k  k  c


hearer's DCs become
speaker's DCs
CS is inherited
This term modifies the utterance context in such a way that the coordinates for the speaker and
the hearer and their discourse commitments are swapped while the context set coordinate is
24
inherited. The full representation of the discourse in (50) is then as in (52). (I assume that a
sequence of overt or covert updates has the discourse effect of conjunction.)
(52)
int p (x  x  matt  richp ( x ))  cdr( k )  decl q (x  richq ( x ))  cdr ( k )  cs( k )  q




A: Is Matt rich?
B: He is rich.
A: OK.
Let us look a bit closer at how proposals are decided. In Section 3, I argued that proposals
need not all be at issue at the same time. Rather, only recent proposals are at issue while older
proposals are likely to have been decided. This fact was reflected in the preference of direct
responses for targeting discourse-final sentences. In order to capture this preference, we allowed
that proposals are silently accepted if not overtly addressed (recall the Default Acceptance
constraint in (34)). This means that the stretch of discourse in (53a) can be represented roughly
as in (53b), assuming that the addressee had the chance to react but did not.21
(53)
a. Matt is rich. He recently bought an apartment in downtown Manhattan.
b. decl p (x  x  matt  richp ( x ))  cs( k )  p  decl q (y  apartmentq ( y )  buyq ( x, y ))
In this discourse, the proposal that Matt is rich is implicitly accepted after the first sentence is
uttered. The only proposal that is still open is the one introduced by the second sentence, i.e. that
Matt recently bought an apartment in downtown Manhattan. Since (53b) is one possible
representation of the discourse in (53a), the more recent proposal is more likely to be judged at
issue.
We have now explained all the major properties of at-issue content in a systematic and
compositional way and with an eye on discourse development. The major claim was that at-issue
content is conventionally marked as putting forward an update proposal that addresses the
current QUD. Such a proposal remains open until the hearer is given the chance to address it; if
unaddressed, the proposal is silently added to the context set. This way of viewing things implies
that both grammar and discourse play an important role in determining at-issue status.
I now turn to the at-issue status of the other constructions discussed in Sections 2 and 3, i.e.
appositive relative clauses and embedded clauses. Starting with the former constructions, we
already know that appositive relative clauses are typically not at issue. For example, they need
not address the QUD.
(54)
A: Who else is coming to the party?
B: I invited my cousin, who lives around the corner.
However, we also saw that when appositive relative clauses appear sentence-finally, their content
is accessible to direct rejections. This is illustrated in (55)-(56), repeated from (32)-(33) above.
21
The QUDs that these two sentences address are not represented here.
25
(55)
(56)
A: Edna, who is a fearless leader, started the descent.
B: #No, she isn’t.
(cf. Amaral et al. 2007: 731)
A: Jack followed Edna, who is a fearless leader.
B: No, she isn’t.
This mixed status of appositive relative clauses can be exhibited by the same sentence: even
when not relevant to the QUD they can be open to direct responses. The appositive content in
(57B), for instance, does not address the QUD but it is still a good target for a direct rejection.22
(57)
A: What did you do last night?
B: We went to the movies and saw Avatar, which was directed by Steven Spielberg.
A: That’s not true. Avatar was directed by James Cameron.
In the terminology of Section 3, appositive relative clauses appear to not be Q-at issue but can be
P-at issue, thus exemplifying an interesting interaction between these two notions of at-issueness.
It is then reasonable to assume that such clauses introduce fresh information that is very much
like a proposal in that it entails commitments for the speaker and is sensitive to linear order. But
appositive content is also unlike classical proposals in that it need not interact with the QUD.23
This way of viewing the status of appositive relative clauses are compatible with the
experimental finding in Syrett & Koev (2014). In their Experiment 2, they set up brief dialogues
in which a speaker delivers an utterance and a hearer voices a direct rejection. Each initial
utterance consisted of a sentence with an appositive and direct rejections targeted either the main
clause or the appositive. Participants were given a forced choice between these two forms of
rejection, as illustrated in (58)-(59).
(58)
A: My friend Sophie, who performed a piece by Mozart, is a classical violinist.
B1: No, she’s not.
