Modalization and bias in questions

Chapter 1 Modalization and bias in questions Anastasia Giannakidou University of Chicago Alda Mari Institut Jean Nicod, CNRS/ENS/EHESS/PSL In this paper, we discuss the presence of modal elements in questions (adverbs, particles, negation) and propose a new theory of bias that relies on the similarities between polar questions and modal assertions. While the two differ in that the first do not have truth conditions, they are deeply similar in presupposing nonveridical spaces, partitioned into 𝑝and its negation. The partition can be indiscriminate, in which case we have nonveridical equilibrium, or bias (positive/negative). We propose an analysis of bias as indicating the presence of a meta-evaluation ranking function O which is also a component of modal structures (Giannakidou & Mari 2018a,b, 2021a,b). Focus adverbials such as REALLY, modal adverbials, and negation are overt lexicalizations of the ranking, and not indicators of verum, as we show. Our paper also discusses the phenomenon of reflection which arises with the presence of modal particles as a pragmatic dual to bias. We identify a number of properties of reflective questions that set them apart from information and biased questions evidencing enhanced uncertainty which we analyze as an effect of the modal element in a reflective question widening the modal base. 1 Questions, bias, and the nonveridical partition In the literature on speech acts the assumption is made that different syntactic types (declarative, interrogative and imperative) map onto distinct speech acts such as assertions, questions and commands respectively (see for a recent discussion Portner 2018). When it comes to assertions and questions, most formal analyses assume a logical language that reflects a clear-cut syntactic distinction Anastasia Giannakidou & Alda Mari. 2025. Modalization and bias in questions. In Tue Trinh, Anton Benz, Daniel Goodhue, Kazuko Yatsushiro & Manfred Krifka (eds.), Biased questions: Experimental results and theoretical modelling, 1–36. Berlin: Language Science Press. DOI: 10.5281/ zenodo.17158176 Anastasia Giannakidou & Alda Mari between declaratives and interrogatives often containing a designated speech act operator such as assert and ?respectively (Krifka 1995). Ciardelli et al. (2013) call those analyses ‘syntactically dichotomous’, and propose further that they are also semantically dichotomous in assigning different semantic values to assertions (propositions) and interrogatives, which are taken to denote questions, i.e., sets of propositions. While categorically different, questions and assertions, however, come closer in the phenomenon of bias. While the denotation of a plain interrogative such as (1) is a request for information, biased questions (2) are not just seeking information but also convey the speaker’s expectation that a positive or negative answer is more likely. This is called bias: (1) Is Ernie a vegetarian? (2) a. Isn’t Ernie a vegetarian? (high negation: positive bias) b. Ernie is a vegetarian, isn’t he? (negative tag: positive bias) c. Is Ernie really a vegetarian? (adverb really: negative bias) A speaker uttering a plain yes/no interrogative is in a state of “true” uncertainty: she does not know if Ernie is a vegetarian and poses the question as a request to find out. The polar question is therefore “information seeking” and does not discriminate towards one answer or the other. This state of neutral uncertainty between 𝑝and its negation has been characterized as nonveridical equilibrium (Giannakidou 2013, Giannakidou & Mari 2016, 2018a,b, 2021a,b) because the two options are entertained by the speaker as equal possibilities upon asking the question: (3) Nonveridical equilibrium (= “True uncertainty” in Giannakidou 2013) A partitioned (𝑝and ¬𝑝) epistemic or doxastic space 𝑀(𝑖)is in nonveridical equilibrium if 𝑝and ¬𝑝are equal options, i.e., they are not ranked; 𝑖is the individual anchor, by default in questions the speaker. Following our earlier work, we take equilibrium to be the default semantic feature of epistemic possibility, questions, and conditionals (for more recent discussion see Liu et al. 2021), regardless of their discourse function. The egaliatarian state of the nonveridical equilibrium is neutral because when asking a plain polar question the speaker has no preconception of assuming which answer (yes or no) is true, no priors (i.e. previously held beliefs or assumptions) as to the positive or the negative answer being more likely. The proposition Ernie is a vegetarian is not challenged in the context prior to asking the question, and the speaker does 2 1 Modalization and bias in questions not have any preference for a positive or negative answer, no expectations that would make them think that Ernie is or is not a vegetarian. Nonveridical equilibrium is, in other worlds, a state of epistemic neutrality with no preconditions on the context or the speaker’s epistemic state regarding the questioned content. When asking a biased question, on the other hand, the speaker reveals that they actually do have some prior expectations that pre-empt them to discriminate between the two possible answers. They now judge a positive or a negative answer as more likely. For instance, upon asking (2a–2b) the speaker reveals that they are considering, prior to asking the question, that Ernie is a vegetarian is a more likely answer. Having prior expectation is not equivalent to believing that Ernie is a vegetarian; if the speaker had believed that the content is true they wouldn’t have asked the question. Likewise in (2c) with really, the