Conjectural questions: The case of German verb-final wohl questions*

The paper analyzes German verb-final questions with the particle wohl, which roughly translate as ‘Q, I wonder?’. It construes German as an instance of a general typological pattern: Conjectural questions (CQs) are marked by evidentials in many languages, and German wohl is an inferential evidential. The analysis proceeds in three steps. First, wohl is shown to pattern with inferential evidentials in other languages. Declarative wohl p asserts p and conveys ‘the speaker defeasibly infers p from secure knowledge’ as non-at-issue content. Second, the analysis is extended to standard wohl Q questions, accounting for the interrogative flip. Third, the analysis integrates conjectural verb-final wohl questions. I propose that CQs ask for answers that are defeasibly entailed by the pooled knowledge of speaker and addressee. Due to the logic of defeasible inference, the addressee is not in a position to answer the CQ unless both interlocutors have pooled their knowledge. In normal utterance contexts, these questions are thus un-answerable. We see two conventionalized reactions: the interlocutors engage in speculative discourse, or the CQ is understood as a statement of curiosity that doesn’t require a response.


Introduction
The paper aims to analyse the following contrast between standard questions and conjectural questions (CQs) in German.
(1) Wo where ist is der the Schlüssel? key 'Where is the key?' (2) Wo where wohl wohl der the Schlüssel key ist? is 'Where might the key be, I wonder.' (1) conveys a standard question. In uttering it, the speaker requests the addressee to answer.
(2) expresses that the speaker is asking herself or wondering. Even if an addressee is present, (2) does not request the addressee to answer. Conjectureal questions like (2) are therefore also described as self-addressed, deliberative, monological or "questions in the absence of an addressee". In terms of syntax (2) differs from (1) in two respects.
(2) shows German subordinate clause syntax with the finite verb in sentence-final position. Moreover (2) contains the particle wohl and (1) doesn't. The particle is mandatory in wh-questions to achieve the CQ reading, as (3) shows.
(3) # Wo where der the Schlüssel key ist is Unavailable 'Where might the key be, I wonder.' There is a considerable body of research on German verb-final questions (Altmann 1987, Oppenrieder 1989, Lohnstein 2007, Truckenbrodt 2006, Gutzmann 2011, M. Zimmermann 2013. Lohnstein and Truckenbrodt maintain that the verb-final syntax of (2) suffices to trigger the conjectural reading, a view that is challenged by constituent questions like (3). The particle wohl marks declaratives as "uncertain knowledge" and its contribution to CQs has remained unexplored so far. Taking a look at CQs at large, we find a broad range of languages where evidential markers serve to indicate CQs, including languages as diverse as Japanese (Japonic; Hara 2006), Gitksan, St'át'imcets and NeìePkepmxcín (Salish;Littell, Matthewson & Peterson 2010, Peterson, Sauerland & Déchaine 2010, Italian (Eckardt & Beltrama  p. 113). The respective evidential markers express uncertain knowledge or inferential evidentiality in declarative sentences. It thus seems attractive to explore the parallels between wohl in German verb-final questions, and evidentials in CQs in general.
The present paper pursues the hypothesis that German wohl verb-final questions are an instance of this general typological pattern. We proceed in three steps. First, I argue that wohl in declaratives is an inferential evidential (Willett 1988). Second, I extend the account to wohl in standard questions and in step three propose how wohl contributes to derive the conjectural question reading for questions like (2).
The paper is structured as follows: Section 2 argues that wohl in declarative sentences like (4) is an inferential evidential.
(4) Der The Schlüssel key ist is wohl wohl im in.the Auto. car 'The key is in the car, I assume' While the translation in (4) follows M. Zimmermann 2004Zimmermann , 2008, I argue that his analysis must be refined. I propose that the declarative sentence wohl p conveys that the prejacent p is defeasibly entailed by the speaker's knowledge. The proposition p is presented not as secure knowledge but as a reasonable assumption by the speaker. Defeasible entailment is captured in a Lewis-Kratzer analysis in terms of possible worlds. Section 3 discusses the particle wohl in standard questions like (5).
(5) Wo where ist is wohl wohl der the Schlüssel? key 'Where, do you assume, is the key?' In (5) wohl is reoriented to the addressee and asks about her assumptions and inferences (M. Zimmermann 2004). This reorientation has been called the 'interrogative flip' and occurs frequently though not universally. 1 While Korean questions with evidentials show the flip reading , Samoyedic languages do not allow evidentials in questions (Künnap 2002: p. 149). A comprehensive survey suggests that the interrogative flip follows from specific properties of individual evidentials rather than universal pragmatic reasoning.
Section 4 starts out by demarcating the meaning of standard questions, standard wohl questions and verb-final wohl questions. The latter express CQs, and I detail their pragmatic profile in 4.1. The analysis in 4.2 proposes that CQs like (2) are conventionalized from a generalized use of the inferential evidential wohl: • In declaratives, wohl is oriented to the speaker and reports the speaker's inferred beliefs.
• In standard questions, wohl is oriented to the addressee and asks for the addressee's inferred beliefs.
• In CQs, wohl is oriented to speaker⊕addressee. The meaning of wohl entails that the addressee cannot answer the CQ unless both interlocutors have pooled their knowledge on question Q. We find two conventionalized possible reactions: the addressee can remain silent or engage in speculative discourse.
The envisaged analysis aims to treat a specific case -German verb-final wohl questions -in a way that aligns with typological trends at large. Section 5 sketches how the proposed analysis can be applied to other languages.

Evidential wohl in declarative sentences
The present section investigates wohl in declarative sentences. I abbreviate these as wohl p and refer to p as the prejacent. The discussion of data in Section 2.1 is divided in two parts. 2.1.1 submits wohl p to the series of tests by Faller (2002) that separate evidentials from other sentential modifiers. The data confirm that wohl patterns with evidentials and differs from modals. Section 2.1.2 investigates the semantic content of wohl, offering more evidence in favour of a treatment as an inferential evidential. I argue that wohl expresses defeasible inference and inference based on subjective experience. Section 2.2 offers a formal analysis. The main novel element is an implementation of subjective defeasible inference in terms of possible world semantics. 2 We also address the scope taking behaviour of wohl and the divi-

Tests for evidentiality
This subsection discusses the properties of wohl with respect to Faller's (2002) tests for evidentials, in their adaption by Matthewson, Davis & Rullmann 2007 in (6 The tests assess basic scope taking, consistency and projection properties of an item and allocate data points that help to distinguish between different analyses. In particular, potential evidential markers are compared to modals and presupposition triggers by their scope taking behaviour and projection properties.

i. (In)felicity if prejacent is known to be true
M. Zimmermann (2004Zimmermann ( , 2008 observes that declarative wohl p is infelicitous if the speaker knows for certain that p, as shown in (7) and (8). 3 The test for (in)ability to raise assertive strength does not apply here.  (7) is a perfectly natural utterance, (8) is incoherent because, as Zimmermann argues, the embedding predicate know is incompatible with uncertainty conveyed by wohl. According to Zimmermann, wohl p conveys that speaker x assumes that p and that ASSUME(x,p) is a weaker commitment than KNOW(x,p). By and large, wohl p is infelicitous if the speaker knows for certain that the prejacent is true. However, Göbel's paradox challenges this generalization (Göbel 2017(Göbel , 2018. He points out that the speaker in (9) can use wohl p although he knows p for certain (example inspired by Göbel 2017: (8), Göbel 2018: (5), (6)).