(target = main clause)
B2: No, she didn’t.
(target = appositive)
(59)
A: The symphony hired my friend Sophie, who performed a piece by Mozart.
B1: No, they didn’t.
(target = main clause)
B2: No, she didn’t.
(target = appositive)
22
It might be that the appositive in this example is relevant to the QUD in some sense. This could be because it
serves as an explanation for the main point, or perhaps because it effectuates a topic shift. I disregard this option
here because of the (potentially simplifying) assumption made in Section 2.1 that overt questions spell out the
current QUD.
23
I thank an anonymous S & P reviewer from a previous submission of an older stage of this work for suggesting
this way of looking at the mixed at-issue / not-at-issue status of appositive relative clauses.
26
Importantly, Syrett & Koev found a statistically significant difference between sentences with
medial and final appositive relative clauses: participants chose to target a final appositive 35.5%
of the time while they chose to target a medial appositive only 21% of the time. This finding
shows that appositive relative clauses are indeed more likely to be P-at issue, in line with (55)(56). It is also clear though that appositives are not in direct competition with main clauses: even
in sentences with final appositive relative clauses participants chose to target the main clause
64.5% of the time. This general preference for direct rejections to target the main clause is
expected if appositive relative clauses do not enjoy a full at-issue status.
Following Potts (2005; cf. p.92), I propose that appositive relative clauses are headed by a
comma operator. This operator is responsible for their prosodic and semantic independence, i.e.
the fact that they are separated from the rest of the sentence by intonation breaks and introduce
an independent proposition. The sentence in (60a) can then be logically represented as in (60b),
where the comma operator abbreviates the sequence of conjuncts given in (61).
(60)
a. Edna, who is a fearless leader, started the descent.
b. decl p (y  y  edna  comma q ( fearlessq ( y ))  start.descent p ( y ))
(61)
comma q ( ) : q    dc.sp( k )  q
The comma operator looks a lot like a declarative operator (recall (42)), as it entails
commitments to the proposition introduced. But it differs from declarative operators in one
crucial respect: it lacks a conjunct like q  cs( k )qud , which would require that the appositive
proposition addresses the QUD. This assumption explains why appositive relative clauses need
not interact with the QUD, as demonstrated in (54) and (57) above. In addition, given the
constraint of Default Acceptance, the appositive content in (60a) may be tacitly accepted midway
through the sentence. This means that appositive content could lack both ingredients of atissueness: QUD-relevance and open proposalhood. This would explain why appositives are
generally dispreferred as targets of direct responses.
Why are appositive relative clauses more amenable to direct responses when they occur at
the end of the sentence (recall (55)-(56))? Apparently, this is because sentence-final appositive
relative clauses can be construed as introducing the most recent information. For example, the
sentence in (62) can be logically represented either as in (62a), where the appositive contribution
is placed inside the main sentence, or as in (62b), where it completely follows the main sentence
and thus carries the latest information introduced in discourse.
(62)
Jack followed Edna, who is a fearless leader.
a. decl p (x  x  jack  y  y  edna  comma q ( fearless.leaderq ( y ))  follow p ( x, y ))
b. decl p (x  x  jack  y  y  edna  follow p ( x, y ))  comma q ( fearless.leaderq ( y ))
27
The representation in (62b) implies that sentence-final appositive relative clauses can
optionally attach to the top node of the sentence. There is indeed independent evidence that
points at the availability of such high attachment. First, while appositive relative clauses are
usually string-adjacent to the anchor, lexical material (e.g., a temporal adverbial) can sometimes
intervene. The two examples below illustrate a fairly common pattern in colloquial English.
(63)
a. I was talking to an American yesterday, who has lived in Kuwait for 20 years.
b. I was just with George McGovern today, who looks with great graciousness upon
Richard Nixon as a formidable opponent.
(both examples from COCA, see Davies 2008–)
In addition, appositive relative clauses are usually only allowed to attach to referential DP
anchors (see e.g. Rodman 1976; Jackendoff 1977). However, Del Gobbo (2007) notices that final
but not medial appositive relative clauses can sometimes occur with quantificational anchors, as
in (64). Such data hint at a possible contrast in structure: if the appositive in (64b) is attached not
to the anchor but to a higher node, such sentences would not violate the general ban on
quantificational anchors.
