1 Introduction
In stating a belief, a speaker may reveal the basis of that belief. This observation is no more than a truism for typologists: there are languages and language families with grammatical markers that express the evidentiary basis on which the speaker is asserting a proposition (Chafe & Nichols Reference Chafe and Nichols1986, Aikhenvald Reference Aikhenvald2004, Boye Reference Boye2012, Matthewson & Glougie Reference Matthewson, Glougie, Stich, Mizumoto and McCready2018). But if construed as a statement about evidential implicatures attached to exponents of temporal expressions (e.g. tense, aspect, adverbs) on particular occasions of use, it raises new questions: how do these implicatures arise, and are they calculable from conversational reasoning? Studies of evidential implications range from those that examine the use of perfect forms to report situations known of through abductive reasoning and hearsay (Slobin & Aksu Reference Slobin, Aksu and Hopper1982, Lau & Rooryck Reference Lau and Rooryck2017) to those that relate the use of future tense in inferential and mirative utterances to canonical functions of future tenses, as in conjectures (Escandell-Vidal Reference Escandell-Vidal, De Brabanter, Kissine and Sharifzadeh2014). These treatments view evidential inferences as being ‘strengthened’ (in the sense of Traugott Reference Traugott1988, Brinton Reference Brinton1996): they are present where original temporal significations are absent, as when the Turkish past-tense morpheme -mış is used in present-tense mirative utterances, or the Spanish inflected future is used to express suppositions about current situations.Footnote [2] In this paper, we instead examine evidential inference on the fly, formed from a ‘perfect storm’ of interpretive constraints (lexical, aspectual, temporal and conversational).
We base our study on an English temporal adjunct used in predications that describe resultant states: the by temporal adjunct (BTA), whose combinatoric potential – so far as tense and illocutionary force are concerned – is no different from that of temporal adverbials like on Friday. The BTA is a prepositional phrase (PP) headed by by, whose complement is a nominal that describes a time t; the resulting combination means ‘no later than t’ (Thomas & Michaelis Reference Thomas, Michaelis, Leow, Campos and Lardiere2009). Examples are given in (1)–(5):Footnote [3]
In line with Thomas & Michaelis (Reference Thomas, Michaelis, Leow, Campos and Lardiere2009), we see the time described by the BTA complement as a time at which a particular state holds, i.e. is in force (Copley Reference Copley and Truswell2018): the state that is described by the verb and its arguments. We hypothesize that the state is necessarily a resultant state of some event that has culminated: the BTA describes a time that follows the state’s time of inception. Thus, for example, (1) describes a possible state (use of G.M. driverless cars by ride-hailing services) with an onset prior to the end of next year. This state is understood to result from some event (or a series of events) that can be easily accommodated given our world knowledge, e.g. satisfactory testing of driverless cars. Similarly, (2) describes a possible state (a rifled box) that results from an event (of leaving the box in a salient location).
Example (3), however, seems to pose a challenge for our hypothesis: the BTA by late morning is paired with a patently perfective predicate (leave), thereby suggesting that the BTA is not aspectually restricted in the way proposed. In line with Thomas & Michaelis (Reference Thomas, Michaelis, Leow, Campos and Lardiere2009), we view such combinations as exemplifying pragmatic resolution. In particular, we assume that the preterit predication in (3) describes a state (of their absence from the house) that started just after the end of the event (of departure) described by the verb (Michaelis Reference Michaelis2011). This interpretation is comparable to the ‘covert past-perfect’ reading that attaches to when clauses in contexts like (6):
If the BTA expresses a (potential or actual) time of verification of a state qua resultant state, then the semantic representation of the BTA obligatorily includes a change component, as reflected in the pattern of variation observed in the constructed examples (7)–(10):
The contrasts in (7)–(10) suggest that Aktionsart is relevant to BTA use conditions: a BTA sentence is felicitous only when a transition prior to reference time can be inferred. In this respect, BTAs contrast with most (though not allFootnote [4]) temporal adverbials. An activity predicate like walk around, as in (9), is BTA-incompatible because it has no entailed resultant state. On the other hand, (10) suggests that state descriptions that are not readily construed as consequences, intended or unintended, of prior events are also incompatible with BTAs.Footnote [5] Recall that (1), which also contains a state description, is BTA-compatible because one can easily accommodate an event (or a series of events) that result in the use of G.M. driverless cars. Such cannot be said for the state of loving hot toddies; there is no obvious candidate event that would result in such a state.Footnote [6]