(9)
A: Athens is in Turkey, as we all know. In the given situation, the speaker knows perfectly well that he has been wrong. We'd hence expect that wohl p is inadequate. In fact it is not. According to Göbel's intuition -with which I agree -A presents p 'Obviously I've been wrong' as an inference that rests on (a) A's earlier claim and (b) the evidence supplied by B. 4 In summary, wohl p is infelicitous when the prejacent p is known to be true and thus patterns with inferential evidentials. Exceptions are possible when the speaker intends to highlight that p is inferred knowledge. The analysis of wohl has to reconcile the general pattern illustrated in (7) and (8) with Göbel's paradox in (9).

ii. (In)felicity if prejacent is known to be false
If a declarative with wohl is conjoined with the negated prejacent, the result is incoherent. Exchanging the coordination und 'and' by contrastive aber 'but' doesn't improve the example. There is no conceivable context that would render (10) acceptable. This shows that the speaker who utters wohl p is committed to p. The particle wohl thus differs from existential modals like could as well as certain hearsay evidentials (e.g., Cheyenne sėste, Murray 2009Murray , 2010a. It patterns with inferential evidentials and eye-witness evidentials which express that the speaker is committed to the truth of the prejacent.

iii. Scope-taking under negation and in questions
M. Zimmermann (2004Zimmermann ( , 2008 demonstrates that wohl always takes highest scope over negation and question formation. (11) illustrates the case of negation. In summary, wohl takes high scope over negation and question formation.

iv. Assent/dissent
Faller's tests for assent and dissent are designed to reveal which parts of an utterance are explicit proposals for a common ground update. The data show that assent and dissent target the prejacent of wohl. The content of wohl, 'the speaker assumes p', can not be targeted by assent/dissent.  (17). 5 The assent/dissent test allows us to conclude that "the speaker supposes or infers p" is non-at-issue content and not accessible as target of replies (Murray 2014). Wohl patterns with inferential evidentials in other languages and differs from modal might and must.

v. Embedding under conditionals
Various authors observe that the use of wohl in the antecedent of a conditional is unacceptable (Krifka 2004, reported in Faller 2006, M. Zimmermann 2008. This is illustrated in (18). The speaker in (19) presupposes that the antecedent is true, which leads to a factual conditional reading (Iatridou 1991). We will return to this effect later.

vi. Readings in standard interrogatives
M. Zimmermann (2004Zimmermann ( , 2008  This confirms the interrogative flip for wohl in questions. Evidential markers don't pattern uniformly in questions. San Roque, Floyd & Norcliffe (2017) report on languages that prohibit the use of evidentials in questions, and questions with evidentials that have only a CQ reading. German wohl is special in that it exhibits the flip reading in standard questions and the conjectural reading in verb-final wohl questions.

vii. Indirect evidence not cancellable
A final test concerns the question whether the content of wohl can be retracted. If this were the case, an analysis as pragmatic implicature would be 9:10 Conjectural questions warranted. However, the data confirm that, unlike implicatures, the content of wohl can not be cancelled.
Unavailable: 'I can see Hein right there sailing on the Cutty Sark: Hein is at sea.' The first sentence presents p 'Hein is at sea' as directly witnessed. Direct perception counts as stronger evidence for p than assuming or inference. The second sentence conveys that the speaker infers or supposes 'Hein is at sea'. If this came about by scalar implicature, we would expect that the implicature can be cancelled and the discourse is coherent. In fact, it is marked.
Example (22) thus shows that the content of wohl p does not come about by conversational implicature (pace Hara's (2018) account of Japanese daroo in assertions and questions in terms of implicature).
In summary, the tests show that wohl patterns with evidentials in other languages and differs from modals. However, its scope taking and projection behaviour is not sufficient to unveil wohl as inferential evidential, as wohl shares scopal properties with German particles in general (M. Zimmermann 2011). The hypothesis that wohl is an inferential evidential must thus build on more specific data. These are reviewed in the next subsection.

Specific observations about wohl p declaratives
We start from M. Zimmermann (2004Zimmermann ( , 2008 who posits that wohl p is analyzed as "the speaker x assumes p": ASSUME(x,p). The lexical content of ASSUME is left vague and could subsume belief with a high probability, belief without verification, belief by faith or other epistemic relations. Once we review possible and impossible uses of wohl, it becomes clear that the lexical content of wohl p is more specific. Göbel's paradox in 2.1.1 is a first challenge but not the only one.

Wohl does not express high likelihood
Zimmermann potentially includes cases where x assumes p because x knows that p is highly likely. His analysis predicts that wohl p is acceptable in such situations. In actual fact, however, it is not. Consider the following scenario: A is requested to draw a marble from a box that contains one black and 9:11 Regine Eckardt nine white marbles. A knows this and has now drawn a marble but can not see its colour yet. In this situation (23a) is inappropriate whereas (23b) is an appropriate utterance. Native speakers share the intuition that wohl p is inappropriate to express that the speaker holds p as statistically likely. The situation in (23) lacks witnessed facts that allow the speaker to infer p. In order to explain why (23a) is inappropriate we must get a better understanding what counts as witnessed facts and how these license inferences.
The notion witnessed fact is easy to illustrate but difficult to define. In example (17), the witnessed facts in play are q 1 = 'Hein's house is locked' and q 2 = 'the shutters are closed'. Witnessed facts often coincide with what counts as "direct evidence" in languages that lexify this category. Suitable evidence improves example (23a): Assume that a bystander C observes A's drawing and can see the result. If A sees C's unsurprised face he can infer that the result of the drawing was unsurprising, i.e. as likelihood suggested. In this alternative scenario A has witnessed facts in favour of p and (23a) is acceptable. 6 The nature of inferencing is the second factor in play. The next sections argue in favour of defeasible inference. (23a) shows that defeasible inferences are not the same as likelihoods. The particle wohl is not synonymous to likely, highly likely or almost certainly and the relation ASSUME is too unspecific to account for this observation.

Defeasible inference from speaker's knowledge
This section discusses an example where all factors behind the wohl p inference are explicit. Consider a situation where A and B wonder where Granny might be. A knows the following.
q 1 : Granny often goes shopping on Friday afternoon.
6 Thanks to Sven Lauer (p.c.) who brought up this example.

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Conjectural questions q 2 : Her shopping bag and purse are missing.
q 3 : Her slippers are in the hall.
While q 0 and q 1 are general world knowledge, q 2 and q 3 are witnessed facts. In view of her knowledge, A utters (25). By using wohl, A conveys the following complex message: (26) The issue at hand is "Where is Granny?". The relevant facts I know (q 0 -q 3 ) lead me to infer p = 'Granny went shopping'. Further facts may force me to withdraw my conclusion.
A's claim rests on A's body of relevant knowledge q 0 -q 3 about Granny's whereabouts. Yet q 0 -q 3 are just indications, not a logical proof for p. If A finds out later that q 4 = 'Granny's Wellingtons are missing' (which she never wears downtown) she will withdraw the inference and conjecture that Granny went searching for mushrooms. Inferences of this kind were studied as defeasible inferences in AI (Gabbay, Hogger & Robinson 1994, Strasser & Antonelli 2016), and are illustrated by the Tweety example. When I know that 'Tweety is a bird', I am likely to infer 'Tweety can fly'. If I learn 'Tweety is a penguin' in addition, I no longer infer 'Tweety can fly'. More knowledge can defeat earlier inferences.
Let us take a closer look at the knowledge behind wohl-inferences. For one, it is a limited body of knowledge. Speaker A may be an expert in nuclear physics but her knowledge about nuclear physics is irrelevant for (25). Moreover, it includes witnessed facts (like Granny's missing bag). Sensory evidence also counts as witnessed fact. An experienced cook could take a look at cookies in the oven and state Sie sind wohl fertig ('they are wohl finished') based on the witnessed fact q = their smell and colour.
Another kind of witnessed fact brings wohl p close to hearsay evidentials. This is illustrated in ( 'Hein is at sea, I hear.' At first glance (27) looks like a hearsay evidential (A has heard that p) but this is not what is conveyed. At the back of A's mind is knowledge as q 1 = Hein's wife said that he's at sea, q 2 = she is usually trustworthy and q 3 = she should know where Hein is. A defeasibly infers from q 1 , q 2 and q 3 that Hein is at sea. The same overlap between reportative and inferential evidentials was pointed out for Cheyenne (Murray 2010b).
The common pattern behind all examples is this: The speaker knows witnessed facts q. These do not offer conclusive evidence for prejacent p but regarding the issue Q at hand ("where is Hein?", "What is Granny doing?"), q is sufficient for the speaker to tentatively infer p. Lastly, the inference rests on the maximal set of relevant facts known to the speaker. For instance, if speaker A in (26) knew in addition that q 4 = 'Granny's wellingtons are missing' she would no longer infer 'Granny went shopping' even though she still knows q 0 -q 3 .
Inference from witnessed facts resembles what von Fintel & Gillies (2010) call inferences from privileged knowledge in their analysis of epistemic must in English. They analyse epistemic must p as inference from kernel K , the set of privileged knowledge of agent a. Likewise, Murray (2010b) assumes that the "kernel of information, evidence" is the source of information for inferential evidentials in Cheyenne. I leave the exact alignment of these terms for another occasion and conclude with the following diagnosis: Wohl p expresses that p is an uncertain inference that rests on secure knowledge q.