(64)
a. *Few/Most students, who were late, came to the party with their parents.
b. They invited few/most students, who arrived very late.
(both from Del Gobbo 2007: 176)
The representation in (62a) can be compositionally derived from the following (simplified)
lexical
translations:
Jack x   P p.x  x  jack  P( x )( p ) ,
follow 
Q x.Q( y p. follow p ( x, y )) , Edna y 
fearless leader 
 P p.y  y  edna  P( y )( p ) , who y 
 x p. fearless.leaderp ( x ) , and COMMA q 
y,
 P.comma q ( P( q )) . Since the
appositive translation comma q ( fearless.leaderq ( y )) is of type update (a function from
information states to information states), it cannot be directly composed with
Edna y   P p.y  y  edna  P( y )( p ) . I thus introduce the following special-purpose
composition rule. (I abbreviate  t , the type of propositions, as  , and ( st )st , the type of
updates, as [ ] . Following Muskens (1996), I adopt the convention that [ ] :  ( st )st , for any
type  .)
(65) If DP x 
[[ e ] ] and ARC 
[] , then DP x ARC 
 P p. (  y q. )( p )  P( x )( p )[[ e ] ] .
This rule inserts the appositive contribution into the translation of the anchor and leaves the rest
of the formula untouched, thus doing justice to the parenthetical nature of appositives. We now
get
Edna y , COMMA q who y is a fearless leader   P p.y  y  edna 
28
comma q ( fearless.leaderq ( y ))  P( x )( p ) ,
which
is
of
the
same
logical
type
as
Edna y   P p.y  y  edna  P( y )( p ) and can compose with the surrounding discourse in
the usual way. Regarding the representation in (62b), I assume that it simply arises from a
sequence of two update terms. The possibility of such construals explains why appositive relative
clauses are more likely to be a target of direct responses when they occur sentence-finally,
despite lacking all the trappings of regular at-issue content.24
Finally, I turn to complement clauses. Above, I discussed complements of non-factive and
factive predicates and noted that such complements cannot take on at-issue status. Why this is so
can be seen from the semantics for complement clauses proposed below. The sentences in (66)(67), for example, can be represented as shown. The representations given are derived from the
believeq   P x p.believe qp ( x, P( q ))
lexical
translations
and
regret q 
 P x p.regret qp ( x, P( q )) , which only differ as to whether or not the content of the
embedded clause is presupposed (marked in the logic by underlining). In these translations, I use
the abbreviations for non-factive and factive predicates as in (68).25
(66)
a. Billy believes that it is raining.
b. decl p (x  x  billy  believe qp ( x, raining q ))
(67)
a. Billy regrets that it is raining.
b. decl p (x  x  billy  regret qp ( x, raining q ))
(68)
a. believe qp ( x, ) : q    believep ( x, q )
b. regret qp ( x, ) : q    regret p ( x, q )
Attitude predicates introduce a proposition (represented above as q) for the content of the
complement clause and are relativized to the proposition (represented above as p) that is
introduced by the declarative operator of the matrix clause. For example, (66b) says that the
24
The suggested analysis of appositive relative clauses raises the question of whether there is semantic content that
has the reverse combination of properties, i.e. content that necessarily interacts with the QUD but is not open to
direct responses. Relevance implicatures might be a case in point, as these address the QUD by definition but do not
seem accessible to direct responses.
(i)
A: Is Jimmy coming to the party?
B: His car broke down. (Implicature: Jimmy is not coming to the party.)
C: Not true -- his car is fine. / #Not true -- he’ll be coming to the party.
25
The attitude predicates in the representation language can be further unwrapped as part of the interpretation
procedure. For example, following the classic analysis of Hintikka (1969), we could define
 believe p ( x , q )  {g   | for all w   p  : DOX ( x  , w )   q
g
g
29
max

 }.
thinking happens in the proposal worlds while the raining happens in the worlds compatible with
the mental state of the attitude holder. Factive predicates as in (68b) differ from non-factive
predicates as in (68a) in that the former require the complement proposition to hold in all the
worlds of the context set. This is the sense in which their complement proposition is
presupposed.