There is another important respect in which BTAs differ from many temporal adverbials: BTAs are downward compatible with respect to the evoked time scale, while temporal adverbials are not. Thus (11) below is contradictory, but (12) is not:Footnote [7]
Key to the analysis that we propose in this paper is the observation that BTA time reference is indefinite. For example, the BTA predication I arrived home by midnight effectively means ‘I arrived home at some point prior to midnight’. Clearly, a speaker may choose non-specific time reference over specific time reference when the exact time of a state’s inception is irrelevant, so long as it falls within a certain range of times. What is of particular interest to us is the manner in which non-specificity contributes to a particular evidential reading. One of our major aims in this paper is to describe the constellation of factors that give rise to this reading, illustrated in (14):
While (13) could be spoken by someone at home, who thereby has firsthand knowledge of Shira’s presence at home, (14) could not. The report in (14) is naturally seen as the product of an inference: the speaker is not at home and is merely offering a conjecture about Shira’s whereabouts.Footnote [9]
Interestingly, some present-tense BTA tokens are redeemed only by the presence of an epistemic-stance indicator, e.g. a modal such as must or probably:Footnote [10]
Moreover, the infelicitous example noted in (10), repeated below, improves when we add an epistemic-stance indicator, e.g. will, as in (17):
What is the nature of the relationship, if any, between the indirect-evidence implication of present-tense BTA sentences like (14) and the implied epistemic stance of uncertainty or supposition? And why do BTA sentences like (15)–(17) appear to require overt indication of epistemic stance when others apparently do not?
In addressing these questions, we illustrate the close relationship between evidentiality, understood as the indication of evidentiary source, or epistemic justification (Boye Reference Boye2012), and epistemic modality, understood as the indication of degree of certainty or commitment (referred to by Boye as epistemic support). A BTA predication contrasts two phases: that in which the expressed state holds and that in which it does not. The only certitude in a BTA sentence is that there was a period in which the state at issue did not or will not hold. Since a BTA sentence does not tell us exactly when that period ended or will end, the denoted state may exist only as a supposition or inference about the evoked reference time. For example, a language user who directs another to be home by five, as in (5), anticipates a period of indeterminate length in which the addressee is absent. Because BTA sentences describe states that come to exist only at the outer margins of the intervals they delimit, they are natural vehicles for illocutionary acts likes guesses, directives and predictions.
The remainder of this paper is structured as follows. In Section 2, we describe the BTA change schema by appealing to a theory of contextual operators, which we make more precise using a Neo-Davidsonian event semantics. After doing so, we offer a pragmatic account of how the inferential construal of present-tense BTA reports arises from the present-tense reports considered above. With this analysis in place, we then show how our analysis naturally extends to reports in the past tense, which, owing to its anaphoric reference and logical relation to the present, can, but need not, trigger the inference that the speaker has first-hand knowledge. Subsequently, in Section 3, we hypothesize the manner in which the BTA change schema is instantiated with epistemic modals and discuss the relationship between intensional and evidential contexts. Finally, in Section 4, we offer concluding remarks about the interplay of tense, aspect, evidentiality and modality that we have observed.
2 Semantics of BTAs
2.1 Contextual operators and the transition component
Following Thomas & Michaelis (Reference Thomas, Michaelis, Leow, Campos and Lardiere2009), we identify BTAs with the class of contextual operators, described by Kay (Reference Kay1990, Reference Kay1997) as ‘lexical items and grammatical constructions whose semantic value consists, at least in part, of instructions to find in the context a certain kind of information structure and place the information presented by the sentence within that information structure’ (Kay Reference Kay1997: 159). Other examples of contextual operators are: (i) even, which suggests that the asserted proposition is to be construed as an extreme case along a scale of eventualities (Kay Reference Kay1990),Footnote [11] (ii) already, which instructs the hearer to interpret the denoted state as one that holds prior to the inception of a process or procedure known to effect that state (Michaelis Reference Michaelis1996)Footnote [12] and (iii) let alone, which conjoins a contextually given proposition, e.g. They were never convicted, to one judged to be more informative, as in, e.g. They were never charged, let alone convicted (Fillmore, Kay & O’Connor Reference Fillmore, Kay and O’Connor1988).