Requests to explicate evidence
Declaratives wohl p permit the interlocutor to ask for evidence more naturally than plain assertions p. A plain declarative sentence conveys that the speaker has sufficient evidence to make an assertion. Declaratives with wohl not only convey uncertainty but invite 'Why do you think so?' as a natural reaction. 7 Imagine that colleague A opens conversation with B on Monday morning by either (28)  In the dialogue in (28), B can take up A's cue wohl and ask for A's evidence. In (29), B's reaction suggests that she doesn't consider A as trustworthy. Given that A offered no reason for doubt, B's reaction is slightly offensive. 8 In (28), B's asking back seems invited by A's using wohl. It is not offensive to refer to p as a belief rather than certain knowledge.

Subjective inference
A final contrast shows that wohl p indicates subjective inference. This becomes clear when we consider defeasible inferences that are part of an objective scientific theory. Medical diagnoses are defeasible inferences from a set of symptoms. Given that wohl signals defeasible inference, we would expect that the use of wohl is appropriate in medical diagnoses. In actual fact, it is not, as the measles example (32) shows: Assume that the symptoms patient has red spots, fever and sore throat justify the medical diagnosis patient has the measles. Nevertheless, the doctor in (32a) expresses a personal estimate ("according to my experience" The speaker in (32a) suggests that other persons, faced with the same facts, might draw different conclusions. The speaker in (32b) conveys that the assertion is supported by medical science. The contrast between diagnosis and personal estimate shows that wohl p indicates inferences p that rest on the speaker's personal experience. The contrast systematically arises in situations where experts assert defeasible inferences in a scientific framework, as in weather forecasting or when identifying a specimen. Wohl p inferences are hence subjective in several respects: • p follows defeasibly from the speaker's privileged knowledge q.
• If the speaker learns more, he may be justified to utter wohl p at time t 1 but no longer at a later time t 2 (modified ex. (25) wellingtons).
• The same witnessed fact can entail p for one speaker but not for others (see (32)).
9 While several speakers agreed, one reviewer doesn't share the judgement.

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Conjectural questions The analysis of wohl, to which we now turn, should account for these subjective aspects.

Earlier accounts
There are to date two formal treatments of wohl in declaratives. M. Zimmermann (2008) proposes that wohl denotes .ASSUME( , ) where the predicate ASSUME(x,p) is true iff x assumes that p is true. 10 ASSUME contrasts with KNOW and indicates belief with less confidence than KNOW. The scope-taking properties of wohl are predicted by assuming that wohl is situated in Spec-ForceP at LF, thus taking high scope over negation, question and focus operators. Syntactic heads decl and int in ForceP serve to anchor x to speaker or addressee in declaratives and questions by spec-head agreement. Wohl composes with the sentence denotation late, which predicts its taking high scope. M. Zimmermann (2004Zimmermann ( , 2008Zimmermann ( , 2011 argues against an analysis in terms of conventional implicatures (Potts 2005) or a separation in terms of assertion versus presuppositions. He considers wohl to be a speech act operator that updates the common ground CG by ASSUME(speaker, p) (M. Zimmermann 2008: p. 216). The addressee is invited to believe p if he shares the speaker's assumption. If the addressee expresses doubt the CG maintains the information that sp assumes that p. Alternative analyses in terms of a lowered threshold of reliability (Davis, Potts & Speas 2007, McCready & Ogata 2007 are mentioned but not further pursued (M. Zimmermann 2011).
While Zimmermann successfully predicts scope-taking and the interrogative flip in standard questions, his relation ASSUME is too unspecific to account for the inferential content of wohl. The properties of wohl p in the assent/dissent test remain unaccounted for; specifically it is open why reactions can target the prejacent p. Finally, the account in its present form does not extend to conjectural questions with wohl. Göbel (2017Göbel ( , 2018) challenges Zimmermann's analysis on basis of Göbel's paradox in (9), from which he concludes that wohl p presents p as an inference. He analyses the content of wohl in terms of a predicate INF(v 0 , i, p), which he paraphrases as 'the individual i infers p at index v 0 '. While this resonates with the present analysis, Göbel fails to spell out the logical content of INF. According to his paraphrase, German wohl could be synonymous to 10 Notation slightly adapted.

Regine Eckardt
English epistemic must, which fails to acknowledge the defeasible and subjective nature of wohl inferencing. 11 A final precursor of the present paper is Kratzer 1991 where must p is analysed as asserting p with a lower level of certainty than plain assertion (pace von Fintel & Gillies 2010). While her analysis resembles the present proposal, the division of labour differs in detail. Kratzer assumes that must p presents p as uncertain because p follows by logical (i.e. reliable) inference from unreliable belief. The utterance wohl p, in contrast, presents p as uncertain because it follows from reliable knowledge by defeasible (i.e., unreliable) inference. Due to this fundamental difference, our implementation deviates from Kratzer's classical anaysis of must in detail.

Defeasible inference
I propose that wohl is an inferential evidential that expresses defeasible inference. The present section develops an analysis in terms of possible worlds, in the tradition of Lewis 1973, Kratzer 1991.
The underlying idea is the following. Assume that agent A knows in w 0 that proposition q holds true. Hence A knows that she is in one of the qworlds. In some of these, q is true under circumstances that match A's expectations about q-worlds -these I call stereotypical q-worlds (as to A's experience in w 0 ) -but in others, q is true under circumstances that A considers as non-normal. For instance, assume that A knows q = 'Tweety is a bird'. A knows that birds include flying birds and non-flying birds like penguins. But if pressed, A will tentatively assume that Tweety is a flying bird. In other words, worlds where Tweety is a flying bird are stereotypical 'Tweety is a bird'-worlds for A whereas worlds where Tweety is a penguin or an ostrich are not. 12 I propose to capture this idea by the relation STEREO.
(33) Let STEREO be a relation on × × ⟨ , ⟩ × with the following truth conditions: For any individual A, world w 0 and proposition q, STEREO(A,w 0 ,q,w) holds true iff w is an epistemic alternative for A in w 0 and w is a world where q holds true under circumstances that A considers stereotypical.
The STEREO relation also contains parameter q, the relevant knowledge of agent A. When A in (17) asserts that Hein is at sea then A does not mean to say ''in stereotypical worlds per se, Hein is at sea" but ''in stereotypical worlds where Hein's house is locked and shutters closed, Hein is at sea". I leave it open whether stereotypical q-worlds are ordered, as such an ordering does not matter for the present analysis. Let me review more facts about STEREO. According to the definition, stereotypical q-worlds are worlds where q is true. Yet, the actual world need not be stereotypical for q.
Finally, different propositions q, q' can lead to different sets of stereotypical worlds w.STEREO(A,w 0 ,q,w), w.STEREO(A,w 0 ,q ′ ,w). This holds in particular for propositions q and q ∧ r, laying the basis for defeasible inference. We now turn to the definition of defeasible inference.
(36) Let q, p be propositions. Assume that agent A in w 0 knows q. A can defeasibly infer p from q iff ∀w(STEREO(A,w 0 ,q,w) → p(w)). ''All epistemic alternatives of A where q is true under circumstances that A considers stereotypical are also worlds where p is true." 9:19