speaker is having reasons to think that Ernie is not a vegetarian is a more likely answer. Again, this is not a belief that Ernie is a vegetarian; if the speaker believed that already, there would be no need to ask a question. With biased questions uncertainty still exists about what the true answer is, but the speaker comes to question not from a neutral stance but from a discriminating one: she ranks the two possible answers, and has prior assumptions that favor the one or the other. Bias thus modifies the neutrality of equilibrium in a positive or negative direction by the speaker’s priors which are revealed in that the speaker chooses to add certain devices to the question, such as high negation (2a), a negative tag (2b), or the adverb really (2c). The choice to add these devices reveals to the audience that the speaker abandons neutrality and questions with preference towards a (positive or negative) answer (Sadock 1971, Ladd 1981a, Abels 2003, Van Rooy & Šafářová 2003, Romero & Han 2004, Reese 2007, Asher & Reese 2007, Krifka 2015, Malamud & Stephenson 2015, Roelofsen & Farkas 2015, Larrivée & Mari 2022, Giannakidou & Mari 2021a,b a.o.). In (2b–2c) the speaker has a positive bias and seems to believe it more likely that Ernie is a vegetarian; in (2c), by adding really, the speaker intends to show that they doubt that Ernie is a vegetarian, and we talk about negative bias.1 1Negative bias is also famously observed with negative polarity items (NPIs) (see Borkin 1971, Giannakidou 1997, 2007, Van Rooy & Šafářová 2003, Guerzoni 2004, Guerzoni & Sharvit 2007, a.o.): (i) a. Have you spoken to Mary even once? (NPI: negative bias) b. Did Mary lift a finger to help? (NPI: negative bias) The speaker here has a negative expectation that the addressee has not spoken to Mary or that Mary did not help. In both cases, bias arises because the speaker decided to augment the questions with a focused NPI. 3 Anastasia Giannakidou & Alda Mari Biased questions, then, are not mere requests for information but rely on the speaker’s prior doxastic and epistemic assumptions and expectations.2In this respect, they lie on a continuum between questions and assertions: they ask whether 𝑝but also discriminate towards 𝑝, or its negation. Notice that in the tag question (2b) we actually do have a hybrid declarative and interrogative sentence. Importantly, the bias can also famously be cancelled with an answer of the unexpected polarity. Bias is a choice that the speaker makes based on their assumptions and contextual knowledge but it is not a common ground presupposition, as we will emphasize, hence it can be objected to. In the case of positive bias, the speaker seems to rank 𝑝as more likely, hence they are more epistemically committed to it; in the negative bias, ¬𝑝is considered more likely and there is less epistemic commitment to 𝑝. Speaker commitment is a notion that plays a key role in modality (see Giannakidou & Mari 2021a), and a handy way to refer to the judgment of an epistemic agent towards the veridicality of 𝑝. In our view, commitment is private (we thus differ for instance from Krifka 2015 and Geurts 2019 who consider commitment a public attitude). Giannakidou (2013) connected questions to modal sentences (which she called inquisitive assertions), and Giannakidou & Mari (2018b, 2021a,b) establish a parallel in modality between neutral possibility modals and biased ones (necessity modals): with possibility modals, the speaker is in a nonveridical information state where 𝑝and its negation are equally open possibilities, but with a necessity modal such as MUST there is bias towards the prejacent 𝑝. Consider: (4) a. Ernie is a vegetarian. b. Ernie must be a vegetarian. c. Ernie may/might be a vegetarian. d. Is Ernie a vegetarian? Of the sentences above, only the unmodalized assertion conveys the information that Ernie is a vegetarian, and adds it to the common ground. Only this one is, then, an assertion of 𝑝. The modal sentences, just like the plain question, reveal uncertainty, which we represent as a nonveridical epistemic state, that is to say, a modal base partitioned between Ernie being a vegetarian and not being a vegetarian. The speaker, in choosing to utter modalized sentences, just like with 2There is also contextual bias relating to evidence available in the context, i.e., the common ground (evidential bias, Büring & Gunlogson 2000; Romero & Han 2004; Sudo 2013; Northrup 2014; Domaneschi et al. 2017), or answer bias (Krifka 2015; Malamud & Stephenson 2015). We will not discuss common ground bias here; for more details on factors determining belief formation see Giannakidou & Mari (2021a,b) 4 1 Modalization and bias in questions questions, takes a nonveridical stance (Giannakidou & Mari 2021a, Giannakidou & Mari 2021b). The nonveridical stance can be neutral, as with neutral information question and possibility modals, or biased when the speaker chooses to use MUST. This parallelism between possibility modals and unbiased questions on the one hand, and necessity modal MUST and biased questions on the other will play an important role in our analysis. While we maintain that the categorical difference between modal assertions and questions lays in the first having and the second lacking truth conditions, we also acknowledge that both convey nonveridical states with two alternatives: 𝑝and its negation. Nonveridicality thus “allows us to see that the distinction between assertion and question is not as basic as we thought”, Giannakidou (2013) states, and this, she continues, “seems to support an approach to meaning as semantically non-dichotomous” (Giannakidou 