Along these same lines, Thomas & Michaelis (Reference Thomas, Michaelis, Leow, Campos and Lardiere2009) postulate that ‘BTA-bearing predications require interpreters to retrieve or construct frames containing time series’ (p. 140), and that such time series may be understood either as schedules or as developmental sequences (p. 133). This analysis seems intuitively valid. For example, BTA sentences commonly express deadlines, as in (18), and points of culmination, as in (19):
We assume that in (18), the hearer imagines a series of permissible submission times, just as the hearer of (19) imagines an incremental increase in the monetary value of the investment.
It happens, however, that a BTA sentence need not describe a state that is ordered with respect to another:
It seems implausible to assume that (20) imposes a construal in which the rain had been in the offing throughout the retrieval operation. It is simply the case that a transition from dry to wet conditions had begun sometime prior to the past reference time (the time at which the retrieval operation had finished). By the same token, (21) could not be said to presuppose a knowledge scale along which knowledge of leprosy was increasing prior to the past reference time. Finally, we could not reasonably suppose that (22), repeated from (4) above, implies that the speaker would be dying throughout his twenties and thirties.
In light of these considerations, we propose that a BTA sentence simply expresses a state that is necessarily construed as the result of a transition that occurred at some time prior to the reference time of the predication. The interpreter of a BTA sentence may be required to guess what event led to the onset of the state at issue. In the next subsection, we make our proposed analysis of BTAs more precise.
2.2 A toy analysis
As noted at the outset, we assume that as far as tense and illocutionary force are concerned, BTAs are no different from temporal adverbials like on Friday. A toy analysis of Ava left on Friday is provided below to illustrate one way that we can model the compositional contribution of on Friday. We then show the contribution of BTAs.Footnote [13]
In (23), we assume that that the extension of a tenseless VP like Ava leave is a set of leaving events by Ava, who is the agent. In (24), we assume that on Friday is a function from a set of eventualities to a set of times, requiring that there be an eventuality v in the extension of the VP such that: v overlaps some time 
$t^{\prime }$ (i.e. 
and 
$t^{\prime }$ is temporally included within a time t, which has the property of being a Friday. Finally, PAST in (26) saturates the time argument in (25) via existential closure, ensuring that this time is in the past. The resulting formula is provided in (27), which characterizes an event e of Ava’s leaving at a time 
$t^{\prime }$ that is within a past time t, which has the property of being Friday. This correctly characterizes the truth conditions of Ava left on Friday.
Below, we show how this toy analysis generalizes to stative descriptions like Ava was happy on Friday. Following Parsons (Reference Parsons1990) and subsequent work we distinguish events from states in our ontology by means of e vs. s variables ranging over events and states, respectively. Since on Friday does not discriminate between eventive and stative descriptions, we use the eventuality variable v in (24)/(29), which ranges over events and states (Bach Reference Bach1986). We also follow Parsons (Reference Parsons1990) in distinguishing the thematic role, AGT, which stands for the agent of an event, from IN, which stands for the state that an individual is in (e.g. in Ava was happy on Friday, Ava is in the state of being happy).
As noted above, this is just one way in which we can model the compositional contribution of on Friday. We will not provide independent motivation for the idea that temporal adverbials existentially bind the eventuality variable.Footnote [14] Moreover, we will not specify the semantics of PASTFootnote [15] and FRIDAY.Footnote [16] What is crucial for us is the idea that the preposition on contributes temporal inclusion (‘
$\subseteq$’) and the observation that on Friday contributes an indefinite statement of the following kind: ‘there is a time at which the eventuality described by the VP held/occurred’.