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Let us apply (36) to the Tweety example. Let q 1 = 'Tweety is a bird' and p = 'Tweety can fly'. Assume that agent A knows that q 1 is true. According to (33), w.STEREO(A,w 0 ,q 1 ,w) contains only worlds where Tweety is a bird under circumstances that A considers stereotypical. Assume that, among other things, A expects that Tweety can fly. Thus w.STEREO(A,w 0 ,q 1 ,w) ⊂ p and A can hence defeasibly infer from q 1 that p = 'Tweety can fly'.
Assume that A gathers new information q 2 = 'Tweety is a penguin' and now knows q 1 ∧ q 2 . The stereotypical worlds w.STEREO(A,w 0 ,q 1 ∧ q 2 ,w) are different from those for q 1 . Among other things, p = 'Tweety can fly' is false in these worlds. Based on new knowledge, A draws new inferences and discards former beliefs.
As a consequence of definition (36), classical inference is a limit case of defeasible inference. If q → p in terms of classical logic, then q also defeasibly entails p. Likewise if A knows p, and p is thus true in all epistemic alternatives of A, then A can defeasibly infer p from any premiss. This will be relevant when we consider the pragmatics of conjectural questions in Section 4.

Analysing wohl
We can now define the lexical entry for wohl. Following M. Zimmermann (2008), I assume that wohl takes scope in the ForceP at LF; specifically above negation, conditionals and question formation. 13 The utterance context c supplies several parameters. First, wohl refers to the speaker sp(c). Second, it provides a current issue Q that the speaker has to settle, minimally whether p. 14 Third, there is a maximal body of relevant knowledge of sp(c) that pertains to the issue. This lays the ground for the (pre-final) lexical entry for wohl in (37).
13 Like earlier authors, I refrain from extending the data to clauses embedded under verba dicendi. 14 I refrain from using the term "question under discussion" QUD to stay away from phenomena that are orthogonal to the present case.

Updates:
The utterance wohl p asserts the at-issue content p. The CG is updated by wohl (p) as non-at-issue content in the sense of Murray 2014.
The presupposition provides the issue Q. In the absence of other issues I assume that Q = whether p? by default. The relevant knowledge q(c) comprises knowledge that could be useful to Q ; it must include witnessed facts. The maximality clause (37ai) ensures that A isn't licensed to utter wohl p and wohl not-p at the same time. 15 It states that when uttering wohl p, A does not currently know facts that defeat p. Let me illustrate (37) for example (7), uttered in a context c and world w 0 .
Assume a context c* where Maria utters (38) with issue Q = Where is Hein? She knows q = 'Hein's house is locked and shutters are closed'. Her utterance rests on q. (38) can thus be paraphrased as "given what I know (about issue Q ), I infer that Hein is at sea". Maria's utterance contributes the claim p = 'Hein is at sea'. At the same time she adds at the non-at-issue level: "I have evidence q that defeasibly entails p".

Predictions
The present section evaluates the predictions of the proposed analysis, starting with Faller's tests for wohl.
Declarative wohl p competes with the plain assertion p. The plain assertion lacks the hedge that p is defeasibly inferred. The use of wohl p thus gives rise to the scalar implicature that the speaker does not know p for certain. This predicts the contrast in examples (7) and (8).
The implicature does not arise when the non-at-issue content is justified for other reasons. This offers an explanation for Göbel's paradox (9). In the given situation, the sentence da hab ich mich wohl geirrt ('I have been wrong I suppose') is uttered in a context where the addressee has just pointed out A's error. Speaker A conveys that he has (defeasibly) inferred p. This is relevant as A presents herself as capable of learning. Therefore the complex utterance wohl p is justified and does not give rise to further scalar implicatures. 16 Whenever the non-at-issue content of wohl p is not justified as a relevant information about A's drawing inferences, the scalar implicature remains, as (22) confirmed for test (vii).
The present analysis predicts that declarative wohl p is infelicitous if the speaker believes p to be false. We predict that the speaker proposes a CG update by p, which is tantamount to asserting p. The speaker is committed to p by the maxim of quality. Note that the maximality clause also ensures that A cannot propose contradicting prejacents for CG update. This is again in line with the data.
The observation that wohl scopes over negation and question formation is predicted in the same manner as in M. Zimmermann 2004Zimmermann , 2008. We adopt Zimmermann's assumption that wohl takes scope at the highest CP level at LF. It follows that the semantic contribution of wohl outscopes negation as well as question formation.
The assent/dissent tests showed that the prejacent p is at-issue content, whereas the information that the speaker infers p is not. We predict this by assuming that the speaker proposes a CG update with p and at the same time, the proposition 'given what I know, I defeasibly infer that p' enters the CG by non-at-issue update (Murray 2014). The latter content can therefore not be targeted by expressions of assent or dissent. In this, wohl p differs from probability or possibility statements about p.
We could capture the observation that wohl doesn't scope below conditionals as an island violation, following M. Zimmermann 2008. However, the division into at-issue and non-at-issue content allows for an interesting alternative explanation. Consider (19), repeated below. 16 For further examples see Göbel 2018, who assumes an explanation along the same lines. Allowing for wohl to take scope at the CP-level of the conditional clause, we predict a non-at-issue update of the CG by wohl('Hein is at sea'). We thus correctly predict that the speaker of (39) believes that Hein is at sea, i.e., utters a factual conditional. The analysis so far does not account for the interrogative flip, to which we turn in Section 3. With a slight generalization of (37) we can account for standard wohl questions (Section 3) as well as verb-final wohl questions (Section 4).
We now turn to the specific differences between the ASSUME-based analysis and the one proposed here. The present account rests on the intuition that wohl p presents the prejacent as a defeasible inference. Example (25) is analysed as follows (where I focus on the non-at-issue content added by wohl). The non-at-issue content is true in w 0 iff all worlds that A considers stereotypical for q 0 -q 3 are worlds where Granny went shopping. Hence if the world is stereotypical for q, Granny went shopping. 9:23

Regine Eckardt
The addressee can ask for A's evidence, why do you think so?. A indicates that p is defeasibly inferred from q. B inquires into the tacit premise q of the inference. We can also explain how short questions why? can ask for two levels of reasons. In (40), B could ask about the reasons for Granny to go shopping, or else for the reasons q to infer that Granny went shopping. A detailed analysis is left for the future.
Finally, the analysis captures the subjective nature of wohl inferences. Whether or not speaker A is inclined to utter wohl p depends on two factors. First, the content of wohl p depends on A's body of relevant knowledge q pertaining to the issue whether p. What A knows can differ from what B knows and therefore A can be in a position to utter wohl p when B is not. Second, the set w.STEREO(A,w 0 ,p,w) reflects A's personal experience with q-worlds. It can differ from B's stereotypical q-worlds w.STEREO(B,w 0 ,p,w). This accounts for the difference between defeasible inference from scientific theory and subjective opinion that we saw in (32) measles.
Let me lastly turn to the observation that wohl p cannot express that p is statistically likely, as shown in example (23). So far, this doesn't strictly follow from the analysis but offers further insights into what speakers of German consider stereotypical courses of events. In the example, the speaker saw a container with one black and nine white marbles. This is a witnessed fact as other witnessed facts ('Granny's slippers in the hall', 'Hein's house locked'), and translates into a 90% chance to draw a white marble. But is being likely the same as being a stereotypical outcome?
The data suggest that this is not the case. Speakers seem to reason as follows: Thinking about worlds where A draws a marble, stereotypical worlds for 'A drew a marble' include worlds where the marble is white (the majority outcome) as well as worlds where the marble is black (the minority outcome). One type of outcome may be statistically less likely than the other, but nothing in the unlikely outcome violates our normal manipulation of marbles or the normal physical movement of objects in containers. 17 Therefore the stereotypical 'A draws a marble' worlds include both types of outcomewhence A is not justified to utter Ich habe wohl eine weiße Murmel gezogen.
17 German informants generally agree with surprising consistency that wohl is not licensed in the marble scenario. It may be worth pointing out, however, that individual speakers and in particular expert statisticians are able to take probably p as weak evidence in favour of p and thus accept wohl p in this case.

