Discourse, Grammar, and At-issueness

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1 Discourse, Grammar, and At-issueness Todor Koev Abstract This aer exlores the layered ways in which sentences convey meanin in discourse. It takes a fresh look at the elusive notion of at-issueness, or the fact that art of the information exressed 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 uestion under discussion and constitutes a roosal to udate 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 rammatical and discourse restrictions on at-issueness. The account is imlemented in an udate semantics which searates the main assertion from other roositional content and can interret sentences without addin their descritive content to the context. Keywords rammar at-issueness, uestion under discussion, roosal, udate semantics, discourse, 1 Introduction When sentences are used to convey meanin in context, certain information exressed 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 oint of the utterance and is oen for neotiation amon seech articiants, 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 examle, after hearin the utterance in (1), the addressee is likely to treat the main clause as addressin the issue at hand and view the aositive as addin secondary information. (1) Messi, who once scored a oal with his hand, won the Ballon d Or. This aer is devoted to exlicatin the roerties of the elusive concet of at-issueness. I defend a unified view accordin to which at-issue content interacts with the uestion under discussion and constitutes a roosal to udate 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 rammatical and discourse restrictions on at-issueness. More secifically, the discussion is centered around the followin two uestions: (A) THE GRAMMATICAL QUESTION 1

2 What content exressed by the sentence can be at issue? (B) THE DISCOURSE QUESTION If multile roositions that can in rincile be at issue are introduced, what discourse factors determine which of those roositions are actually at issue? Question A asks about otential rammatical restrictions on at-issueness. For examle, is it ossible 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 uestion, I discuss the at-issue status of a small samle of Enlish constructions, which includes main clauses, conjunctions, restrictive and aositive relative clauses, factive and non-factive comlements. 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 brins u the role of discourse in determinin at-issue status. Discourses are fairly comlex systems and it is likely that only certain ortions are at issue at a iven oint. One of the major claims of the aer is that at-issueness is tied to content that is relatively recent. Given the answers rovided to Question A and Question B, the exlanation mechanism is based on both semantic comosition and recency in discourse. I imlemented these ideas in an udate semantics which searates the main assertion from other roositional content and can interret sentences without addin their descritive content to the context. The structure of the aer is as follows. Section 2 discusses two related but distinct notions of at-issueness: a discourse toic-based notion and a roosal-based notion. In Section 3, I arue for a unified account of at-issueness that builds on those revious notions. Section 4 resents the formal account. Section 5 is the conclusion and the Aendix briefly addresses formal issues related to comositionality. 2 On the notion of at-issueness The notion of at-issueness has recently enerated 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 contrastin concetions of at-issueness. In Section 3, I arue for a sinle notion of at-issueness that slihtly modifies and unifies those two revious views. When discussin the way the term at-issue content is used in revious literature, there are several factors to consider. First, what is the informal or intuitive characterization of this term? Second, how is the roerty of at-issueness emirically dianosed? Clearly, if certain content is claimed to be (not) at issue, there should exist aroriate dianostics that detect such status. Finally, one should also ask whether the theoretical exlanation rovided derives the retheoretical sense in which this term is used. For examle, it could be that a articular 2

3 construction is claimed to trier imlications with certain discourse roerties but that the theoretical account does not actually derive those roerties. Potts (2005; 2007) was amon the first to use the term at-issue in the relevant sense. For him, at-issue content is reular asserted content, or truth-conditional content. Potts contrasts atissue content with secondary entailments triered by aositives or exressives. He calls such entailments CONVENTIONAL IMPLICATURES, thus modifyin Grice s (1975) oriinal concet alon the lines suested in Bach (1999). The followin excerts illustrate his view of at-issueness (the emhasis is mine): I use at-issue entailment as a coverterm for reular asserted content [ ]. At-issue entailment sets u a useful contrast with CIs [=conventional imlicatures], which are secondary entailments that cooerative seakers rarely use to exress controversial roositions or carry the main themes of a discourse. (Potts 2005: 6 7) [ ] at-issue [ ] is tyically the content that seakers offer as rimary and also the content that they are most exectin to have to neotiate with their interlocutors before it is acceted into the common round. [ ] robably the most common label for it is truth conditional content. (Potts 2007: 666) Potts suests that at-issue content has two imortant discourse roerties. First, it is rimary, in the sense that it carries the main theme or toic of discourse. This roerty is often exressed by sayin that at-issue content is the main oint of the utterance. Second, at-issue content is content that is neotiated amon interlocutors before it is added to the common round. This second roerty is sometimes characterized by sayin that at-issue content constitutes a roosal to udate the context. Potts does not elaborate on how these discourse roerties of at-issue content are emirically dianosed. Neither does his semantic account tell us much about the ramatic status of at-issue entailments. His two-dimensional semantics merely searates at-issue content from conventional imlicatures and eleantly accounts for the fact that conventional imlicatures tyically roject. 1 An illustration of Potts treatment of sentences with aositives is iven below. (2) a. Lance, who was about to retire, admitted to doin. b. admit.to(lance,doin), about.to.retire(lance) at-issue content conventional imlicature The sentence in (2a) triers two imlications: the at-issue imlication that Lance admitted to doin and the conventional imlicature that Lance was about to retire. However, just treatin those two imlications as loically indeendent, as in (2b), does not make secific redictions 1 See e.. Böer & Lycan (1976), Chierchia & McConnell-Ginet (2000), Dever (2001), AnderBois et al. (2013), Koev (2013), and Smith & Hall (to aear) on the rojection roerties of aositives. 3