As can be seen from (68), this analysis does not require complement propositions to interact
with the QUD in any way. Unlike proposals, there is no restriction that such propositions address
the QUD. In addition, embedded clauses do not express commitments for the speaker and thus
are not likely to be viewed as proposals by the addressee. This does not exclude the possibility
that non-factive complements enter into various relationships with the current discourse,
including stating what the current topic is. Thus, it is possible that such complements appear to
be at issue, in the weak sense of the word (see Simons 2007). In turn, factive complements
express information that is entailed by the context set. Such complements are thus not likely to
address the discourse topic, which would typically be about information that is not yet part of the
context set. Overall then, the proposed semantics correctly predicts that complement clauses do
not express at-issue content.
4.3 Summary
This section presented a model that could explain the nature and properties of at-issueness. The
semantics achieved that by keeping separate different types of propositional content and
interpreting sentences without modifying the context set. We have analyzed a wide range of
clausal constructions, i.e. main clauses, conjunctions, restrictive and appositive relative clauses,
and factive and non-factive complement clauses. We saw that the proposed update semantics, the
rule of Default Acceptance, and certain specific and well-motivated assumptions about these
constructions are able to predict the correct at-issue status in each case.
5 Conclusion
This paper offered a fresh look at the notion of at-issueness. It investigated the different ways atissueness has been characterized in the literature and arrived at unified view according to which
at-issue content has two conventionally-encoded properties: it interacts with the discourse topic
and it constitutes a proposal to update the context set. We found that these two properties single
out the main assertion of the sentence as at issue. This means that only constructions that
contribute to the main assertion can express at-issue content. The proposed semantics was able to
compose meanings in such a way that asserted content is kept separate from other types of
content expressed by the sentence. In addition, at-issue content was argued to be subject to a
recency requirement: at a given point of discourse, only recent proposals are likely to be at issue.
If this analysis is on the right track, it follows that both grammar and discourse restrict the scope
of at-issue content. The main contribution of this paper can then be sought in enriching our
30
understanding of the possible ways in which at-issue content comes into being and the way it
interacts with grammar and discourse.
Acknowledgements
This work owns a lot to discussions with David Beaver, Maria Bittner, Veneeta Dayal, Cornelia
Ebert, Hans Kamp, Philippe Schlenker, Roger Schwarzschild, Kristen Syrett, Judith Tonhauser,
the audiences at the University of Düsseldorf, and the reviewers at Semantics & Pragmatics. For
English judgments, I am indebted to Matt Barros, Sarah Hansen, Jeremy Perkins, and Peter
Sutton. All mistakes are my own.
References
Amaral, Patricia, Craige Roberts, & E. Allyn Smith (2007). “Review of The Logic of Conventional
Implicatures by Chris Potts.” Linguistics and Philosophy 30: 707--749.
AnderBois, Scott, Adrian Brasoveanu, & Robert Henderson (2013). “At-issue proposals and appositive
impositions in discourse.” Journal of Semantics.
Asher, Nicholas & Alex Lascarides (2003). Logics of Conversation. Cambridge University Press.
Bach, Kent (1999). “The myth of conventional implicature.” Linguistics and Philosophy 22: 327--366.
Barwise, Jon (1987). “Noun phrases, generalized quantifiers and anaphora.” In Peter Gärdenfors (ed.).
Generalized Quantifiers, 1--29. Dordrecht: Kluwer.
Beaver, David I. (2001). Presupposition and Assertion in Dynamic Semantics. Stanford: CSLI
Publications.
Bittner, Maria (2011). “Time and modality without tenses or modals.” In Renate Musan & Monika
Rathert (eds.). Tense across Languages, 147--188. Tübingen: Niemeyer.
Bittner, Maria (2012). “Perspectival discourse referents for indexicals.” Semantics of Under-Represented
Languages in the Americas 7.
Böer, Steven & William Lycan (1976). The Myth of Semantic Presupposition. Bloomington: Indiana
University Linguistics Club.
Büring, Daniel (2003). “On d-trees, beans, and b-accents.” Linguistics and Philosophy 26: 511--545.