With these assumptions in mind, let us now consider how BTAs can be incorporated into the toy analysis outlined above. Below, we provide a semantics for the sentence Ava left by Friday, where the only difference between (23)–(27), on the one hand, and (33)–(37), on the other, is the contribution of on Friday in (24) as against by Friday in (34). The key difference is that by ensures that the time interval that has the property of being a Friday precedes or is equal to the time that overlaps the time of the eventuality in the extension of the VP that the by phrase attaches to.Footnote [17]
Like on Friday, by Friday is a function from a set of eventualities to a set of times. When the input to the function is a set of events, as above, then the onset (ONS) of a prominent state 
$s_{i}$ that is the resultant state (RES) of an event e must overlap a time 
$t^{\prime }$, which is prior or equal to a time t that has the property of being a Friday. As shown in (37), this amounts to the following. The onset of the resultant state of Ava’s past leaving (i.e. the onset of Ava having left) must be on or precede Friday. That is, Ava left by Friday is true iff Ava had left at some point on or before Friday. As noted in the introduction, we assume that there is a prominent resultant state associated with an achievement verb like leave. We further assume that this resultant state comes from the discourse context (as suggested by the formula above), although we do not rule out the possibility that it is entailed by the verb’s Aktionsart representation, as in the case of achievement and accomplishment VPs (e.g. She had fixed the situation by Friday). What is crucial is that we rule out an activity description like ??Ava walked around by Friday, because resultant states are typically not associated with such descriptions.Footnote [18]
Now, if the input to the extension of by Friday a set of states, as in (38),Footnote [19] then the requirement is that the onset of a state s in the set results from some prominent event 
$e_{i}$. Moreover, as before, s must overlap a time 
$t^{\prime }$ that is prior to a time t that has the property of being the Friday under discussion (see (39)).Footnote [20]
For a sentence like Ava was home by Friday, we assume that there is a prominent event that can be accommodated from the discourse context – Ava’s arriving – that results in the state of Ava being at home. The onset of this state would, then, be correctly predicted to overlap a time that precedes Friday. By contrast, Ava loved hot toddies by Friday (a variant of (10)) is odd simply because its successful interpretation requires the addressee to construct a peculiar, or at least highly particularized, scenario in which Ava’s love of hot toddies is the result of some earlier event. Like an indexical expression, the BTA has minimal semantic constraints, requiring the interpreter to search the conversational common ground for the appropriate specifications (Kay Reference Kay1997), including abductive reasoning to whatever causal event could yield the denoted state. In what follows, we will further consider the hearer’s contribution, which includes inferences about speakers’ evidentiary bases for assertions conveyed by present-tense BTA sentences. This is especially clear with BTA sentences containing the temporal adverb, now, already mentioned in previous sections.
There is a rich literature on now, going back to influential work by Kamp (Reference Kamp1971). More recently, Altshuler & Stojnić Reference Altshuler and Stojnić2015, Carter & Altshuler Reference Carter, Altshuler, Burgdorf, Collard, Maspong and Stefánsdóttir2017, and Stojnić & Altshuler Reference Stojnić and Altshuler2019 have argued that now can be treated as a prominence-sensitive indexical, which (among other things) selects for a state in the discourse that results from a prominent event. They show that this is an essential component of now’s meaning by analyzing a wide range of uses, including deictic, bound and discourse-bound uses. While exploring the meaning of now would take us too far afield, we end this section by noting that it should not be surprising that now has an affinity with by: their semantics both require prominent events and their resultant states.
2.3 Evidential implications of BTA predications
In the introduction we considered a minimal pair that we repeat below:
Recall that while (43) could be spoken by someone at home, who thereby has firsthand knowledge of Shira’s presence at home, (44) could not. The report in (44) is a supposition: the speaker is not at home and is merely reporting what she believes ought to be the case.
To see that this contrast is not particular to the data above consider the pair of sentences in (45) and (46). While (46) implicates that the speaker never tried the soup, (45) lacks this implicature.
Why should this be the case and what is the nature of the relationship, if any, between the indirect-evidence implication of present-tense BTA sentences like (44) and (46), and the implied epistemic stance of uncertainty or supposition?
To answer this question, recall that according to our proposed analysis, (43) would be analyzed as follows:
According to (47), there was a prominent event that culminated in Shira being home at some time 
$t^{\prime }$ prior or at the speech time. Given this assertion, one can reasonably infer that if the speaker had directly witnessed Shira’s coming home at 
$t^{\prime }$ (e.g. by being in Shira’s home), then the speaker would know when Shira had gotten home. But if this were the case, the speaker would presumably have used the present-tense report (43) above, or an event report like Shira got home a little while ago, Shira came home 5 minutes ago, Shira came home at 5, and so on. The speaker’s failure to employ these more informative options triggers a conversational implicature. The implicature is Q(uantity)-based, arising from the hearer’s assumption that the speaker is respecting informational sufficiency in making her report as precise as possible. That is, when reasoning according to the Q-principle, the interpreter of (44) infers that the speaker lacks knowledge of Shira’s exact arrival time; otherwise, the interpreter reasons, one of the more informative options noted above would be the appropriate (i.e. most cooperative) choice. The simplest explanation for the speaker’s knowledge gap is that she was in a different location from Shira’s location at 
$t^{\prime }$. Note that such an implicature does not arise from (43) because event reports like Shira got home a little while ago, Shira came home 5 minutes ago, Shira came home at 5, and so on, are not viable alternatives to (43). The reason is that such reports do not convey what (43) entails – that Shira is at home at the speech time. The Q-based implicature is part of the construal of (44) precisely because (44) does not entail that Shira is at home at the time (44) is uttered, though such a state of affairs is compatible with the truth-conditions of this sentence.Footnote [21] (Recall that our semantic analysis of (44) (in (47)) specifies only that the onset of Shira’s presence overlaps a time that either precedes or holds at the speech time (‘t
$^{\prime }$ < NOW’).) The foregoing observations suggest the remarkable quality of sentences like (44): they carry an evidential-source implication that cannot be traced to evidential ‘marking’ of any kind, but is rather the product of conversational reasoning.