4 about the discourse roerties of at-issue content (or those of conventional imlicatures). The atissue roosition can be stiulated to be the main oint of the utterance or to introduce an udate roosal, or both. Potts semantic treatment is then comatible with any broader assumtions about what at-issue content is. Subseuent works have ut the emhasis on one of the roerties of at-issueness, while tyically failin to searate it from other roerties. Below, I discuss a discourse toic-based notion and a roosal-based notion of at-issueness and show that they make different redictions 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 oint 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 exlain at-issueness in terms of a relationshi to the main toic of the conversation, also called the QUESTION UNDER DISCUSSION (or QUD). The main idea behind QUD aroaches to discourse is that conversation is hierarchically structured by uestions, which introduce the toics that interlocuters address durin their interaction in conversation (see van Kuevelt 1995; Ginzbur 1996; Roberts 1996/2012; Bürin 2003). With this backround in mind, Simons et al. (2010) roose the followin basic definition of at-issueness: 2 A roosition is AT-ISSUE relative to a uestion Q iff [ ] is relevant to Q. (Simons et al. 2010: 317) The authors define relevance of a roosition to a uestion in terms of (artial or comlete) answerhood to that uestion. Accordin to their view, a roosition 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 uestion iff it addresses that uestion. Since Q-at-issueness is defined relative to a uestion, it is crucial to find ways of identifyin what the QUD is at any stae of conversation. This task is comlicated by the fact that QUDs are usually imlicit. Unfortunately, the works cited above do not rovide us with reliable emirical dianostics for identifyin QUDs, which makes it hard to test the redictions of the discourse 2 Simons et al. actually allow subuestions to count as relevant to some more eneral uestion and define relevance as a relation between two uestions rather than a roosition and a uestion. A roosition is at issue relative to a uestion Q if and only if?, the yes/no uestion corresondin to, has an answer that is relevant to Q. I loss over this subtlety here. 4

5 toic aroach to at-issueness. In order to have a workable notion of Q-at-issueness, I will always sell out the QUD as an exlicit uestion that sets the stae for the ucomin utterance. In doin so, I make the imortant assumtion that an exlicit uestion is identical to the current QUD. It is in rincile ossible that the two divere and that an answer further secifies or even redefines an overt uestion in order to better fit the actual QUD. In fact, if somethin like this is allowed, one could state that Q-at-issue content always comletely resolves the QUD. For examle, if Abby asks Jared What tye of food do you like? and receives the non-exhaustive resonse I like sushi, one could claim that Jared comletely answered the subuestion Do you like sushi?, which is the immediate QUD. In what follows, I will inore the ossibility that QUDs and exlicit uestions differ from one another. This discussion and the definition in (3) above suest the followin emirical dianostic for Q-at-issueness (see also Tonhauser 2012). (4) ANSWERABILITY TEST Let A ask a uestion and B address it with the semantic content exressed by some art of a sentence. If the discourse is accetable, then that content is Q-at issue. The definition of Q-at-issueness and the closely related answerability test are urely ramatic and thus fairly liberal, in the sense that they do not imose any rammatical restrictions on the tye of semantic content that can be Q-at issue. For examle, can roositional content in eneral, includin non-asserted content, address QUDs? I will show below that this indeed seems ossible for most tyes of content. It is uncontroversial that the main assertion of an utterance can address QUDs; in fact, this is the aradim case of a uestion-answer relationshi. As the examles below demonstrate, asserted content that is QUD relevant can oriinate not just in the main clause, as in (5), but also in a conjunction (6) or a restrictive relative clause (7). This suests 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 lans for today? B: I will finish the aer and send in the job alication. (7) A: What kind of uy did Svetlana end u marryin? B: She married a uy who was born in Ukraine. Aositive relative clauses come close to contributin asserted content. Indeed, aositive content shares a lot of roerties with reular assertions. First, there is lare consensus in the 5