Chierchia, Gennaro & Sally McConnell-Ginet (2000). Meaning and Grammar: An Introduction to
Semantics. Cambridge, Massachusetts: MIT Press, Second edition.
Ciardelli, Ivano, Jeroen Groenendijk, & Floris Roelofsen (2013). “Inquisitive semantics: a new notion of
Meaning.” Language and Linguistics Compass 7(9): 459--476. DOI: 10.1111/lnc3.12037.
Condoravdi, Cleo & Jean Mark Gawron (1996). “The context dependency of implicit arguments.” In
Makoto Kanazawa, Christopher Piñón, & Henriëtte de Swart (eds.). Quantifiers, Deduction, and
Context, 1--32. Stanford: CSLI.
Davies, Mark (2008–). The Corpus of Contemporary American English: 450 million words, 1990-present. Available online at http://corpus.byu.edu/coca/.
Faller, Martina (2002). Semantics and Pragmatics of Evidentials in Cuzco Quechua. Ph.D. dissertation,
Stanford University.
31
Farkas, Donka & Kim B. Bruce (2010). “On reacting to assertions and polar questions.” Journal of
Semantics 27: 81--118.
Frege, Gottlob (1892/1980). “On sense and reference.” In Peter Geach & Max Black (eds. and trans.).
Translations from the Philosophical Writings of Gottlob Frege. Oxford: Blackwell, Third edition.
von Fintel, Kai & Anthony Gillies (2007). “An opinionated guide to epistemic modality.” In Tamar Szabó
Gendler & John Hawthorne (eds). Oxford Studies in Epistemology 2, 32--62. Oxford: Oxford
University Press.
Ginzburg, Jonathan (1996). “Interrogatives: Questions, facts, and dialogue.” In Shalom Lappin (ed.). The
Handbook of Contemporary Semantic Theory, 385--422. Oxford: Blackwell.
Groenendijk, Jeroen (2007). “Inquisitive semantics: two possibilities for disjunction.” Proceedings of
Tbilisi 2007: Seventh International Tbilisi Symposium on Language, Logic, and Computation.
Groenendijk, Jeroen & Floris Roelofsen (2009). “Inquisitive semantics and pragmatics.” Stanford
Workshop on Language, Communication and Rational Agency. Available online at
http://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CDEQFjAA
&url=http%3A%2F%2Fdare.uva.nl%2Fdocument%2F131043&ei=LHMgUoK_NInUswa3uYGoDw
&usg=AFQjCNGMh563fK9tOyOdlFD1FWDpTpNqhA.
Groenendjik, Jeroen & Martin Stokhof (1984). “On the semantics of questions and the pragmatics of
answers.” In Jeroen Groenendjik & Martin Stokhof. Studies on the Semantics of Questions and the
Pragmatics of Answers. Ph.D. dissertation, University of Amsterdam.
Gunlogson, Christine (2001). True to Form: Rising and Falling Declaratives as Questions in English.
Ph.D. dissertation, UC Santa Cruz.
Hamblin, Charles (1973). “Questions in Montague English.” Foundations of Language 10: 41--53.
Haug, Dag T.T. (2013). Partial dynamic semantics for anaphora: compositionality without syntactic
coindexation. Journal of Semantics. DOI: 10.1093/jos/fft008
Heim, Irene (1982). The Semantics of Definite and Indefinite Noun Phrases. Ph.D. dissertation, MIT.
Hintikka, Jaakko (1969). Semantics for propositional attitudes. In J. W. Davis et al. (eds.). Philosophical
Logic, 21--45. Reidel Publishing.
Hobbs, Jerry (1985). On the coherence and structure of discourse. CSLI-85-37 report, Stanford
University.
Jackendoff, Ray (1977). X-bar Syntax: A Study of Phrase Structure. MIT Press.
Kaplan, David (1989). “Demonstratives.” In Joseph Almog, John Perry, & Howard Wettstein (eds.).
Themes from Kaplan, 481--563. Oxford: Oxford University Press.
Karttunen, Lauri (1977). “Syntax and semantics of questions.” Linguistics and Philosophy 1: 3--44.
Karttunen, Lauri & Stanley Peters (1979). “Conventional implicature.” In Choon-Kyu Oh & David A.