An analogous analysis applies to (46), which has the representation below.
If the speaker had tried the soup at 
$t^{\prime }$, she would, we presume, have been able to say something about the circumstances that obtain at encoding time, e.g. The soup is cool now or at a time immediately prior, e.g. The soup was cool (just now), The soup was cool 5 minutes ago, The soup was cool at 5, and so on. The fact that she did not say either of these things leads to the inference that she has not directly experienced the temperature of the soup. The natural explanation is that the speaker has not (yet) tried the soup. The lesson here yet again appears to be that evidential-source information is calculable as well as conventional (in those cases where it is encoded by a marker of evidential source).
With this analysis in place, let us now consider past-tense reports, which were briefly discussed at the outset. Here are the past-tense versions of the examples we just considered:
These ‘backshifted’ versions are acceptable, at least insofar as they are construed as embedded within a narrative.Footnote [22] But the former seems to lack the implicature that the speaker has been absent from Shira’s home throughout the period that included her return home, while the latter seems to lack the implicature that the speaker has not yet tried the soup. Note, however, that (49) and (50) nonetheless carry a negative implication traceable to the BTA ‘onset’ schema – that the speaker was not at home/did not try the soup at some time prior to the past time t described by the adverb now. Of course, the present-tense reports (49) and (50) share this negative implication with their past-tense counterparts, but, unlike their past-tense counterparts, they have no time depth,Footnote [23] and so the reporter’s inferred knowledge state at reporting time cannot differ from her knowledge state at reference time. These present-tense sentences therefore impart that the speaker was never at home and never tried the soup.
Now consider the following naturally occurring past-tensed discourse with by now:
The discourse context tells us, explicitly, that the speaker was at home during the entire part of the affair described, including during some unspecified time at which Richard, her husband, came home. Note the strong implication of ignorance; the speaker did not witness his entering, as she was busy hunting a lion that possibly killed her cat. This implication of ignorance is to be derived exactly like with the present-tensed by now described before. As before, it concerns the use of an indefinite to describe some time prior to the time t described by the adverb now rather than some specific time.
Unlike present reports with now, (51) leaves open the possibility that the speaker witnessed her husband being at home after the time described by the adverb. It’s not relevant in the story. If a present tense were used in (51), however, there is a drastic shift in what is inferred:
Here we infer that the speaker never witnessed Richard coming home. We imagine the speaker in a different room of the house. This is an effectively identical inference pattern to those described above – that the speaker never witnessed Shira at home, that the speaker never tried the soup, and so on.
In sum, because by now is a form of indefinite reference, we observe an ignorance inference attached to both past- and present-tense reports containing by now. There is, however, a crucial difference between the past predications and the present predications: while the indirect evidence implication always manifests in present-tense reports, which require that the speaker’s ignorance persist to speech time, the indirect evidence implication need not attach to past-tense reports. The past-tense schema allows for a period between the past time of orientation and the present encoding time at which the speaker might have remedied her ignorance.