Evidential wohl in standard questions
This section extends the analysis of wohl to standard questions with the interrogative flip, as in example (2)  While evidential markers in many languages show the flip reading in questions, counterexamples have been reported and it would therefore be mistaken to derive the flip reading on basis of general pragmatic principles. M. Zimmermann's (2008) feature-based analysis successfully captures the binary distinction by features decl and int. Yet, an extension to CQs would require additional features and thus conflict with the aim to integrate German in the typological landscape of conjectural questions. I propose Lim's analysis of Korean evidential -te , Lim & Lee 2012) which rests on a elegantly simple idea: Evidentials are context dependent, as they refer to the epistemic background of the speaker sp(c) in c. This context dependence is captured in terms of Kaplan's (1989) character theory. According to Kaplan, sentences denote characters, functions from contexts to propositions, which capture the meaning of indexical expressions (T. E. Zimmermann 2012, Schlenker 2018). While questions normally denote sets of propositions, questions with evidentials instead denote sets of characters. Each answer contains the evidential, which is taken into account in future answering contexts. As the addressee of the question will be the speaker of the answer, this models the evidential flip.
In order to apply Lim's idea, we have to adjust the lexical entry of wohl as in (41). Wohl takes scope over the remaining clause S and combines with the denotation * in utterance context c * . c.

Updates:
The utterance wohl p asserts the at-issue content p. The CG is updated by wohl (p) as non-at-issue content in the sense of Murray 2014.
The contribution of wohl in assertions is the same as in the earlier version (37), as the derivation in (42) The sentence denotes a character that can be paraphrased as "Given context c, the stereotypical worlds of sp(c) plus the speaker's knowledge p(c) about the given issue entail that Hein is at sea". Following Lim, the c argument in assertions is instantiated by the utterance context. Let us assume that Maria utters (42) in context c * , relying on knowledge q(c * ) = 'Hein's duffel bag is missing'. (42) in c * thus conveys the following.
(43) w 0 . ∀w(STEREO(Maria,w 0 ,'duffel bag missing',w) → HEIN-AT-SEA(w)) 'All stereotypical worlds where Maria's relevant knowledge is true (namely, Hein's duffel bag is missing) are worlds where Hein is at Sea.' Maria proposes a CG update by Hein is at sea and conveys non-at-issue that she knows something that allows her to infer Hein is at sea.
While the two semantic entries for wohl make identical predictions for assertions, only (41) can account for the interrogative flip. We adopt a Hamblin semantics for questions, where Q denotes the set of propositions that 9:26 Conjectural questions are answers of Q. 18 Wohl scopes over question operators and thus combines with the denotation of Q. 19 Following Lim, I assume pointwise semantic composition, indicated by +. We thus derive a set of characters for the question wohl Q, which is illustrated in (44) for the question 'where is Hein?'. I assume the possible answers 'Hein is at Sea', 'Hein is on Hawaii' and 'Hein is at home'. The account leaves open the possibility that speakers answer the questions without using wohl, in particular if they know the answer for certain. I assume that this is licensed by general cooperativity principles that always allow the speaker to offer more information than requested. The principle also underlies indirect questioning acts, as well as answers to self-addressed questions. Given the variety of patterns, it is appropriate that our analysis correctly links the flip reading to specific lexical properties of individual evidentials. 21 German wohl is special in that it contributes both to the flip reading and to conjectural questions. These show nonstandard verb-final syntax as a further cue. We now turn to the core part of the paper, verb-final wohl questions in German and their interpretation as conjectural questions.

Verb-final wohl questions in German
Verb-final wohl questions in German like (45) differ from standard questions in that they share the syntax of subordinate clauses with the verb in sentencefinal position. These questions have been studied as self-addressed questions (Altmann 1987, Truckenbrodt 2006, Lohnstein 2007 (45) can however be uttered in the presence of an interlocutor and even with a clear communicative intention (Plunze & Zimmermann 2006). This is problematic for definitions of CQs that are based on the absence of an interlocutor (Jang 1999, Jang & Kim 1998, Miyagawa 2012. 22 We must hence find further criteria to characterize CQs. c. the addressee can remain silent without violating the rules of discourse.
d. the speaker invites the addressee to speculative discourse about the topic.
Standard questions and standard wohl questions show a different profile, as will be detailed in 4.1. While standard questions can also used in CQ contexts, specifically in situations where the speaker is alone, such uses are atypical, whereas they are the only possible ones for verb-final wohl-questions. The pragmatic profile extends to CQs in other languages (see Section 5). Section 4.2 details an analysis for verb-final wohl-questions. Section 4.3 compares the present proposal to earlier analyses of verb-final questions in German and CQs in other languages.

Data
The present section delineates the pragmatic differences between standard questions (46), standard wohl questions (47)  In uttering questions like (46), the speaker requests the addressee to provide an answer (Searle 1969). The speaker wants to gain information and believes that the addressee can provide it. Posing a standard question only makes sense if the speaker expects that the addressee knows the answer. 23 Standard wohl questions like (47) request the addressee to conjecture an answer that is true in their relevant stereotypical worlds. They are typically posed if the speaker wants to gain information and believes that the addressee does not know but may be able to guess an answer. Allowing for answers that rest on defeasible inference instead of knowledge, the speaker makes it easier for the addressee to fulfill the request.
The utterance of a verb-final wohl questions (48) doesn't constitute a request. These are typically posed if the speaker wants to know the answer but believes that the addressee doesn't know more about the issue than herself. Getting an answer is not of importance for the speaker's immediate tasks. The addressee is invited to react in some way (Plunze & Zimmermann 2006), for instance by engaging in joint speculations about the topic.
The following scenarios offer contexts of use for the standard question (46), the standard wohl question (47) and the verb-final wohl question (48).

(I) Standard question: A will empty B's mailbox while B is on holiday. Receiving instructions, A realizes that the mailbox has a lock. A asks B: (46)
A's question is a request for an answer. A expects that B knows the answer, and knowing the answer is necessary for A's job of taking care of B's mail.
(II) Standard wohl: A and B are Airbnb guests. They decide to take care of their absent host's mail. A realizes that the mailbox is locked. A asks B: (47) A requests B to guess an answer to (47). A knows that B doesn't know more about the key than herself, but hopes for smart conjectures. Getting an answer is necessary for A's task, taking care of the mail.

(III) Verb-final wohl: Walking on the beach, A and B find a wooden box sealed with a huge lock. Taking interest in the object, A asks B: (48)
A knows that B doesn't know the answer. A does not request B to provide an answer. Knowing the answer is not of immediate importance for A's aims. It would be natural for B to start speculating with A about the question.
The difference between Scenarios II and III is subtle. In either situation, B cannot be expected to know the answer. In scenario II the speaker is pursuing a task that requires an answer to where is the key?. In scenario III the speaker is interested in the question just for curiosity's sake. The following minimal pair highlights a further difference between wohl questions in standard and verb-final syntax. The standard question in (51) is appropriate as A wants to see whether B can name characters and thus answer the question. A conveys that B should be able to answer the question without much thinking. In (52), the standard wohl question is appropriate, as A wants to convey that defeasible inferencing can be part of finding an answer. The verb-final wohl question in (53) can be posed even though there is no "true" answer in this scenario at all. Answering (53) is tantamount to inventing a story about the princess. The question is not a request for information but an invitation to speculate. In the reported situation, A did not assume that B knew or could guess the answer. The utterance was intended as a starter of a conversation on the nature of stranded mattresses in general. Similar discourse aims for CQs were reported for Shipibo-Konibo (Valenzuela 2003), Gitksan (Peterson p.c.) and Italian (Zucchi, p.c.). Finally, if the addressee happens to know the answer s/he can assert it. The particle wohl will not occur in the answer. The scenarios list ideal question-situation pairs. Other pairings may happen, but the speaker's choice of question indicates how she conceives the 25 Gisela Disselkamp, p.c.