6 literature that aositives are truth-conditionally relevant, either in the sense that seakers consider their truth value when calculatin the truth value of the entire sentence (see Free 1892/1980; Böer & Lycan 1976; Chierchia & McConnell-Ginet 2000; Schlenker 2009; AnderBois et al. 2013; Syrett & Koev 2014) or in the sense that they roject a second truth value on to of the truth value for the main sentence (see Berckmans 1994; Bach 1999; Dever 2001; Potts 2005). Second, aositive relative clauses routinely introduce discourse-new information. Chierchia & McConnell-Ginet (2000) illustrate this oint with the followin short discourse, where the aositive content in the second sentence is clearly novel to the hearer. (8) Let me tell you about Jill Jensen, a woman I met while flyin from Ithaca to New York last week. Jill, who lost somethin on the fliht from Ithaca to New York, likes to travel by train. (Chierchia & McConnell-Ginet 2000: 351) Potts (2005) makes an even stroner claim, aruin that aositives must exress new information, a condition he calls an ANTIBACKGROUNDING REQUIREMENT. For examle, the aositive in (9) reeats old information and the discourse sounds infelicitous. 3 (9) Lance Armstron survived cancer. #When reorters interview Lance, who is a cancer survivor, he often talks about the disease. (Potts 2005: 34/112, slihtly modified) Given all these similarities between reular assertions and aositive content, the latter content is exected to be able to address QUDs as well. This is indeed so. The aositive content in both (10) and (11) rovides information that artially answers the initial uestion. (10) A: What haened last niht at the arty? B: Kevin, who ot drunk, started ole dancin in front of everybody. (11) A: Why was John out of the office for so lon? B: He took care of his husband, who had rostate cancer. (Syrett & Koev 2014: 47) As it turns out, roositional information that oes well beyond assertions can be Q-at issue as well. Embedded clauses are a case in oint. Simons (2007) notices that certain embeddin verbs can ive rise to interretations whereby the embedded clause carries the main oint of the 3 Potts antibackroundin reuirement is certainly not arochial to aositives but also overns the use of reular 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 Armstron survived cancer. #Lance is a cancer survivor and when reorters interview him, he often talks about the disease. A ramatic rincile which rohibits that asserted content is entailed by the context is roosed in Stalnaker (1973; 1978). 6

7 utterance while the main clause serves a secondary function, tyically rovidin evidential information about the source of the embedded roosition. Here is an examle. (12) A: Who was Louise with last niht? B: Henry thinks / believes / said that she was with Bill. (Simons 2007: 1036) Simons calls such uses of embeddin verbs PARENTHETICAL USES and emhasizes that these are not encoded in the semantics but rather are urely a matter of ramatics. This is reasonable, as none of the answers in (12B) entails that Louise is with Bill. Finally, resuosed content often seems unable to address uestions. For examle, the factive comlement in (13B) has the riht shae to resolve the uestion in (13A) but the discourse is deraded. However, Simons (2007) notices that factive comlements can sometimes address uestions, as in (14). 4 It would then aear that factive comlements can, at least to some extent, carry the main oint of the utterance. (13) A: How is your wife doin? B:?It s reat that she has a new job. (14) A: Where did Louise o last week? B: Henry discovered / learned / found out that she had a job interview at Princeton. (Simons 2007: 1045) In summary, one rominent view is that at-issueness is about the relationshi of semantic content to the current QUD. I called this notion Q-at-issueness. This view does not redetermine where in the sentence Q-at issue content oriinates. This is indeed in line with the data. We found that a vast majority of semantic content can, in fact, address uestions, includin content stemmin from main clauses, conjunctions, restrictive and aositive relative clauses, embedded clauses, and ossibly factive comlements. It should be obvious that the notion of Q-at-issueness is very different from what Potts (2005; 2007) envisaed. Accordin to Potts, at-issue content is rimarily 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, roosal-based notion of atissueness. As we will see, this second notion is much more selective and comes close to Potts oriinal intuition. 2.2 P-at-issueness 4 However, Simons also notes that factive redicates under arenthetical interretations lose their resuositional roerties. 7

8 Other authors have focused on the roosal-like nature of at-issue content. AnderBois et al. (2013) and Murray (2014) osit a binary, rammatically-encoded distinction between at-issue vs. not-at-issue entailments. These two tyes of content differ in the way they udate the context: while at-issue content udates the context indirectly, i.e. by means of constitutin a roosal that can be neotiated, not-at-issue content is directly imosed on the context without neotiation. 5 To cite the authors themselves: We [ ] will take at-issue meanins to be roosals to udate the inut CS [=context set] [ ]. In contrast, aositive content is imosed on the CS and not u for neotiation by normal means. (AnderBois et al. 2013: 3 4) This distinction between at-issue and not-at-issue content can be catured as a distinction between information directly added to the common round and information roosed to be added to the common round [ ]. (Murray 2014: 4) Accordin to these authors, main clauses conventionally introduce roosals and thus are invariably at issue. Any content that falls outside the roosal exressed by the main clause is not at issue. This includes not-at-issue entailments, e.. those triered by Enlish aositives or evidential markers in some lanuaes. 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 udate roosal. The entailment reuirement on the riht-hand side in (15) is imortant. 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 reuirement also revents us from concludin that Miley likes to twerk is at issue just because the roosal is The maazine reorted that Miley likes to twerk. In other words, nonentailed arts of roosals, e.. embedded roositions, are not at issue. The main dianostic for P-at-issueness relies on the amenability of semantic content to direct resonses. The basic idea is that content that constitutes an udate roosal is neotiable and thus is oen to direct areement or disareement by the addressee. Other semantic content, e.. 5 The idea that assertions constitute udate roosals is already resent in Stalnaker (1978; 1999) and has been further exlored in Groenendijk & Roelofsen (2009), Farkas & Bruce (2010), a.o. Consider, for examle, the followin excerts: An assertion can then be understood as a roosal to alter the context by addin the information that is the content of the assertion to the body of information that defines the context [ ]. (Stalnaker 1999: 99) [ ] the addressee accets or rejects the roosal either addin the content of the assertion to the contextual information, or leavin the context as it was [ ]. (Stalnaker 1999: 102) 8