2013 : 117). In the end, what seems to matter is whether a sentence presents the epistemic agent with one or more possibilities about the world, i.e. whether it reflects a homogeneous or non-homogenous (partitioned) epistemic space. “Superficially, this appears to correspond to the contrast between assertion vs. question. However, the more fundamental distinction is between a partitioned or not epistemic space” (Giannakidou 2013: 126). In this paper, we expand on the idea that the distinction between assertion and question is not categorical semantically, and use the phenomenon of bias as a testing ground to establish a parallel between the structure of questions and the structure of modality. We argue that questions and possibility modals share an important piece of meaning: they express nonveridical equilibrium by not discriminating between the two alternatives 𝑝and ¬𝑝; they are by default egalitarian. When a bias device is used, the device manipulates the equilibrium by introducing a ranking function. This is grammaticalized in modality with necessity modals such as MUST, SHOULD and their equivalents (Giannakidou & Mari 2016, 2018b, 2021a,b) – and the expressor of the ranking function can be an overt adverb such as She must definitely be a doctor, or a covert one. We will argue, similarly, that bias inducing devices in questions contribute or manipulate a ranking. The different effects, positive or negative, are due to the lexical contribution of the bias inducing device as we will show. The discussion proceeds as follows. In Section 2 we outline the framework of modality we will be using with the bias inducing ranking function 𝒪. In Section 3 and 4 we will propose that biased questions are equivalent to biased modal conjectures in containing a meta-evaluation function 𝒪which ranks the two possibilities, 𝑝and its negation. Specifically in Section 3 we derive negative bias with the adverb REALLY, and, in Section 4, we discuss positive bias with negation 5 Anastasia Giannakidou & Alda Mari proposing that negation provides the ranking function. The discourse function of a biased interrogative is still that of a question, but its definedness conditions are those of a biased modal verb. Finally, in Section 5, we discuss questions with possibility modals and particles and identify reflectiveness as the inverse of bias, offering an analysis within the modal framework we have established. 2 Nonveridical structure and bias inducing meta-evaluation Modal expressions in human languages – modal verbs, adverbs, particles – are common devices to reflect the speaker’s judgement towards the truth of a proposition. Almost all analyses of modality assume that non-alethic modal expressions as a class are nonveridical, i.e., they reflect epistemic states that do not entail that the proposition is true (Kratzer 1977, 1986, 1991, Giannakidou 1997, 1998, 1999, 2013, Condoravdi 2002, Portner 2009, Beaver & Frazee 2016, Giannakidou & Mari 2016, 2018b, 2021a,b, Lassiter 2016; von Fintel & Gillies 2010 being a notable exception). In the modal framework of Giannakidou & Mari (2016, 2018b, 2021a,b) (henceforth GM) the function of epistemic modal expressions is to convey the nonveridical attitude of the speaker: upon hearing or reading a modal sentence, the audience understands that the speaker cannot be fully committed to the truth of the propositional content of the sentence. Modal expressions are therefore characterized as anti-knowledge markers in GM: a speaker cannot use a modal if she knows 𝑝to be true, e.g. if I see rain falling I cannot say It might be raining, or It must be raining. Likewise, when a speaker asks a question they are in a state of not knowing. Both questions and modals, then, convey epistemically nonveridical spaces, they have this common logical basis (see also Sherman 2018). What does it mean for an expression to be veridical or nonveridical? Consider the following declarative sentences: (5) a. It is raining. b. It must be raining. c. It may/might be raining. Let us call the tensed unmodalized sentences bare. In asserting a bare sentence the speaker is saying something that they know or believe to be true – they are veridically committed to it. GM call this the Veridicality Principle of co-operative communication, and it follows from abiding by Gricean Quality, which is fundamental to co-operative conversation: 6 1 Modalization and bias in questions (6) Principle of veridicality for cooperative communication (Giannakidou & Mari 2021a,b) A sentence S can be asserted by a speaker A if and only if A is veridically committed to the content 𝑝of S (i.e., if and only if A knows or believes 𝑝 to be true). Thus, upon hearing an unmodalized sentence the hearer understands that the speaker knows, or has grounds to believe that it is raining. The epistemic attitude of the speaker can therefore be thought of as a veridical state. For a given judge 𝑖(by default with epistemic modals, the speaker): (7) Veridical epistemic state An epistemic state M(𝑖)is veridical with respect to a proposition 𝑝iff: ∀𝑤[𝑤∈𝑀(𝑖)→𝑝(𝑤)]. A veridical state entails 𝑝, thus conveying epistemic (or doxastic, or mixed) commitment of 𝑖to 𝑝.3But when a speaker chooses to modalize, just like when she choses to pose a question, she is uncertain about 𝑝. The epistemic state now is partitioned into 𝑝and ¬𝑝: (8) Nonveridical epistemic state An epistemic state (a set of worlds) 𝑀(𝑖)relative to an epistemic agent 𝑖is nonveridical with respect to a proposition 𝑝iff 𝑀(𝑖)is partitioned into 𝑝 and not ¬𝑝worlds. In a nonveridical state 𝑀(𝑖),𝑝and not 𝑝are open possibilities. The partition can be neutral, as