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Conjectural questions utterance situation to be. 26 For instance, asking a standard wohl question in (53) would invite the child to guess the answer, suggesting that there is yet a true answer in some sense. A verb-final wohl question in (52) would indicate that A will share conjectures with B in their joint search for the princess. The data corroborate our initial choice of the term conjectural questions for German verb-final wohl questions.
Before turning to the analysis, let me briefly review other possible grammatical cues of CQs in German. Earlier authors on German CQs assume that any question in German can be turned into a CQ by verb-final syntax (Lohnstein 2000, Truckenbrodt 2013, Oppenrieder 1989. This is mistaken, as the use of evidential wohl is mandatory in constituent CQs. (55)  Mandatory wohl in constituent CQs also offers a strong argument against an analysis of CQs in terms of ellipsis. At first sight, it could be tempting to assume a tacit embedding clause like "Ich frage mich, wo …" ('I ask myself where …'). Yet, the particle wohl isn't mandatory in questions embedded under rogatory verbs. If verb-final questions were elliptical, we would expect that every overt embedded question has a CQ counterpart. Given that Ich frage mich, wo der Schlüssel ist ('I ask myself where the key is') is perfectly grammatical, (55) should be an acceptable CQ which in fact it is not. 27 A further way to express CQs are verb-final questions with modal mag. These can lack wohl, as illustrated in (56) German mag is cognate to English may, might but is no longer in use as a possibility modal in contemporary German. While the parallel between mag-26 Additional instructions extend the appropriate uses of standard questions. A could utter the German equivalent to: Give me a guess: where is the princess? thus using a standard question to elicit the kind of answer that is appropriate for standard wohl questions. I will not go into these data. While this could lend support to the claim that verb-final syntax triggers CQ readings, some native speakers find CQs like (57) marked at the beginning of discourse (Gutzmann 2011). 28 Informants however agree that polar verbfinal questions with wohl are acceptable without any contextual restrictions. This suggests that polar verb-final questions with wohl should be viewed as the normal case. In this, I deviate from earlier authors who take (57) to be the standard case of German conjectural questions and posit that verbfinal syntax alone suffices to trigger conjectural readings (Oppenrieder 1989, Lohnstein 2000, 2007, Truckenbrodt 2006, M. Zimmermann 2013. Finally, verb-final CQs can include the particle bloß ('only') which turns them into an extreme ignorance question (Obenauer 2004, den Dikken & Giannakidou 2002, Rawlins 2009, Eckardt & Yu 2020. The contribution of bloß to standard and verb-final questions is worth a study in its own right but I leave it aside here.

Analysis
The analysis of verb-final wohl questions in German should predict the following facts: It must predict that the addressee is not requested to answer and that the question can be an invitation to joint speculation. Moreover, it must explain why evidential wohl is mandatory and should offer a basis to understand why evidential markers serve as cues for conjectural questions in many languages.
28 Acceptance is facilitated in situations where the polar question is interpreted as a guess ('the key is in the car') rather than a question (Oppenrieder 1989). The restrictions on licensing contexts are however unclear and speakers report shifting intuitions. 9:34 I will elaborate the idea that verb-final wohl questions denote answers that are defeasibly inferred from pooled knowledge of speaker and addressee. They are asked in the spirit of "let us jointly conjecture an answer". To achieve this, I propose that wohl is oriented to speaker and addressee A⊕B as a plurality (Link 1983). Verb-final wohl questions can be paraphrased as "which answers do we get if we pool knowledge and draw defeasible inferences?" As defeasible inferences are not conservative, B cannot start inferring from his private knowledge because A might know facts that defeat B's inferences.
The formalization rests on a silent operator SHARE that serves two purposes. In syntax, SHARE blocks movement of the verb to C 0 and thus ensures verb-final syntax. Semantically, the operator instantiates the sentient agent of wohl with sp(c)⊕ad(c), the plurality of speaker and addressee in the utterance context. Section 4.2.1 presents the analysis for constituent verb-final questions and 4.2.2 extends the account to polar verb-final questions. The analysis is tailored for German where CQs are marked by two cues: wohl and verb-final syntax. Section 5 discusses how the pragmatic ingredients of the present account can be recombined to account for evidentials as CQ markers in other languages.

Constituent verb-final wohl questions
I follow Bayer & Obenauer's (2011) analysis for German root clauses where CP and ForceP are identified. In standard main clauses, the verb is fronted to C 0 , yielding V2 syntax (in declaratives) or V1 syntax (in questions and imperatives). Open or silent elements in C 0 block verb-movement and thus force the verb to stay in clause-final position.
I propose that the syntax and pragmatics of verb-final constituent questions is determined by a silent operator SHAREwhich is situated in C 0 of questions and must be licensed by the presence of a wh-feature. The whconstituent is fronted to SpecC like in standard questions, but SHARE in C 0 prevents the verb from moving to second position and thus forces verb-final syntax. At LF, SHARE takes highest scope over the remaining clause, including wohl. SHARE is restricted to questions with wohl for reasons of logical type, as will become clear when we turn to the meaning of SHARE. 29 In pragmatics, SHARE effects a context shift, defined in (59). The function ** maps context c 29 SHARE is restricted to questions by stipulation as I see no convincing evidence in German or other languages I know of that would justify its application in declaratives. I thank reviewers The context c** is thus like c with speaker and addressee as joint speakers. 30 (59) extends our earlier notion of context in that it includes the maximal relevant knowledge of the addressee about Q. We can now define the denotation of SHARE .
(60) SHARE = * * SHARE makes context c * * available for its sister constituent. The operator is syntactically restricted to questions, and only shows pragmatic effect if the question denotes a set of characters (rather than a set of propositions). Section 3 argued that German questions with evidential wohl denote sets of characters. The context c * * combines pointwise with the set of characters. As before, I use + to indicate this in the derivation. 31 We predict that SHARE is only felicitous if wohl is part of the sister clause and the sister clause is a question. The operator is predicted to be restricted to questions with wohl. Let us apply the analysis to (61).  In the last step, the set of characters combines with context c * * . As a result, we derive answers to Q that are supported by joint defeasible inference by A⊕B together.  When A⊕B together draw defeasible inferences on issue Q they must adhere to the maximality condition together. Before A proposes an inference p, she must ensure that B doesn't know something that defeats p. Similarly if B proposes an inference. A and B must base their inference on the maximal body of knowledge available to them as a group. They have to pool their relevant knowledge or else they run the risk of drawing conflicting inferences. 33 What is, then, a rational reaction to question (61)? In normal situations, neither A nor B alone knows q ( ) ∧ q ( ) and hence, neither A nor B is authorized to assert a proposition in (61d). Joint speculation is in fact one rational reaction to verb-final wohl questions. Ideally when A raises question (61), B should contribute her relevant knowledge, wait for A to contribute and before jointly making conjectures. In actual practice, however, speculations take a more open course where B immediately makes a conjecture, the interlocutors exchange relevant premises, A conjectures etc. until the issue is settled or dropped.
A second type of reaction is motivated by Searle's felicity conditions of questions and requests (Searle 1969: p. 66), which include the felicity condition that A must believe that B can give the answer to Q. In uttering a verbfinal wohl question, the speaker A implicates that she believes that B neither knows nor can conjecture the answer. (Otherwise, A would have uttered a standard question or a standard wohl question). Given this, B is justified to infer that A does not request her do to anything -and will remain silent (but see special scenarios below). 34 The case is comparable to conventionalized indirect speech acts like can you pass the salt? Under normal circumstances, this question violates the Maxim of Relevance. To make sense of it, we infer that the speaker requests the salt. The conventional character of the request is evidenced by the fact that very similar questions (Are you able to pass me the salt? can not be used felicitously as requests for salt. In a similar vein, verb-final wohl questions are interpreted as expressions of interest to which silence is a conventional reaction. 35 33 This is not the same as inferences based on CG knowledge. While CG comes about by intersection, pooled knowledge means forming the union of (limited parts of) A's and B's knowledge. 34 This should not be mistaken to predict that unanswerable questions never require answers.
Q is not unanswerable by content, but by form: The speaker chose a particularly complex form instead of simply asking a standard question. 35 Compare silence as conventional means to accept a claim (Farkas & Bruce 2010). Interestingly, Littell, Matthewson & Peterson (2010) argue along the same lines why conjectural questions remain unanswered.