We already know, of course, that the reference time of a state report does not restrict the state itself, but only the interval for which the speaker is prepared to vouch for that state (Dowty Reference Dowty1986, Altshuler & Schwarzschild Reference Altshuler, Schwarzschild, Chemla, Homer and Winterstein2012): a sentence like She was in London yesterday, if interpreted as an alibi statement, is perfectly compatible with her being in London thereafter. Thus, a tensed state sentence always has what might be called epistemic import: it describes the known (or relevant) segment of a state. What is special about sentences like (44) and (46) is that they feature combinations of tense, adverbial meaning and (stative) aspect that reveal not merely what state segment is known to the speaker but also how the speaker knows of it. Indirect evidence is relatively weak evidence. As Karttunen (Reference Karttunen and Kimball1972: 13) observes, ‘indirect knowledge – that is, knowledge based on logical inference – is valued less highly than ‘direct’ knowledge that involves no reasoning’. Sentences like (44) and (46) invite paraphrases like Shira must be home by now and The soup is probably cool by now. In the next section, we offer an account of why such inferential paraphrases are apt and in some cases preferable to their terser counterparts.
3 BTAs in intensional contexts
In Section 1, we noted that some present-tense BTA tokens are apparently salvaged only by the presence of an epistemic-stance indicator. The relevant examples are repeated below:
Given the toy analysis of BTAs proposed in the last section, we are now in a position to make sense of the data above. Recall the key idea of the analysis of BTAs presented in Section 2.2: BTAs require the onset of a resultant state to overlap a time that precedes the time described by the adverb. On this analysis, the reason that (53)–(54) are odd in the absence of epistemic-stance indicators is that the described states are not naturally interpreted as resultant states of an event – no such event can be deduced in the absence of elaborate context. We are left asking: what caused them to (now) prefer white wine? What caused them to (now) live in Mountain View?
But why should inferences like those required by such contexts be facilitated by the presence of epistemic markers? We are left with two plausible hypotheses about why epistemic-stance indicators alleviate the infelicity above:
In what follows, we will provide some reasons to believe that, depending on the epistemic-stance indicator, either Hypothesis 1 or Hypothesis 2 is valid, leading to outstanding questions about how the toy analysis in Section 2.2 should be extended.
According to Kratzer’s (Reference Kratzer, Eikmeyer and Rieser1981, Reference Kratzer, von Stechow and Wunderlich1991) seminal analysis of modals, must in (53) requires the described eventuality to hold in all of the most ideal worlds of the modal base. Hence, for (53) to be true, the described wine preference holds in all of the normal worlds (e.g. that in which red wine has become prohibitively expensive). But what about the actual world? What does (53) say about the described wine preference in the world of the speaker? Here, things are more complicated. There are (at least) two well-known answers to this question.
The first comes from von Fintel & Gillies (Reference von Fintel and Gillies2010), henceforth F&G, who argue that must 
$\unicode[STIX]{x03C6}$ is felicitous only if the evidence for 
$\unicode[STIX]{x03C6}$ (the prejacent) is indirect. They consider the minimal pairs below,Footnote [25] noting that must is felicitous only in the case where the speaker had indirect evidence for the assertion that it is raining.Footnote [26]
F&G further claim that the putative indirect-evidence inference is cross-linguistically robust, and while they ultimately conclude that it should be derived as a quantity implicature (Grice Reference Grice1989, Geurts Reference Geurts2010, Franke Reference Franke2011, Frank & Goodman Reference Frank and Goodman2012), they settle for a lexical stipulation, owing to various challenges faced by a quantity-based-analysis.Footnote [27]
Another proposal, recently defended by Goodhue Reference Goodhue2017, comes from Giannakidou & Mari (Reference Giannakidou, Mari, Błaszczak, Giannakidou, Klimek-Jankowska and Migdalski2016), henceforth G&M, who argue that epistemic modals require the speaker to be ignorant of the prejacent; there is no requirement that the evidence for the prejacent be indirect. The ignorance requirement is formally modeled as a presupposition on top of Kratzer’s semantics for epistemic modals, noted above. On this analysis, (55a) does not satisfy the presupposition; it is correctly predicted to be infelicitous because the speaker (Billy) knows that it is raining. By contrast, (55b) does satisfy the presupposition, because the speaker (Billy) is not certain of the ambient conditions – she can only speculate. Hence, (55b) is true if it is raining in all of the most ideal worlds of the modal base.
In what follows, we will consider how and whether these two analyses could be used to support Hypothesis 1 and/or Hypothesis 2 above. We start with an application of G&M’s analysis to (53) with the modal must. As noted above, for (53) to be true, the described wine preference holds in all of the most ideal worlds of the modal base. Now, let us assume, following G&M, that (53) also presupposes that the speaker does not know whether the described wine preference holds in the actual world. Could the conjunction of the asserted and presupposed content support either Hypothesis 1 or Hypothesis 2?