in the case of equilibrium, or discriminating as is the case with bias inducing necessity modals (cf. infra). Both modals and questions are evaluated with respect to nonveridical modal spaces 𝑀(𝑖), where 𝑖is by default the speaker.4Giannakidou & Mari (2016) formulate nonveridicality as a definedness 3As we mentioned already, our notion of commitment is private and subjective, i.e., it represents the set of propositions held by individual linguistic agents (e.g., the speaker, the subject of the attitude in embedding) which Giannakidou (1997) and Giannakidou & Mari (2016, 2018b, 2021a,b) call individual anchors, recycling a term from Farkas (1985); in our definition above the anchor is called judge. Our commitment therefore differs from Krifka’s which is “modelled as a set of propositions, containing the propositions that are publicly shared by the participants” (Krifka 2015: 328–329). Krifka’s commitment corresponds to common ground assumptions, and the goal of speech acts is to “change a commitment state”. Speaker commitment in our view can be entirely private, even solipsistic (Giannakidou & Mari 2016, 2018a,b, 2021a,b), as with verbs of belief, imagination, dreaming and pretending. 4Both questions and modals can be anchored to the addressee or a third party, and we return to the interrogative flip later in the paper. We assume that, by default, 𝑖is the speaker. 7 Anastasia Giannakidou & Alda Mari condition of modals in the form of the Nonveridicality Axiom – which appears to be also a definedness condition of questions: (9) Nonveridicality Axiom of modals and questions a. modal(𝑀(𝑖))(𝑝)can be defined if and only if the modal base 𝑀(𝑖)is nonveridical, i.e. only if 𝑀(𝑖)contains 𝑝and ¬𝑝worlds. b. ques(𝑀(𝑖))(𝑝)can be defined if and only if the modal base 𝑀(𝑖)is nonveridical, i.e. only if 𝑀(𝑖)contains 𝑝and ¬𝑝worlds. The Nonveridicality Axiom is a definedness condition which lexically encodes a speaker presupposition in the Stalnakerian sense of modals and questions. We will revisit the presuppositional nature of bias and offer more comments in Section 3. Now consider the difference between possibility and necessity modals. (10) a. Ariadne might be at the party. b. Ariadne must be at the party. In both cases, the speaker is uncertain about Ariadne being at the party, and leaves open the possibility that she might not be. The uncertainty is in nonveridical equilibrium with MIGHT: Ariadne being at the party is considered a mere possibility, and the speaker has no reason to believe Ariadne being in the party is closer to what is the case than Ariadne not being at the party. Possibility modals are thus very much like information seeking questions in this regard: in both cases the speaker is in a state of true uncertainty and entertains two alternatives equally.5While questions lack truth conditions and are therefore distinct from modal assertions, it is important to understand that the common semantic core between neutral questions and possibility statements is the nonveridical state: they both generate alternatives – and presuppose equilibrium where the speaker entertains two possible alternatives that are not ranked. On the other hand, when a necessity modal such as MUST/SHOULD is used, the equilibrium is manipulated towards the prejacent being considered more likely by the speaker. GM coin the term biased modals for necessity modals: the speaker is positively biased in favor of the prejacent proposition, though they still are not veridically committed to it. Modal bias reveals an epistemic stance supported by evidence in favor of the proposition, but it does not mean that the speaker knows or believes 𝑝to be true, i.e, they are not doxastically or epistemically committed to it. Modals, according to GM and what von Fintel & 5As we noted earlier, this also holds for the conditional protasis; see Liu et al. (2021) for recent discussion and experimental results. 8 1 Modalization and bias in questions Gillies (2010) call ‘the mantra’, remain indicators that the speaker reasons with uncertainty and that they leave both options, 𝑝and ¬𝑝, open. With biased modals, in addition, the speaker positively discriminates towards 𝑝, she appears to think of 𝑝as a better possibility than ¬𝑝. Bias thus reveals that the two possibilities are ranked. The ranking is done, GM propose, with a metaevaluation function 𝒪 which is always present in a modal structure – and in a nonveridical structure more generally. Let us see what the epistemic MUST modal structure is precisely. First, we have the modal base of epistemic MUST which is nonveridical about the prejacent and contains both 𝑝and ¬𝑝worlds. To derive the truth conditions of MUST the literature assumes (see e.g. Kratzer 1991, Portner 2009, Giannakidou & Mari 2016, 2018b, 2021a,b) that MUST uses a set of propositions 𝒮which describe shared stereotypical/normalcy conditions. The Kratzer/Portner semantics posits an ordering source Best which ranks worlds according to how close they are to the stereotypical ideal. Our account encodes that the modal base is partitioned into stereotypical and non-stereotypical worlds, but we dissociate stereotypicality from ranking. As an epistemic modal, MUST associates with an epistemic modal base 𝑀(𝑖)that contains the worlds compatible with what the speaker knows or believes. 