9 resuosed content, can tyically only be accessed throuh less direct linuistic means. I call this dianostic the DIRECT RESPONSE TEST and define it as follows. 6 (16) DIRECT RESPONSE TEST Let A utter a sentence and B use a direct resonse to taret some content exressed by some art of a sentence. If the discourse is accetable, then that content is P-at-issue. This formulation emloys the notion of a DIRECT RESPONSE, which needs to be exlicated. Intuitively, direct resonses sinal straihtforward areement or disareement on art of the seaker. In Enlish, direct resonses are tyically exressed by I aree, That s not true, Yes, she is smart, No, he isn t, etc. To be sure, it is ossible for the addressee to also reject content that is not P-at issue, thouh only indirectly. The mechanism of indirect rejection has a more severe conversational effect as it disruts the natural flow of discourse, indicatin that information that has already been acceted needs to be withdrawn. It also involves different rammatical tools, e.. indirect resonses are tyically flaed by hedes like Actually,..., Well,..., Yes, but, Hey, wait a minute!, etc. 7 At the heart of the distinction between direct vs. indirect resonses lies the idea that direct resonses taret content that is currently bein neotiated by seech articiants. There is no such reuirement on indirect resonses, which can taret content that is already art of the common round or content that was never intended to enter the common round. The notion of P-at-issueness turns out to be much more restrictive than the notion of Q-atissueness, discussed in the revious section. Rouhly, only the main assertion can be P-at issue; other semantic content is tyically not P-at issue. First, notice that any art of the main assertion of a sentence can be a taret of a direct resonse, includin information stemmin 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 reorted to the Dean.) (19) A: The deartment hired a rofessor who was born in Jaan. B: He was born in South Korea. 6 The direct resonse test is known in the literature under different names and has been used to distinuish the main assertion of the sentence from imlications triered by resuosition markers (see Strawson 1950; Shanon 1976; Karttunen & Peters 1979; Chierchia & McConnell-Ginet 2000), eistemic modals (see Lyons 1977; Paafraou 2006; von Fintel & Gillies 2007), evidentials (see Faller 2002; Matthewson et al. 2007; Murray 2010, 2014), and aositives (see Amaral et al. 2007; Tonhauser 2012; AnderBois et al. 2013; Koev 2013; Syrett & Koev 2014). 7 A more rammatical way to distinuish between direct and indirect resonses would be to say that the latter but not former include off-track articles or hedes like the ones just cited. 9

10 However, other tyes of content aear unable to be P-at issue. Aositive content is usually not amenable to direct areement or disareement. 8 In (20), for instance, the hearer can reject the main clause content but not the aositive 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 redicates is not a ood taret of direct resonses either. (21) A: Simon believes that Beyoncé is an amazin siner. B: Not really. (Simon doesn t believe that. / #Beyoncé isn t such a reat siner.) Similarly, factive comlements cannot be directly areed or disareed with. (22) A: Obama rerets that the Senate killed the bill. B: I doubt he does. / #I doubt they did. In short, we see that content that is not art of the main assertion is tyically not oen to direct resonses. 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, thouh, can be Q-at issue but is tyically not P-at issue. These two notions of at-issueness then seem to sinificantly differ from each other. Desite aearances, I will roose in the followin section that, once certain restrictions are alied, 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 comin from revious literature. One is based on the relationshi of semantic content to the QUD and the other is anchored in the idea that utterances of declarative sentences introduce roosals to udate the context. I called those two notions Q-at-issueness and P-at-issueness, resectively. We observed that, as they stand, these notions sinificantly differ in emirical scoe: while various sorts of semantic content can 8 One excetion are sentence-final aositive relative clauses, which can be a ood taret of direct resonses (see AnderBois et al. 2013; Koev 2013; Syrett & Koev 2014). This issue is discussed in more detail in Section 3. 10