For the conjunction to support either Hypothesis 1 or Hypothesis 2, we would have to derive a possible change of state by juxtaposing the state in which they do not prefer white wine (in the actual world) to that in which they prefer white wine (in all of the most ideal worlds). Only after deriving this possible change of state can we entertain the question of whether the modal (a) facilitated the accommodation of a prominent event whose resultant state is the state described or (b) merely alleviated the need for this form of accommodation. Unfortunately, such a derivation is not possible.Footnote [28] To see this, suppose that the modal base f (w) consists of the following set of worlds: 
Let 
$\unicode[STIX]{x03C3}$ be the state of them preferring white wine. Now suppose that for all times t, 
$\langle \text{w},\text{t}\rangle \notin \unicode[STIX]{x03C3}$ and 
$\langle \text{v},\text{t}\rangle \in \unicode[STIX]{x03C3}$. In other words, suppose that they never prefer white wine in w, and that they have always preferred white wine in v. Finally, suppose that 
is the set of ideal worlds in f (w). Then, for any time in the actual world, 
There is no change of state in any world in f (w).
Despite our inability to derive the change of state in this manner, one may still be tempted to conjoin the presupposed and asserted content of must and derive the change of state by other (pragmatic) means. As we shall see below, we think this is plausible in the case of F&G’s analysis. For G&M’s analysis, however, this seems more challenging (at least for us). How, under G&M’s analysis would we derive the conclusion that 
$\unicode[STIX]{x03C6}$ does not hold at some prior time in w?
With this question in mind, let us now apply F&G’s analysis to (53) above.Footnote [30] Instead of presupposing that the speaker does not know whether the described wine preference holds in the actual world, F&G would say that there is some mechanism that led the speaker to know that the described wine preference holds in the actual world, at her time of utterance. In other words, the speaker came to know that there is a white wine preference in the actual world, prior to encoding time, by some indirect means. And this indirect evidence warranted the use of must in (53).
Note that this analysis involves the following change of state: the speaker lacks knowledge of the wine preference at some point prior to speech time and has knowledge of the wine preference at speech time. Note further that this change of state does not guarantee that there was a change of state in the wine preference itself; the speaker may have come to know something that always held. However the speaker came to such knowledge, it was not through witnessing the subjects choosing white wine over other options, or through hearing them declare their preference. This, of course, would be direct evidence. Instead the means by which the speaker gained the knowledge must be some event that enabled the speaker to deduce their preference for white wine, just as Billy’s seeing someone enter the building holding a wet umbrella in (55b) led her to deduce that it is raining.
Given this line of reasoning, we hypothesize that (53) implicates that whatever event provided the indirect evidence for the speaker’s claim, it is an event that led the speaker to log a new wine preference at speech time, whether or not that wine preference is, in actuality, a new state. Note in this connection that the speaker can append the following statement to (53) without contradiction: And perhaps they always did. Put differently, we hypothesize that the BTA onset schema is satisfied by must in (53) because any conjecture about a state of the world can be construed as a new state: if I am now prepared to make a guess about a state of the world, whether on the basis of reasoning or observation, I was not previously prepared to do so.
With this in mind, we can come back to the two hypotheses noted at the outset of this section and ask whether must provides information that would facilitate the accommodation of the onset event (Hypothesis 1), or whether must alleviates the need to accommodate this event (Hypothesis 2) by identifying the onset event as the evidentiary basis on which the speaker makes her assertion. Everything we have said thus far would suggest the latter hypothesis. However, Mandelkern (Reference Mandelkern and Truswell2016) provides intriguing data suggesting that must differs from other epistemic distancers like probably in the following respect: when a speaker uses must 
$\unicode[STIX]{x03C6}$, she has to share her evidence for 
$\unicode[STIX]{x03C6}$.Footnote [31] To see this, consider the following data:
While (56a–e) are all felicitous responses to the question in (56), (56f) is odd, and crucially odder than (56e), where the speaker shares her evidence for the claim that she is doing ok. Assuming such data are robust, it would suggest that (53), which has must, is not as felicitous as (54), which has probably, and that (53) is improved when the modal is replaced by probably, since no prior context is provided. We share this intuition, which in turn suggests that, on the extended F&G analysis just proposed, must supports Hypothesis 1, while other epistemic-stance indicators, like probably in (54), support Hypothesis 2.Footnote [32] In other words, the use of must 
$\unicode[STIX]{x03C6}$ requires the speaker to describe what caused her to know that 
$\unicode[STIX]{x03C6}$, and we claim that this evocation of a prior act of inference facilitates the construction of the BTA state as a resultant state. Probably in (54), by contrast, alleviates the need to accommodate the event required by BTA (Hypothesis 2) by identifying that event with the observation or act of reasoning that provided the basis for the speaker’s claim.