𝑤0is the world of evaluation, by default the actual world: (11) 𝑀(𝑖)(𝑡𝑢)(𝑤0)=𝜆𝑤′(𝑤′is compatible with what is known by the speaker 𝑖 in 𝑤0at 𝑡𝑢)6 Epistemic modality is thus by default subjective, and knowledge changes with time. Epistemic modality is therefore parametric to knowledge at 𝑡𝑢, as is often acknowledged in the literature (see Portner 2009, Hacquard 2006, 2010, Giannakidou & Mari 2016). In the epistemic modal base 𝑀(𝑖)(𝑡𝑢)(𝑤0), we define Ideal𝒮as a function over 𝑀(𝑖)(𝑡𝑢)(𝑤0), still in the spirit of Portner (2009). The output Ideal𝒮is a subset of 𝑀(𝑖)(𝑡𝑢)(𝑤0): (12) Ideal𝒮(𝑀(𝑖)(𝑡𝑢)(𝑤0)) = {𝑤′∈𝑀(𝑖)(𝑡𝑢)(𝑤0)∶∀𝑞∈𝒮⟨𝑤′∈𝑞⟩} So defined, Ideal𝒮delivers the worlds in the modal base in which all the propositions in 𝒮are true. 𝒮is a set of propositions that corresponds to common ground norms.7The truth condition for MUST says that 𝑝is true in the Ideal𝒮 6Our notation 𝑀(𝑖) corresponds to the Kratzerian notation using set intersection ∩𝑓epistemic(𝑤0,𝑖,𝑡𝑢), where this returns the set of worlds compatible with what it is known in 𝑤0 by 𝑖. 7Since only those worlds are considered in which 𝑎𝑙𝑙the propositions in 𝒮are true, the function Ideal𝒮determines a cut-off point. 9 Anastasia Giannakidou & Alda Mari (ii) ¬𝑝worlds are better possibilities than 𝑝worlds Jques REALLY (pres(𝑝))K𝒪,M,𝑖={𝑝,¬𝑝} We assume the structure above for both main and embedded questions. The question still denotes the nonveridical partition 𝑝and ¬𝑝– but the worlds are now ranked by the speaker, and the negative worlds are judged to be better possibilities by the speaker upon asking the question. That the negative worlds are better possibilities means that the answer to the question will more likely fall in the negative space of the partition. In other words, prior to the question, the speaker considers ¬𝑝more likely. This captures the negative bias accurately both in terms of it being a precondition on using REALLY and in terms of the contribution of REALLY being speaker-driven. The ranking is driven by the speaker’s priors, as we said including beliefs, but REALLY is not itself an attitude of belief. REALLY does not have truth conditional (assertive) contribution in questions because questions do not have truth conditions and do not assert. It is unclear to us whether REALLY has assertive content even in assertions: I am really tired seems to simply settle the statement (contested in the prior context, we we noted earlier) in the positive, but whether there is additional contribution in the assertion, e.g., a degree reading, is an open question that we will not address here. 3.2 Why verum doesn’t get things right Our analysis above differs from the well-known account of Romero & Han (2004) in substantial ways. Romero & Han (2004) acknowledges the epistemic root of bias, but makes a number of assumptions that are empirically unjustified thus failing to properly capture the nature of bias. Firstly, it posits that the bias is an ‘epistemic implicature’. We have shown that bias is stronger than that, it is a definedness condition on the question, a precondition on its use, not a postcondition as an implicature is. The bias, crucially, cannot be cancelled by the same speaker: (31) Is Ernie really a communist? #I think so. If bias were merely an implicature, the positive continuation above should be fine. Secondly, while claiming that bias is an epistemic implicature, Romero & Han (2004) propose a semantics for REALLY-as-verum that is too strong. The claim is that REALLY is the verum operator: verum “is coming from the lexical item really” (Romero & Han 2004: 641). Romero & Han (2004) offer two versions of verum both rendering it an attitude of certainty or subcase thereof. 16 1 Modalization and bias in questions In one version, verum is a a veridical operator akin to knowing or believing; Romero & Han (2004) call it “the run-of-the-mill epistemic operator denotation [...], where 𝑥is a free variable whose value is contextually identified with the addressee (or with the individual sum of the addressee and the speaker)”: (32) Jverum𝑖K𝑔𝑥/𝑖=Jreally𝑖K𝑔𝑥/𝑖=Jbe sureK(J𝑖K𝑔𝑥/𝑖)= 𝜆𝑝⟨𝑠,𝑡⟩𝜆𝑤.∀𝑤′∈Epi𝑥(𝑤)[𝑝(𝑤′)=1] ((40) in Romero & Han 2004) The function defined here is, according to Romero & Han (2004), “the correct denotation for straightforward epistemic expressions like be sure, be certain. But note that, though really or verum is often epistemically flavored, it is not interchangeable with pure epistemic expressions like “be sure”” (Romero & Han 2004: 626). We agree, it is not interchangeable with epistemic or doxastic attitudes, and this is because REALLY is not an epistemic or doxastic attitude. Had verum conveyed the certainty or knowledge of 𝑝, it should have been unusable in questions which by definition presuppose uncertainty: if the speaker, or speaker and addressee jointly know or believe that 𝑝is true, then why bother asking the question? verum cannot be a veridical operator as above, it cannot entail 𝑝.11 Romero & Han (2004) acknowledge the problem and admit that “the intuition is that really or verum is used not to assert that the speaker is entirely certain about the truth of 𝑝, but to assert that the speaker is certain that 𝑝should be added to the Common Ground (CG). That is, rather than a purely epistemic, really or verum is a conversational epistemic operator [emphasis ours].” (Romero & Han 2004: 627). They then offer a definition “FOR-SURE-CG𝑥” in example (43), where “Epi𝑥(𝑤) is the set of worlds that conform to 𝑥’s knowledge in 𝑤, Conv𝑥(𝑤′) is the set of worlds where all the conversational goals of 𝑥in w are fulfilled CG𝑤″ is the Common Ground or set of propositions that the speakers assume in 𝑤″to be true (Stalnaker 1978, Roberts 1996)”. (33) Jverum𝑖K𝑔𝑥/𝑖=Jreally𝑖K𝑔𝑥/𝑖= 𝜆𝑝⟨𝑠,𝑡⟩𝜆𝑤.