11 be Q-at issue, tyically only the main assertion of an utterance is P-at issue. These findins brin u the imortant uestion of whether the two notions are in fact distinct or rather can still be viewed as describin the same roerty. I will ot for the latter osition here. I will demonstrate that, once certain adjustments are made, the two notions do not differ from each other after all. I choose to ursue this otion for several reasons, both theoretical and emirical. First, and erhas most imortantly, Q-atissueness and P-at-issueness are based on the same intuition about the layered ways in which sentences convey meanin in context. In fact, there is a sinificant amount of overla between Q-at-issueness and P-at-issueness, e.. when it comes to the main assertion of an utterance. Such overla suests that main oint and roosalhood are not indeendent notions but are closely related. Second, workin with two distinct notions of at-issueness would be theoretically unarsimonious. It is much referable to assume a sinle notion of at-issueness while at the same time ay closer attention to its fine-rained roerties. One obvious asect of the data resented in Section 2 is that P-at-issue content carves out a subset of Q-at-issue content. We miht then look for ways to limit the scoe of Q-at-issueness such that it matches P-at-issueness in emirical scoe. Recall from (3) that Q-at-issueness was defined as content that addresses the QUD. What I roose 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 ste in made the two notions of at-issueness become euivalent. 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 examles in which the main clause content does not answer the QUD while some other art of the sentence does. In (23)-(25), only an aositive relative clause, an embedded clause or a factive comlement rovides an answer to the uestion and the discourses are infelicitous. (23) A: Where did your husband row u? B: #Jacue, who rew u in Paris, has a reat sense of humor. (24) A: Where is Lizzie? B: #I dreamed that she is at her mom s house. (25) A: Did Amanda uit her job? B: #She is uset that she did. In contrast, non-asserted content need not address the QUD. If the uestions above are modified in such a way that they are only answered by the main clause, the exchanes become accetable. (26) A: What do you like most about your husband? B: Jacue, who rew u in Paris, has a reat sense of humor. 11

12 (27) A: What haened last niht? B: I dreamed that Lizzie is at her mom s house. (28) A: How is Amanda doin? B: She is uset that she uit her job. The above discussion shows that while a wide rane of semantic content can address the QUD, there are restrictions on the tye of content that is reuired to do so. In order to accommodate this fact, I make the followin adjustments to the definitions of Q-at-issueness. (29) Q-AT-ISSUENESS (final version) Semantic content is Q-AT ISSUE relative to a uestion iff it is reuired to address that uestion. Given the data in (23)-(25), this strenthened definition imlicitly imoses rammatical restrictions on the notion of Q-at-issueness by effectively limitin 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 reuirement that such content does so and thus, accordin to the definition in (29), non-asserted content is not truly Q-at issue. If this analysis is on the riht track, Q-at-issueness is a more restricted notion than oriinally envisaed in Amaral et al. (2007), Roberts et al. (2009), and Simons et al. (2010). Thouh ramatic in nature, Q-at-issueness is also rammatically encoded, as the oriin of the roosition inside the sentence matters. In turn, the notion of P-at-issueness, as resented in AnderBois et al. (2013) and Murray (2014), is rimarily a matter of rammar. Accordin to that view, main clauses are conventionally encoded as contributin roosals 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 lay an imortant role as well. Only recent roosals are likely to be P-at issue; less recent roosals would tyically have been decided, e.. after bein exlicitly neotiated or by bein imlicitly acceted. This means that the order in which roosals are introduced in discourse matters, with later roosals bein more likely to be amenable to direct resonses than earlier roosals. Consider, for examle, the short exchane below. (30) A: Matthew is rich. He recently bouht an aartment in downtown Manhattan. B: That s not true. The referred interretation of (30B) is one in which the addressee disarees with the second and not the first claim made by the seaker 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

13 immediately after the first sentence was uttered and thus could be taken to tacitly aree with it. The content of the first sentence is then silently added to the context and the conversation moves forward to neotiatin the issue raised by the second sentence. One miht wonder whether the reference for neotiatin recent roosals is continent on the coherence relations between sentences. It aears that it is not. There is a sizeable amount of coherence relations cited in the literature and various researchers have aimed to rovide a viable tyoloy (see e.. Hobbs 1985; Mann & Thomson 1988; Kehler 2002; Asher & Lascarides 2003). Here, I take BACKGROUND, ELABORATION, EXPLANATION, OCCASION, and RESULT as a samle of commonly discussed coherence relations and show that they have no noticeable effect on P-at-issueness. In (31) below, A utters a seuence of two sentences which stand in the coherence relation as indicated. B disarees with A by utterin a direct rejection. Imortantly, the second sentence is invariably the referred taret of B s resonse. This suests that which roosal is currently bein neotiated rimarily deends on recency rather than discourse structure. (31) A: Ryan stormed into the secretary s office. He looked very uset. (BACKGROUND) A: Max had a lovely meal last niht. He ate a lot of salmon. (ELABORATION) A: Billy was in a foul mood. He recently ot fired. (EXPLANATION) A: Geore took to the odium. He bean to read off the teleromter. (OCCASION) A: Sarah ushed Jeremy. He fell to the round screamin. (RESULT) B: That s not true. There is another iece of data that oints at the imortance of recency. We saw that while aositive relative clauses are not Q-at issue (in the stroner sense secified in (29)), they share a number of roerties with asserted content (recall Section 2.1). It has reviously been noticed that their amenability to direct resonses varies deendin on linear osition: while aositive relative clauses are in eneral not oen to direct resonses, they can be when they occur sentence-finally (see AnderBois et al. 2013; Koev 2013; Syrett & Koev 2014). The asymmetry in uestion is illustrated below. (32) A: Edna, who is a fearless leader, started the descent. B: #No, she isn t. (cf. Amaral et al. 2007: 731) (33) 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 eneral tendency of recent content to be more easily accessible to direct resonses. If we assume, uite lausibly, that the content of sentence-final aositive 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