Dinneen (eds.). Syntax and Semantics 11: Presupposition. London: Academic Press, 1--56.
Kehler, Andrew (2002). Coherence, Reference, and the Theory of Grammar. CSLI, Stanford
University.
Koev, Todor (2013). Apposition and the Structure of Discourse. Ph.D. dissertation, Rutgers University.
Lyons, John (1977). Semantics 2. Cambridge: Cambridge University Press.
Mann, William C. & Sandra A. Thompson (1988). Rhetorical Structure Theory: Toward a functional
theory of text organization. Text 8(3): 243--281.
Matthewson, Lisa, Henry Davis, & Hotze Rullmann (2007). “Evidentials as epistemic modals: Evidence
from St’át’imcets.” Linguistic Variation Yearbook 7: 201--254.
Murray, Sarah (2014). “Varieties of update.” Semantics & Pragmatics 7-2:1--53.
32
Muskens, Reinhard (1996). “Combining Montague semantics and discourse representation.”
Linguistics and Philosophy 19:143--186.
Papafragou, Anna (2006). “Epistemic modality and truth conditions.” Lingua 116: 1688–1702.
Partee, Barbara (1989). “Binding implicit variables in quantified contexts.” Chicago Linguistics Society
25: 342--356.
Potts, Christopher (2005). The Logic of Conventional Implicatures. Oxford: Oxford University Press.
Potts, Christopher (2007). Into the conventional-implicature dimension. Philosophy Compass
2/4: 665--679.
Roberts, Craige (1996/2012). “Information structure: Towards an integrated formal theory of pragmatics.”
In Jae-Hak Yoon & Andreas Kathol (eds.). Ohio State University Working Papers in Linguistics 49:
Papers in Semantics: 91--136. Also in Semantics & Pragmatics 5-6: 1--69.
Roberts, Craige, Mandy Simons, David Beaver, & Judith Tonhauser (2009). “Presupposition,
conventional implicature, and beyond: A uniform account of projection.” Workshop on New
Directions in the Theory of Presupposition, ESSLLI 2009.
Rodman, Robert (1976). “Scope phenomenon, movement transformations and relative clauses.” In
Barbara Partee (ed.). Montague Grammar, 165--176. New York: Academic Press.
de Ruiter, J., H. Mitterer, & N. Enfield (2006). “Projecting the end of a speaker’s turn: A cognitive
cornerstone of conversation.” Language 82(3): 515--535.
Sacks, Harvey, Emanuel E. Schegloff, & Gail Jefferson (1974). “A simplest systematics for the
organization of turn-taking for conversation.” Language 50: 696--735.
Schlenker, Philippe (2009). “Supplements within a unidimensional semantics.” Amsterdam Colloquium:
62--70. Berlin/Heidelberg: Springer.
Shanon, Benny (1976). “On the two kinds of presupposition in natural language.” Foundations of
Language14(2): 247--249.
Simons, Mandy (2007). Observations on embedding verbs, evidentiality, and presupposition. Lingua 117:
1034--1056.
Simons, Mandy, Judith Tonhauser, David Beaver, & Craige Roberts (2010). “What projects and why.”
Semantics and Linguistic Theory 20: 309–327.
Stalnaker, Robert (1973). “Presuppositions.” Journal of Philosophical Logic 2(4): 447--457.
Stalnaker, Robert (1978). “Assertion.” In Peter Cole (ed.). Syntax and Semantics 9: Pragmatics, 315–332.
New York: Academic Press.
Stalnaker, Robert (1999). “On the representation of context.” In Content and Context: Essays on
Intentionality in Speech and Thought, 96--113. Oxford: Oxford University Press.
Stivers, Tanya, N. J. Enfield, Penelope Brown, Christina Englert, Makoto Hayashi, Trine Heinemann,
Gertie Hoymann, Federico Rossano, Jan Peter de Ruiter, Kyung-Eun Yoon, and Stephen C. Levinson
(2009). “Universals and cultural variation in turn-taking in conversation.” Proceedings of the
National Academy of Sciences of the United States of America 106 (26): 10587--10592.
Stone, Matthew (1999). “Reference to possible worlds.” RuCCS TR 49.