∀𝑤′∈Epi𝑥(𝑤)[∀𝑤″∈Conv𝑥(𝑤′)[𝑝∈CG𝑤″]]= FOR-SURE-CG𝑥((43) in Romero & Han 2004) Unfortunately, this understanding of verum is just a variant of their entry (40). verum is now driven by common ground assumptions – but the REALLY bias (and bias more broadly, as we showed) is tied to the speaker. The speaker 11Even if questions “flip” epistemics to the addressee (Eckardt & Beltrama 2019) as in Are you sure that Ernie is a communist?, without an explicit signal to the addressee, the question remains anchored to the speaker. 17 Anastasia Giannakidou & Alda Mari may be making assumptions about Ernie being a communist that could be entirely at odds with the hearer’s assumptions, thereby raising the stakes for the latter as we mentioned earlier. More importantly, verum in this new definition continues to be an attitude (now that the speaker is certain that 𝑝should be added to the Common Ground), and as such the problem of conflicting with the question remains. There is no evidence that REALLY has any assertive content in questions – and in an actual assertion (I am really tired) REALLY contributes only a degree meaning and no “epistemic implicature”. The most important problem with the verum analysis of REALLY, in our view, is that the verum meaning is akin to a veridical attitude itself, but the bias is, as we argued, at the non-at-issue level (see also Liu 2012, Liu et al. 2021), and it is not an attitude. REALLY is not a propositional attitude: if, in asking REALLY 𝑝?, the speaker believed 𝑝or were certain that 𝑝should be added to the common ground, then why ask the question? It should be pointless. As an attitude, REALLY asserts content, but this is too strong. In our analysis, REALLY is an adverb that affects the ranking: it ranks the two possibilities given in the nonveridical space, the negative being more likely. REALLY thus turns out to be the dual of MUST. The only additional assumption that we make is that the modal ranking can be realized by expressions that are not strictly speaking modal, such as the adverbs meaning REALLY – and as we argue next, negation. But this assumption is not extraordinary as the possibility of ranking exists in all nonveridical contexts which can be ranked and have bias, or be left unranked in the egalitarian state of equilibrium. 4 Focus negation and bias The bias arising with so called high negation (HNQ) also relies on the speaker’s ranking. Since Ladd (1981b) the observation has been that high negation indicates that the questioner believes that 𝑝is true or likely: (34) a. N’est-il not.is pas neg la def.f maison? house Je 1sg pensais think.pst.1sg qu’il that.he l’était was # Je I ne not pensais think.pst.1sg pas neg qu’il that.he l’était. was ‘Isn’t he home? I thought he was / #I did not think he was.’ b. Isn’t he home? I thought he was / #I did not think he was. c. Dhen Not ine is spiti? home? (Greek) ‘Isn’t he at home?’ 18 1 Modalization and bias in questions These questions expect a confirmatory answer, which should be positive (see also Büring & Gunlogson 2000, Romero & Han 2004, Goodhue 2018); a contrario Krifka (2015) states that with negated questions, the speaker checks whether the addressee is ready to express lack of commitment towards the proposition, which is compatible with expecting a positive answer. In English, syntactically high negation can be interpreted in a high or low position. (35) Isn’t John at home? a. High negation: Isn’t John at home? (neg > ques) b. Low negation: Is John not at home? (ques > neg) Across languages the ambiguity does not always arise, and high negation can only be interpreted in a high position. The two readings have different intonational patterns, and only high neg bears focus as the following French example shows: (36) Il He n’est not.is pas neg venu? come French ‘Hasn’t he arrived?’ a. Intended interpretation: It is not true that he has arrived? b. Impossible interpretation: Is it true that he has not arrived? This data can be replicated for Greek, with focused negation dhen: (37) DHEN not irthe? came.3sg ‘Hasn’t he arrived?’ a. Intended interpretation: It is not true that he has arrived? b. Impossible interpretation: Is it true that he has not arrived? Current accounts agree on a number of facts that hold uniformly across languages. High negation is focus sensitive (henceforth Focus-neg) and (i) triggers the speaker’s expectation that 𝑝is true (38); and in the question (ii) it renders the positive answer more likely: (38) Isn’t he home? I thought he was / #I did not think he was. A variety of approaches to negative biased questions have been developed: (i) verum operator accounts (Romero & Han 2004; see Repp 2013 for falsum). (ii) Double speech-act accounts (Reese 2007). (iii) Commitment (Krifka 2015) and 19 Anastasia Giannakidou & Alda Mari (iv) decision based accounts Van Rooy & Šafářová (2003); (v) Evidence-based accounts (Büring & Gunlogson 2000, Sudo 2013, Roelofsen & Farkas 2015, Goodhue 2018), stemming from the work of Ladd (1981b). It would be impossible to render justice here to the whole literature, and for the purpose of this paper we only focus here on the interrelations between MUST, Focus-neg and bias; for extended recent discussions see Krifka (2017), Larrivée & Mari (2022). Larrivée & Mari (2022) establish a series of correlations between high Focusneg in questions and MUST, pretty much in the sprit we outlined for REALLY. They argue that Focus-neg and MUST share important similarities, namely (i) they are nonveridical, and (ii) they convey the speaker’s prior that 𝑝is likely. However, they are in complementary distribution in evidential contexts. MUST is felicitous in contexts that are compatible with 𝑝, whereas negative questions are felicitous in contexts that are incompatible with 𝑝(called ‘negative evidence’ by Büring & Gunlogson 2000, see also Sudo 2013). The following examples are from Larrivée & Mari (2022). (39) John looked pretty happy coming back from school. a. – Il he doit must avoir have réussi succeded son his examen exam de of math. math ‘He must have passed the big maths test.’ b. – #N’a-t-il not.have-1sg-he pas neg réussi succeeded son his examen exam de of math? math ‘Didn’t he pass the big maths test?’ (40) John looked pretty down coming back from school. a. – #Il he doit must avoir have réussi succeded son his examen exam de of math. math ‘He must have passed the big maths test.’ b. – N’a-t-il not.have-1sg-he pas neg réussi succeeded son his examen exam de of math? math ‘Didn’t he pass the big maths test?’ We argue here that the high Focus-neg introduces a metaevaluation which, like MUST, produces positive bias. The bias is positive because the negation particle functions here as a modal adverb in focus. The negation particle in a question is forced to this meaning for two reasons. First, just like with REALLY, bias inducing negation bears focus and functions as a focus particle. (Low negation, by contrast, is de-accented and functions normally as the expected proposition negating function). Second, being a focus particle means that (i) there is a set of 20 1 Modalization and bias in questions alternatives in the discourse, and (ii) in questions, the relevant alternative will have to be ¬𝑝. If ¬𝑝is the alternative Focus-neg, which needs to express new information, cannot not function as negation. Focus-neg thus has no contribution other than the ranking presupposition. As we noted for REALLY, the focus adverb (here, neg) requires an alternative contextual assumption of the opposite polarity to make sense, i.e., for it to be a reasonable alternative. In other words, the opposite polarity effect follows from the anaphoricity of focus and the requirement that the focused statement provide new information with respect to the alternative. (41) Jques Focus-neg (PRES (𝑝))K𝒪,M,𝑖is defined only if (i) the modal base 𝑀(𝑖)is nonveridical and partitioned into {𝑝,¬𝑝}worlds. (ii) 𝑝worlds are more preferable than ¬𝑝worlds Jques Focus-neg (PRES (𝑝))K𝒪,M,𝑖={𝑝,¬𝑝} Since a question does not assert ¬𝑝the contribution of Focus-neg as 𝒪arises as a meaning reanalysis. Just like with REALLY, we can assume that neg is in the 𝒪position in the question skeleton – recall that that was also the position of REALLY: (42) CP ques whether1 NonveridicalP 𝒪:Focus-neg NonveridicalP ... 𝑡1𝑀(𝑖) 𝒮 TP Putting the effect of REALLY and negation together, then, we must say that their content is only presuppositional. Thus, our account explains their contribution and the polarity reversal in a very simple way by acknowledging their status as focus operators, and allowing an extended syntactic structure in questions parallel to the (independently motivated) one for modals with a position for 𝒪. No other account that we know of offers an explanation of these facts with such simplicity and no additional ad hoc assumptions. 21 Anastasia Giannakidou & Alda Mari Before closing, we want to go back to the strength of veridical commitment, and note that modals and questions mirror each other in terms of strength. In our theory, commitment with modals proceeds according to the following scale: (43) Scale of veridical commitment (Giannakidou & Mari 2016, 2018b, 2021a,b) 〈𝑝, MUST 𝑝, MIGHT 𝑝, *〉; where 𝑖is the speaker, 𝑝conveys full commitment of 𝑖to 𝑝; MUST 𝑝 conveys partial commitment of 𝑖to 𝑝, and MIGHT 𝑝conveys trivial commitment of 𝑖to 𝑝. No modal expression conveys negative commitment. * in (43) indicates that no epistemic modal can convey negative commitment (see Ernst 2009, Homer 2015, Giannakidou & Mari 2018b as for how this relates to the neg-raising property of universal epistemic modals).12 With REALLY and Focus-neg, the commitment, which is a presupposition rather than an assertion, proceeds as a mirror image: (44) Scale of commitment in question presuppositions: 〈𝑝, FOCUS NEGATION 𝑝, MIGHT 𝑝, REALLY 𝑝〉; where 𝑖is the speaker, 𝑝conveys full commitment of 𝑖to 𝑝; HIGH NEGATION 𝑝conveys partial commitment of 𝑖to 𝑝, MIGHT 𝑝conveys trivial commitment and REALLY conveys negative commitment of 𝑖to 𝑝. Like MUST and MIGHT, Focus-neg and REALLY questions are nonveridical. Focus-neg and MUST are equivalent in terms of function and commitment in questions, and likewise REALLY contributed ranking but is negatively biased for the reasons we explained earlier. Why modal assertions and questions are mirror images of commitment is a question that we cannot answer fully; but within the GM system the contrast can be simply due to the fact that, in questions, REALLY and negation are forced to function in an alternative way given their opposite polarity anaphoric property due to focus. We now complete our exploration of the relation between questions and modality by considering questions where modal particles, including a different kind of negation, are used. The particles, we will show, are equivalent to unbiased possibility modals rather than MUST, and do not rank the two alternative propositions. Rather, they widen the options and create vagueness. The effect we observe is 12Cross-linguistically, attitudes like ‘doubt’ can instead convey negative commitment. As far as we are aware, at least in Indo-European languages, there is no modal verb/auxiliary equivalent. 