14 What these data suest is that roosals are normally handled in due course. I cature this intuition by statin the followin constraint on roosals in discourse. (34) DEFAULT ACCEPTANCE A roosal is ket oen until the addressee is iven a chance to react to it. If not exlicitly addressed, a roosal is imlicitly acceted. This constraint is in line with the findins of the literature on TURN-TAKING (see e.. Sacks et al. 1974). Turn-takin has the oal of lettin one arty talk at a time, thus minimizin as or overlas and ensurin that interlocutors exchane roles in an orderly fashion. Imortantly, chanes 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 hrases or sentences. 10 How often such oints occur will deend on the articular discourse we are in. In friendly, natural, unreulated exchanes the addressee will have the oortunity to raise an objection after each meaninful unit. Default Accetance redicts for such discourses that if a sentence is not exlicitly addressed, its content is tacitly added to the common round. Of course, we need to also make room for the ossibility that roosals remain oen for loner stretches, e.. because the addressee has not yet been iven the chance to react. This haens in discourses with more or less exlicitly set rules, such as conference talks or olitical debates. In such reulated discourses, time is often strictly allocated amon various seakers and thus the oints of discourse role chanes are much more sarsely distributed. Given the above discussion, we need to slihtly adjust the definition of P-at-issueness in (15) so that it only includes oen roosals. (35) P-AT-ISSUENESS (final) Semantic content is P-AT ISSUE iff it is entailed by an oen udate roosal. We can now roose a unified notion of at-issueness. It combines P-at-issueness and Q-atissueness as two more or less euivalent characterizations of this roerty. (36) AT-ISSUENESS Semantic content is AT-ISSUE iff it is entailed by an oen udate roosal and is reuired to address the current QUD. This definition imlies that both discourse and rammar ull their weiht in determinin at-issue status. While the uestion-based notion of at-issueness is enerally a discourse notion, it is also sensitive to rammar because it sinles out content that is conventionally marked as addressin 10 See also de Ruiter et al. (2006) for exerimental evidence that the breakin oints are rimarily determined by syntactic structure, not intonation, and Stivers et al. (2009) for the claim that turn-takin is a crosslinuistically robust henomenon. 14

15 the QUD, such as main clause content. In turn, while the roosal-based notion of at-issueness is rimarily a matter of rammar, it only includes roosals that have not been decided one way or another. These findins then answer both Question A (the rammatical uestion ) and Question B (the discourse uestion ) osited in the Introduction. By combinin ideas from uestionbased and roosal-based models, we were able to arrive at a unified notion of at-issueness. The next section resents a formal model that incororates this unified view of at-issue content. 4 A formal model for at-issueness Dynamic semantics views the meanin of sentences as their otential to modify the information state, i.e. the shared body of knowlede (see Heim 1982; Groenendijk & Stokhof 1991; Kam & Reyle 1993; Veltman 1996; Beaver 2001; a.o.). Information states record two tyes of information: anahoric information and factual information. Anahoric information, i.e. information about available discourse referents, is standardly encoded by assinment functions. Ever since Stalnaker (1978), factual information is referred to as the CONTEXT SET and modeled as a set of ossible worlds. 11 When the seaker utters a sentence and the hearer does not object, the worlds that are incomatible with the semantic content of the sentence are removed from the context set. Certain discourse models also records individual discourse commitments (see Gunloson 2001; Groenendijk & Roelofsen 2009; Farkas & Bruce 2010). Keein track of the ever-chanin ublic commitments of aents durin information exchane allows us to model the intuition that an act of assertion involves udatin the commitments of its utterer without also udatin the context set. Finally, QUDs can but need not be indeendently reresented. This is because they can be read off the structure of the context set. After a uestion is asked, the context set is artitioned into subsets that reresent the ossible answers to that uestion. In the revious section, I arued that at-issue content encomasses two major roerties: it is inextricably linked to the current QUD and it aims to introduce fresh information in the context. We saw that these roerties sinle out main assertions that are relatively recent in the iven discourse. The formal account then needs to achieve several imortant thins. It needs to be able to searate the main assertion from other content exressed by the sentence. This searation is uaranteed by the introduction of roositional discourse referents that encode the content of various arts of the sentence. The semantics also needs to ensure that main assertions address the current QUD and ut forward udate roosals. This is stated as restrictions on the roositional referent that encodes the descritive content of the sentence. More secifically, the first restriction is that the main assertion icks out one of the alternatives associated with the QUD and the second restriction says that the main assertion entails commitments for the seaker without also modifyin the context set. The emerin model thus reuires the riht interaction between a sentence and various comonents of the context, i.e. the seech aents, their discourse 11 The term COMMON GROUND is used when factual information is modeled as a set of roositions, i.e. a set of sets of ossible worlds. 15