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Conjectural questions The conventional nature of silence as a reaction is confirmed when we look at special utterance situations. Take example (62) (62). This justifies the assumption that not answering is a conventionalized possible move for B, not one that is forced by pragmatic processes. A second special case arises when B knows the answer to the verb-final wohl question. Assume that, in (61), p = 'Hein is on Hawaii' and B knows this. The logic of defeasible inference thus predicts that B is authorized to answer: As B knows p, the epistemic alternatives of B are included in p. According to our analysis B's stereotypical r-worlds are a subset of B's epistemic alternatives for any r. Thus for any further evidence r that A⊕ B may take into account, the inference that p remains valid. We predict that B is justified to answer p without further speculation. While this is in line with the data, B can alternatively interpret A's utterance as an expression of curiosity and remain (unhelpfully) silent. Again, this confirms that silence is a conventionally possible reaction.
Finally, we can explain why verb-final wohl-questions are restricted to contexts where A believes that B does not know the answer. Verb-final questions show non-standard syntax and an additional evidential and are therefore marked in comparison to both, standard questions and standard wohl questions (Levinson 2000). If speaker A wants to know whether Q and believes that the addressee can conjecture the answer, she prefers the standard (wohl) question. Uttering a verb-final wohl question, speaker A implies that she does not believe that B knows or can conjecture the answer.
It also follows that verb-final questions with wohl do not occur in other non-standard question situations. They cannot be used as rhetorical questions, i.e. when A knows the answer and believes that B also knows the answer. We also predict that verb-final wohl questions are excluded in exam situations: These open the discourse for defeasible inferences based on pooled 9:39 knowledge. In an exam situation, however, A knows the answer and joint speculations are not what the discourse aims at. The prediction is borne out, as verb-final wohl questions in exam situations are unacceptable. 36 In summary, the analysis predicts that joint speculation and silence are the possible (conventionalized) reaction to verb-final wohl questions in German. The next subsection extends the analysis to verb-final polar questions with the complementizer ob.

Polar verb-final wohl questions
Polar verb-final questions in German like (63) differ from the wh-questions in that they show ob in C 0 . (63) Ob Hein wohl auf See ist?
Unlike the question complementizer ob, this 'ob' occurs in a root clauses without being licensed by a matrix predicate. Its syntactic properties thus differ from standard ob which is restricted to embedded questions. Let us call the entry ob for the moment. I propose that ob has the same denotation as SHARE in wh-verb-final questions.
(64) = * * where c * * is derived from c as in (59) As a consequence, the C 0 -head ob is restricted to the same syntactic and semantic environments as SHARE in 4.2.1. At LF, ob takes highest scope above wohl and the question clause. The semantic composition of (63) is illustrated below. The question operator ? derives the polar question meaning and takes scope below wohl and ob . The symbol + in (65e) indicates pointwise functional application of characters to c * * .  (sp(c),w 0 ,q(c),w) → HEIN-AT-SEA(w)), c w 0 .∀w(STEREO(sp(c),w 0 ,q(c),w) → ¬HEIN-AT-SEA(w))} 36 I thank the reviewers for bringing up the issue. Note that the picture-book scenario in (53) is not an exam situation in the sense that A knows the answer. → HEIN-AT-SEA(w)), w 0 .∀w(STEREO(sp(c)⊕ad(c),w 0 ,q ( ) ∧q ( ) ,w) → ¬ HEIN-AT-SEA(w))} The question denotation can be paraphrased as follows: "What -if we pool our knowledge -would we conjecture? Would you and I together say that Hein is at sea or that Hein is not at sea?" As before, the addressee can react in three ways: Engage in speculative discourse, leave the question unanswered or provide the answer, if known. In summary, we have an analysis of conjectural verb-final wohl questions in German that builds on the meaning of wohl. Section 2 argued that wohl in assertions is an inferential evidential. I proposed that wohl p conveys that the speaker defeasibly infers p from privileged knowledge q. When drawing inferences, speakers take into account their maximal body of knowledge q that pertains to the given issue. They don't make claims that are defeated by their own knowledge. Section 3 transferred the analysis of wohl to standard questions. Building on Lim 2010, 2011, I proposed that wohl Q denotes a set of characters. These anticipate that the addressee provides an answer that rests on defeasible inference, thus predicting the interrogative flip. The flip is effected by the lexical properties of wohl. This is justified by the observation that many, but not all evidentials in questions give rise to interrogative flip.
The present section extended the analysis to verb-final wohl questions. I proposed that they denote sets of possible answers where wohl refers to the plurality of speaker A and addressee B, A⊕B. If an answer is to be chosen, A⊕B together have to adhere to the maximality condition. In typical utterance situations for verb-final wohl questions, A has not informed B beforehand about everything he knows about Q. Before drawing defeasible inferences, A and B must hence pool relevant knowledge about Q. B can react by starting speculative discourse about Q. Speculative discourse includes B contributing further knowledge but extends to guessed answers, suggestions or own experience with the issue. Speculative discourse is hence a free way to engage with the question at hand. Alternatively, B can silently acknowledge A's curiosity. In normal utterance contexts, this option might in fact follow from general speech act principles. Among the felicity conditions of requests, Searle (1969: p. 66 questions, this means that A must believe B to be able to answer the question. In the case of verb-final wohl questions with A knowing beforehand that B is not able to answer, A violates against these conditions. The present analysis therefore predicts that the utterance doesn't constitute a request for an answer. It is plausible to assume that 'not replying' or 'tacitly acknowledging the utterance' is a reasonable move in this case. Yet, a specific speech act theory that predict permissible (non-)reactions in this case remains to be explored.
The use of verb-final wohl questions in contexts like (62) shows that B's option to remain silent has turned into a conventionalized reaction. 37 As we saw in example (62), B can remain silent even if A shares knowledge before uttering the question. The option for B to remain silent should thus be viewed as the lexical contribution of SHARE , as suggested in (Roelofsen & Farkas 2017).
The analysis has several advantages over earlier accounts of conjectural verb-final wohl questions in German. It predicts that wohl is a mandatory part of CQs in German and assumes that wohl plays a mayor role in deriving the pragmatic properties of CQs. The analysis can therefore potentially explain why inferential evidentials in other languages also give rise to CQ readings (see Section 5). The analysis moreover motivates the conventionalized reactions to verb-final wohl questions by their pragmatic properties in typical situations of use (i.e., where A believes B is unable to answer). While the pragmatic profile of CQs can also be successfully captured in terms of conversational scoreboard models (Roelofsen & Farkas 2015, the present analysis has the potential to explain why verb-final wohl questions adopt the range of possible reactions that we observe. Finally, the analysis draws a link between CQs and joint speculation. This connection may be worth further pragmatic exploration in the future.