22 1 Modalization and bias in questions an enhancement of equilibrium, not its shrinking (as is the case with bias) – with the opposite effect of creating more uncertainty. This operation, which we call ‘reflection’, targets the modal base. 5 The reflective question: enhancing uncertainty In this section, we consider the use of possibility modal particles and verbs in questions, resulting in the question now becoming vague and potentially unanswerable. We call such questions reflective. In the literature the term ‘conjectural’ has also been used (see Littell et al. 2010, Matthewson 2010, Eckardt & Beltrama 2019, Frana & Rawlins 2019 a.o.). The reflective question is well documented for a number of languages, including Greek, Japanese and Korean (Kang & Yoon 2018, 2019). In discussing it along with bias, we view the two phenomena as pragmatic duals. 5.1 Modal particles in questions: The data For a long time, it was thought that epistemic modals do not occur in questions (Coates 1983, Drubig 2001, Jackendoff 1972, Leech 1971, McDowell 1987). Jackendoff, specifically, claimed that while may can either be interpreted deontically or epistemically in a declarative sentence (John may leave early tonight), it can only be interpreted deontically in a question (May John leave early tonight?). Yet Ernst (2009) presented examples with modal adverbs in questions (Is she possibly the murderer?), and Hacquard & Wellwood (2012) offer corpus data with possibility modals in questions. The following examples are from that work: (45) a. With the owners and the players on opposite sides philosophically and economically, what might they talk about at the next bargaining session? b. Might he be blackballed by all institutions of higher learning? c. What might the Grizzlies have been like if their leading scorer and rebounder, 6-foot-10 center Brent Smith, had not missed his third straight game because of a sprained ankle? The authors conclude that epistemic modals of possibility are very natural in questions. In Greek, we find possibility modal verbs and particles in questions: the socalled evaluative subjunctive (Giannakidou 2017), and the particles taxa, mipos, arage ‘maybe/possibly’, the latter two only used in questions, as we see below 23 Anastasia Giannakidou & Alda Mari with examples from Giannakidou (2017) (see earlier discussions in Giannakidou 2009, Rouchota 1994): (46) Pjos Who irthe came.3sg sto to-the party? party ‘Who came to the party?’ (47) Pjos Who 𝑛𝑎 subj irthe came.3sg sto to-the party? party ‘Who might have come to the party?’ (48) Pjos Who 𝑏𝑜𝑟𝑖 might / / *prepi must na subj irthe came.3sg sto to-the party? party ‘Who might/#must have come to the party?’ (49) (𝑁𝑎) subjV tou him milise talked-3sg (arage/mipos/taxa)? particle ‘Might she have talked to him?’ (50) Tou him milise talked-3sg (#arage/#mipos/taxa). particle ‘She talked to him (as-if).’ (51) Tou him milise? talked-3sg ‘Did she talk to him?’ Here we observe the subjunctive, the possibility modal bori and the particles arage/mipos/taxa in questions (both polar and wh-questions). As we can see, the particles can spread in a fashion reminiscent of modal spread with modal verbs and adverbs (He may possibly be here tonight). The MUST modal is excluded as can be seen in (49), indicating that we are not dealing with a bias related phenomenon. In the declarative context, only taxa can be used, which means literally ‘as if, allegedly’ and casts doubt on the truth of the proposition is attaches to (see Giannakidou 2022 for more details on the Greek particles; Ifantidou 2001). The particles correspond to might, as indicated in the English translations. Giannakidou (2017) argues that the particle question differs from the plain one in being open-ended, vague, and primarily self-addressed. It does not require an actual or full answer; for instance, Pu na evala ta gialia mou? ‘Where might I have put my glasses?’ is a question that one poses to herself in a wondering, reflective manner without expectation of knowing the answer. Bare questions cannot be used this way. (In fact, first person unmodalized questions are quite uncommon). 24 1 Modalization and bias in questions This open-endedness is found also in Japanese and Korean discussed recently in Kang & Yoon (2018, 2019), and with subjunctive questions in Salish (Matthewson’s (2010) ‘conjectural’ questions). English data from Ernst (2009), Hacquard & Wellwood (2012) illustrate the same reflective character for English questions with possibility modals: (52) Is she possibly/*probably a spy? (53) Might/*must she be a spy? These have been described as ‘weaker’ questions. Kang & Yoon (2018, 2019) in their discussion of a similar use of the particle nka in Korean note that by using nka, the speaker “reflects on her own background assumptions and is not simply requesting information from the addressee”. Nka-questions, they argue, are feigned monologues, i.e., the speaker says something as if it were a monologue without expecting an answer necessarily. Because of the monologic nature of the utterance, it does not necessarily obligate the hearer to respond, and while there may be differences between the particles and across languages, these observations hold also for the Greek and English particle questions above. The self-reflective character of particle questions is further evidenced by the fact that directly addressing the hearer is odd. (54) # Ti what na subj efages ate.2sg arage araje xthes? xthes ‘What might you have eaten yesterday?’ (55) Ti what efages ate.2sg xthes? xthes ‘What did you eat yesterday?’ (56) # Na subj efages ate.2sg araje araje xthes? xthes ‘Might you have eaten yesterday?’ (57) Efages ate.2sg xthes? xthes ‘Did you eat yesterday?’ For the Greek particles, Giannakidou (2022) calls this ‘anti-addressee’ effect. Cross-linguistically, the effect is also observed in Korean (Kang & Yoon 2019). 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