16 commitments, the context set, and the QUD. In the formal system resented below, all these notions are modeled as comonents of the UTTERANCE CONTEXT. The formal system thus meres the Stalnakerian notion of a context as areed-uon information with the Kalanian notion of a context as reresentin the seech situation (see Stalnaker 1978; Kalan 1989). More secifically, I model seech contexts as uintules that consist of two individuals and three sets of worlds, reresentin the seaker, the hearer, their individual discourse commitments, and the context set (resectively). 12 (37) c c, c, c., c., c SP HR DC SP DC HR CS In the first art of this section, I resent an udate semantics which incororates the notion of a seech context just outlined. The second art of the section offers an account of at-issueness and its interactions with rammar and discourse. The Aendix outlines a way to recast the dynamic arts of the semantics in static tye-theoretic terms and thus enjoy full comositionality. 4.1 An udate semantics with seech contexts I assume the followin basic loical tyes: e for individuals, for ossible worlds, s for assinment functions, and t for truth values. Amon the more imortant comlex tyes are t (the tye of roositions, i.e. sets of words), e e t t t (the tye of seech contexts, i.e. uintules consistin of two individuals and three roositions), st (the tye of information states, i.e. sets of assinment functions), and ( st) st (the tye of udates, i.e. functions from information states to information states). Models M consist of non-emty and airwise disjoint sets of individuals D M, ossible worlds W M, assinment functions G M, and truth values {T,F}, as well as the basic interretation function I M. 13 Domains for objects of comlex tyes are recursively built from these sets. As is standard, assinment functions interret variables and the basic interretation function interrets the constants of the lanuae. Both functions resect tyin, i.e. they assin to each term of some tye an element of the domain of the same tye. Information states are sets of assinment functions, i.e. G, for any information state. As already mentioned, factual information is art of the utterance context. Since the utterance context fiures into the semantics as a discourse referent (see e.. Partee 1989; Condoravdi & Gawron 1996; Zeevat 1999; Maier 2009; Bittner 2012; Hunter 2013), its interretation will deend on the assinment 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 (Kalanian) coordinates for the world/time/location of the utterance can be added as needed. 13 In what follows, I dro reference to models as non-essential. 16

17 There are two sorts of terms: functional terms and dynamic terms. The interretation rules for functional terms are stated below. 14 (38) FUNCTIONAL TERMS a. s( c) roj 1( c ), hr( c) roj ( c ), dc.s( c) roj ( c ), dc.hr( c) roj ( c ), cs( c) roj ( c ) max b. { w } c ud ' { and there is no ' : } alt d. max ( max ) ( D ), alt (, x) { and d x } d De The five terms in (38a) refer to the different coordinates of a seech context, accessed throuh rojection functions. Where c is a seech context variable, s ( c), hr ( c), dc.s ( c), dc.hr ( c), cs ( c) stand for the seaker, the hearer, the discourse commitments of the seaker, the discourse commitments of the hearer, and the context set of c (resectively). The term max in (38b), the maximized value of the roositional term, reresents the set of worlds that are contained in any of s values in the iven information state. For examle, if { 1, 2, 3} and is a roositional variable such that ( ) {}, 1 2( ) { w1}, and max ( ) { w }, then { w1, w2}. Maximized values thus reresent the full roosition 3 2 exressed by a roositional term. The term ud in (38c) is interreted as the set of maximal values of in the iven information state and will be used to encode the structure of the context set after a uestion is uttered. Where k reresents the utterance context, cs ( k) ud stands for the inuisitive value of the context set, i.e. the different ways in which the context can be settled. Imaine, for examle, that the assinment functions in ma cs ( k) to the followin sets of worlds: { w1, w 2}, { w1, w 3}, ud { w 1}, { w 2}, and { w 3}. If so, cs( k) {{ w1, w2},{ w1, w3},{ w2}}. The two terms in (38d) refer to uestion alternatives. The term alt stands for the set of alternatives triered by the olar uestion? and is interreted as the set consistin of the 14 Strictly seakin, functional terms are interreted with resect to two arameters: an assinment function and an information state σ. In ractice thouh, only one of those is needed. I will only mark the arameter that is actually reuired to interret the iven exression. 17

18 maximized value of D { w, w, w } and max w1 w2, its comlement, and all of their subsets. For examle, let {, }. Then, the first set in the union is the ower set {{ w1, w2},{ w1},{ w 2},{}} and the second set is the ower set {{ w 3},{}}. What alt then amounts to is the union of those two sets, i.e. {{ w1, w2},{ w1},{ w2},{ w 3},{}}. Assumin that the uestion is Did Gabe win?, the two maximal sets { w1, w 2} and { w 3} reresent the Yes and the No answers to that uestion, resectively. Notice that the set subset relation. The term (, x) alt alt is downward closed under the stands for the set of alternatives triered by for x, or the answer set for the content uestion? x ( x ). In order to understand its interretation, note first that { and d x } is the set of values for roduced by any assinment function in which also mas x to d. If we now take the union of such sets er individuals in the domain, we arrive at the interretation of (, x) alt. To illustrate, let D { w1, w2, w3, w4}, D {, } e a b, and let there be eiht assinments in which assin values to for x as secified below. x { w, w } a { w } a { w } {} a { w, w } b { w } { w } a b b {} b Table 1 A hyothetical information state Given that, { and a x } is {{ w1, w2},{ w1},{ w 2},{}} and { and b x } is {{ w3, w4},{ w3},{ w 4},{}}, so (, u) alt is interreted as the union {{ w1, w2},{ w1},{ w2},{ w3, w4},{ w3},{ w 4},{}}. For examle, if the uestion is Who won? and there are only two eole under consideration, { w1, w 2} and { w3, w 4} exress the roosition that one or the other won. As above, the set of alternatives is downward closed under set inclusion. Dynamic terms (intuitively, statements) exress udates, i.e. functions from information states to information states. (39) DYNAMIC TERMS 18