Other analyses of conjectural questions
The present section surveys earlier formal analyses of conjectural questions and compares them to the present account. Lohnstein 2007, Truckenbrodt 2006 investigate German polar verb-final questions and propose that subordinate clause syntax is their key feature. Both authors start from the assumption that verb movement to C 0 is a necessary prerequisite to express a speech act in German. The pragmatic profile 37 See Traugott 1988 and Eckardt 2006 on mechanisms of meaning change.

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Conjectural questions of conjectural questions supposedly emerges as the result of two conflicting cues: The speaker utters a question but one that does not express a proper speech act. Roughly speaking, the addressee interprets these cues as "the speaker wonders about Q" and "I am not supposed to do anything about it". Truckenbrodt 2006 models the two cues in terms of syntactic features in ForceP. While the feature epist indicates that speakers want to change their epistemic state, the feature deont indicates that someone is supposed to do something. In verb-final questions, Truckenbrodt proposes, the feature deont is absent and thus the utterance poses no request on the addressee. This offers a good start to account for the fact that German CQs don't pose a request to the addressee. While the analysis captures the difference between standard polar questions and (conjectural) polar verb-final questions, it fails to situate wohl as an obligatory element in conjectural wh-questions (see (55)). It is also challenged by German verb-final questions that do convey requests: Verb-final questions can serve as repeat questions that draw the interlocutor's attention back to an open question (Oppenrieder 1989, Disselkamp 2017. Plunze & Zimmermann (2006) call into doubt the claim that conjectural questions do not require any reaction by the addressee and point out that "not answering" and "not doing anything" should be kept apart. Finally, the analysis is tailored for German in that subordinate clause syntax is not a triggering feature for conjectural questions in other languages. The present analysis is better suited to understand the interaction between evidentials and the pragmatics of questions, as argued in Section 5. M. Zimmermann (2011) mentions wohl as an element of German conjectural questions and notes a certain harmony between wohl in questions and questions with verb-final syntax, however without detailed analysis.
In Salish languages, inferential evidentials trigger an interpretation as CQ. Littell, Matthewson & Peterson (2010) propose to capture the meaning of evidentials in terms of the presupposition "the agent has evidence that entails p ". They argue that each possible answer p presupposes that the addressee has evidence that entails p . In conclusion, the question as a whole must presuppose that the addressee has evidence in favour of any possible answer p to the question. This being an unlikely and often a contradictory presupposition, they argue, the addressee is relieved from the obligation to answer. Conjectural questions are viewed as too rich in presuppositions to be answered. The analysis, however, overgenerates because the predicted semantic interaction of evidentials and questions should generalize to other languages. This is problematic as evidentials often trigger the interrogative 9:43 flip instead. It is also open whether the authors would maintain their analysis for Salish inferential evidentials like k'a (St'át'imcets), as they argue in other work that evidentials pattern with modal operators (Matthewson, Davis & Rullmann 2007).
Japanese conjectural questions have been at the focus of attention in a series of papers in recent years. Among those are conjectural questions marked with the evidential morpheme daroo. The syntactic approaches in Sugimura 1986, Miyagawa 2012, Tenny 2006, Oguro 2017 take an extended speech act phrase as their starting point. The presence or absence of daroo as well as honorific markers correlates with the presence or absence of a SpeakerPhrase and HearerPhrase in the sense of Speas & Tenny 2003. While the account adequately predicts grammatical and ungrammatical questions, the interface to semantics as well as the meaning of conjectural questions remains open. As the authors fail to spell out how syntactic features, pragmatic restrictions and the world relate to each other, it is unclear whether they claim that a sentence without HearerP is ungrammatical in the presence of an addressee (and, vice versa, a sentence with HearerP is ungrammatical in soliloquy). More interesting for the present account is the work by Yurie Hara. (Hara 2006) analyses daroo in declaratives as an inferential evidential and compares its interpretation in assertions to other Japanese evidentials.  proposes a semantic analysis of daroo in conjectural questions in terms of inquisitive semantics (Ciardelli & Roelofsen 2015). The chosen framework is ideally suited to model discourse where an issue (proposition or question) is in the speaker's mind, disregarding whether a question has been openly posed or not. She assumes that daroo conveys that the denotation of the prejacent is an issue for the speaker, where "issue" in inquisitive semantics covers both declaratives and questions. The complex pattern of Japanese questions and assertions with or without daroo emerges as a joint effect of daroo and an interpretation for sentence accents in Japanese (Hara 2012, Miyagawa 2012. While the analysis correctly predicts the data under investigation, the denotation of daroo no longer contributes the evidential meaning detailed in earlier work (Hara 2006). Evidential assertions of the form daroo S, according to the most recent account in Hara 2018, are synonymous to the proposition 'the speaker knows S'; the observed hedging effect of the evidential is attributed to Gricean implicature. Gunlogson (2003) initiated a strand of ongoing research on the conversational scoreboard (Farkas & Bruce 2010, Roelofsen & Farkas 2017, Farkas 2017, 2020. Farkas and Roelofson envisage a new division of labour between 9:44 Conjectural questions words that determine semantic content, on one side, and other words or morphemes that determine the functioning of the sentence in discourse, on the other side. Farkas (2017Farkas ( , 2020 applies this idea to Romanian conjectural questions with the particle oare. The contribution of oare in questions consists the instruction that the conjectural question may be removed from the table without the addressee providing an answer. She thus predicts that oare questions can remain unanswered without leading to a situation of crisis, and without running the dialogue into an instable state. Farkas 2020 covers verb-final wohl questions in terms of the conversational scoreboard and makes good predictions for German CQs in questionanswer dialogue (assuming that joint speculation can be explained as a general conversational strategy to deal with questions). However, this kind of analysis leaves open why wohl is the conventionalized cue of CQs in German, and why evidentials are also recruited as cues for CQs in many other languages. The final section addresses this wider panorama.

Outlook: Conjectural questions in other languages
preted as evidential (Mari 2010), which triggers a CQ reading in questions (Eckardt & Beltrama 2019). (Valenzuela 2003) explicitly points out that CQs in Shipibo-Konibo, like in German, serve to initiate joint speculation on a topic. This intuition seems to extend to other languages (Zucchi, p.c., Taylor, p.c.).
This section sketches an analysis of evidentials as CQ markers, using ⟨evid⟩ as a cover term. ⟨evid⟩ cannot be context-freezing, or else we would falsely predict the interrogative flip. In assertions, ⟨evid⟩ should have a denotation similar to the one assumed for wohl in (21) whereas in questions, the evidential additionally should trigger the change from utterance context c to c * * . This can be accounted for by the following additional entry for ⟨evid⟩, reserved for questions:. (66) ⟨ evid ⟩ = p. w 0 .∀w(STEREO(sp(c)⊕ad(c),w 0 ,q ( ) ∧q ( ) ,w) → p(w)) The proposed ⟨evid⟩ combines pointwise with the question denotation. It contributes the inferential non-at-issue meaning and, at the same time, establishes an utterance context where speaker and addressee are jointly responsible for defeasible inferences. We thus predict that the question invites joint speculation based on pooled knowledge. In brief, ⟨evid⟩ in questions integrates the semantic factors that play out in German. 39 If we are justified in the assumption that CQs are used when speaker A expects that addressee B cannot answer, and if we are moreover right in hypothesizing that in this case, general laws of speech act theory ensure that A is not requesting B to answer, we will once again expect that in the typical context of use, questions with ⟨evid⟩ do not require B to answer. Extending this pattern, the evidential ⟨evid⟩ will acquire the conventionalized meaning of a CQ marker. The present analysis of German verb-final questions thus provides semantic elements that might be in play in other cases where evidentials mark conjectural questions. We tentatively proposed an independent operator that can turn question meanings into question denotations that allow the range of reactions that are typical for conjectural questions, thus laying out the road map to understanding the contribution of evidentials to conjectural questions in other languages.