Stone, Matthew & Daniel Hardt (1999). “Dynamic discourse referents for tense and modals.” In Harry C.
Bunt & Reinhard Muskens (eds.). Computing Meaning I, 301--319. Dordrecht: Kluwer.
Strawson, Peter F. (1950). “On referring.” Mind 59(235): 320--344.
Syrett, Kristen & Todor Koev (2014). “Experimental evidence for the truth conditional contribution and
shifting information status of appositives.” Journal of Semantics.
33
Tonhauser, Judith (2012). “Diagnosing (not-)at-issue content.” Semantics of Under-Represented
Languages of the Americas 6: 239--254.
Veltman, Frank (1996). “Defaults in update semantics.” Journal of Philosophical Logic 25: 221--261.
Zeevat, Henk (1999). “Demonstratives in discourse.” Journal of Semantics 16(4): 279--313.
Appendix: Compositionality
In Section 4.2, I used lambda terms to derive various logical representations. The update
semantics presented in 4.1 does not provide an interpretation rule for such terms, though. It is in
general not easy to make dynamic systems fully compositional due to the fact that assignment
functions need to interpret variables that are either dynamically bound or lambda bound. Here, I
follow the lead of Muskens (1996) (see also Beaver 2001; Bittner 2011; Haug 2013) and view
the lexical translations presented above as abbreviations for static type-theoretic meanings. The
mapping † , defined below, achieves that in a systematic way. (I use i[ v ] j as abbreviating the
statement that assignments i and j differ at most with respect to the value they assign to the
variable v. The interpretation rules for 
i ,I
, where i is an assignment and I is a function from
assignments to truth values, closely follow those in (38) above.)
(i)
a. ( v. A)†   v. A†
b. ( A( B ))†  A( B )
c. R p (t1 ,..., tn )†   I i.Ii & for all w  p
d. (t1  t2 )†   I i.Ii & t1
i ,I
 t2
i ,I
i ,I
:  w, t1
i ,I
,..., tn
i ,I
 R
i ,I
, where  is , , or 
e. (   )†   I i.  † ( † ( I ))(i )
f.
v †   I  j.i( Ii & i[ v ] j )
 †
if CS ( † (i ))  CS (i ), where i is the input information state for 
g.   
 undefined otherwise
†
To illustrate, the lexical translations in (iia)-(iib) should compose to (iic), which, if fed with the
proposition-denoting term cs(k), should produce the dynamic term in (iid). According to the
semantics of Section 4.1, this last term updates the input information state  to the output state
as described in (iii).
(ii)
a. someone x 
b. smiled 
 P p.x  P( x )( p )
 y q. smileq ( y )
c. someone x  smiled 
 p.x  smile p ( x )
d. x  smilecs ( k ) ( x )
34
(iii)
 x  smilecs ( k ) ( x )
 {h | for some g   : g[ x ]h & for all w  proj5 ( h( k )) :  w, h( x )  smile}
Consider now how the same meaning can be compositionally derived. According to (i), the
lexical translations in (iia)-(iib) can be mapped to the meanings in (iva)-(ivb), which compose to
(ivc). After this last meaning is combined with cs( k )†  cs( k ) , we get the meaning in (ivd). This
meaning is of type update, and when fed with the input information state  it produces the
meaning in (v). As can be seen, (v) is the type-logical equivalent to the set-theoretic meaning in
(iii).
(iv)
a. ( P p.x  P( x )( p ))†   P p I  j.P( x )( p )( a.i ( Ii & i[ x ]a ))( j )
b. ( y q. smileq ( y ))†   y q I i.Ii & for all w  q
c.  p I  j.i( Ii & i[ x ] j ) & for all w  p
j ,I
i ,I
:  w, y
i ,I
  smile
:  w, j ( x )  smile
d.  I  j.i ( Ii & i[ x ] j ) & for all w  proj5 ( j ( k )) :  w, j ( x )  smile
(v)
 I  j.i ( Ii & i[ x ] j ) & for all w  proj5 ( j ( k )) :  w, j ( x )  smile ( )
  j.i( i & i[ x ] j ) & for all w  proj5 ( j ( k )) :  w, j ( x )  smile
35