19 a. b. R ( t,..., t ) { for all w : w, t,..., t R },,,, 1 n 1 n t t { t t }, where is,, or,, c. d. v { ' there is a such that for all u : if u v then '( u) ( u)} e. if CS( ) CS( ) undefined otherwise Atomic dynamic terms describin lexical relations, as in (39a), are relativized to sets of worlds which encode the roositional information exressed (see Stone 1999; Stone & Hardt 1999). For examle, the interretation of sloth ( x ) will only kee those assinments which verify that ( x ) is a sloth throuhout the worlds in ( ). Subscritin lexical redicates with roositional variables is crucial for keein aart the various roositions exressed by the sentence. Dynamic terms for loical relations, as in (39b), do not carry roositional subscrits. As is standard, conjunction is defined as seuential udate first with the left and then with the riht conjunct (39c). The rule in (39d) assins a random value to a variable v by introducin into the information state any assinment ' that differs from some old assinment at most with resect to the value ' assins to v. (39e) tells us that resuosed terms, set out by an underlinin, are interreted as reular udates if they do not modify the context set. (This last condition is exressed in terms of the CS redicate, defined in (40b) below.) Otherwise, resuosed terms cannot be interreted. 15 In the remainin art of this section, I discuss seech contexts in more detail and define some auxiliary concets. First, a uintule of two individuals and three roositions would not count as a seech context unless certain deendencies hold between its coordinates. For any seech context c, we have to reuire that the seaker and the hearer of c are ublicly committed to their discourse commitments. In turn, all individual discourse commitments need to be included in the context set, thus uaranteein that the context set is shared amon all discourse articiants. A second issue arises from the fact that a seech context is reresented as discourse referent and thus different assinments in the information state could assin to it different values. We then need to ensure that, at any oint of conversation, there is a uniue seaker and a uniue hearer across the entire information state. This can be achieved by definin a concet of a DISCOURSE-INITIAL INFORMATION STATE that is anchored to a iven seaker and hearer, and by assumin that discourse roles are flied as interlocutors take turns. From now on, I will use the distinuished variable k to reresent the utterance context. A discourse-initial information state 15 Notice that, whenever defined, is not just as miht introduce new discourse referents and chane the information state. This is the case in John majored in sycholoy but now he rerets that he studied a social science, where the indefinite a social science inside the factive comlement introduces a fresh discourse referent. 19

20 anchored to a seaker a and a hearer b can then be defined as a, b : { a roj 1( ( k)) and b roj 2( ( k))}. A related roblem concerns ossible non-maximal values of the last three coordinates of seech contexts. Assinments could assin to k, the utterance context variable, values in which a context set candidate cs ( k) reresents a roer subset of the actual context set. In an 1 information state like { 1, 2, 3, 4} we could for examle have cs( k) { w1, w2}, 3 4 cs, cs( k) { w }, and cs( k) {}, where only the first assinment encodes 2 ( k) { w1} 2 the entire context set. We can extract the full discourse commitment sets or the full context set in a state as shown below. The uestion under discussion in can be defined as the collection of all maximal values of cs ( k). max (40) a. DC. SP( ) : dc.s( k), DC. HR( ) : dc.hr( k) b. CS( ) : cs( k) max c. QUD( ) : cs( k) ud max There are several relationshis that hold between the sets defined in (40). As stated above, each discourse commitment value is included in the resective context set value, i.e. max max max max dc.s( k) cs( k) and dc.hr( k) cs( k), for any assinment. 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 euivalent to CS( ). In other words, CS( ) is the informative content of QUD( ). Notice also that QUD( ) contains all the maximal answers to the uestion under discussion, or else -- if the most recent uestion under discussion has been resolved -- it would be the sinleton set { CS( )}. We can then say that CS( ) is SETTLED if and only if CS( ) QUD( ) ; otherwise CS( ) is INQUISITIVE. 16 For examle, the context set in the state illustrated in Table 1 above is inuisitive because CS( ) { w1, w2, w3, w4} is not a member of QUD( ) {{ w1, w2},{ w3, w4}}. This concludes the resentation of the semantics. 4.2 Exlainin at-issueness 16 This terminoloy follows work in inuisitive semantics (see Groenendijk 2007; Groenendijk & Roelofsen 2009; Ciardelli et al. 2013). 20