On this analysis, the use of an epistemic modal like must in (53) or probably in (54) will always result in a felicitous BTA construction as long as (i) the aspectual restrictions imposed by BTA are respected and (ii) it is plausible that the speaker could gain indirect evidence for her assertion (whether this evidence is shared, as in the case of must, or not, as in the case of probably). Moreover, on this analysis, if a BTA predication is felicitous in the absence of an epistemic modal (e.g. They had arrived by Friday), then adding an epistemic modal (e.g. They must have arrived by Friday) leads to the implication that the speaker’s assertion is warranted by indirect evidence. If the modal-free BTA predication already has this implication, as in the case of Shira is home by now (discussed in Section 2.3), then adding the modal will simply strengthen the implication (e.g. Shira must be home by now).
Let us now reconsider the contrast below. As noted in the introduction, the use of will in (57b) alleviates the oddity seen in (57a):
Unlike the examples previously discussed in this section, (57b) implicates that the speaker believes that the described eventuality does not hold at the speech time, i.e. that she does not currently love hot toddies. Altshuler & Schwarzschild (Reference Altshuler, Schwarzschild, Chemla, Homer and Winterstein2012, Reference Altshuler, Schwarzschild, Aloni, Franke and Roelofsen2013) call this inference cessation, characterized as follows:
Combined with the semantic contribution of will (there is a time after the speech time when the described eventuality holds), (58) allows us to derive a change of state inference in (57b): the hearer deduces that the individual under discussion does not currently love hot toddies, and that this individual will be in such a state in the future (namely at some point prior to November).Footnote [34] As in (52), the event that would lead to this change of state need not be specified in (57b). If we assume that will is an epistemic modal on a par with probably, then we can apply the leading insight of our F&G-inspired analysis: the use of the modal in a BTA predication evokes an antecedent observation or act of reasoning that permits the speaker to make her assertion, and this inference trigger is identified with the ‘onset event’ in the BTA schema.
In sum, this section has attempted to explain why infelicity in certain types of BTA predications is alleviated by the presence of an epistemic modal. One outstanding issue concerns the means by which we might extend the toy analysis in Section 2.2 to incorporate the contribution of intensional operators. Doing so would likely involve revising the idea (which was sufficient for our purposes in Section 2.2) that temporal adverbs existentially bind eventuality variables. Given the analysis in this section, it would be worthwhile to explore the hypothesis that it is the epistemic modal/attitude verb that has this task, identifying the event that leads to the change of state with the source of indirect evidence that the speaker relies on in making her assertion. We refer the reader to Hacquard (Reference Hacquard2009, Reference Hacquard2010) for some pioneering ideas about how modals interact with tense and aspect, leaving for future research the question of whether the ideas presented there can be neatly implemented in the compositional semantics proposed in Section 2.2.
The other outstanding issue concerns the use of BTAs with other epistemic-stance indicators, such as attitude verbs. The data in (56b, c) may lead one to expect that attitudes can alleviate infelicitous instances of BTAs on a par with the epistemic modal probably. Interestingly, while hope appears to confirm this expectation,
say/tell/think do not:
Why should this be? One relevant observation comes from Simons (Reference Simons2008), who observes that on a parenthetical use of an attitude report, the complement clause carries the main point of the utterance while the matrix clause plays an evidential function, indicating the source of evidence for the proffered content.Footnote [35] On a parenthetical reading of (60)–(62), this evidence is indirect: Susanna is the source of evidence. Of course, the matrix clause of attitude reports does not always convey hearsay evidence. This is especially clear with first-person reports like (63):
Despite not specifying the source of the evidence that warrants the assertion, (63) still implies that the speaker used some indirect means to reach the conclusion that they have a white wine preference: when someone hopes that a given state is in force at the speech time, there is typically a reason for that hope, although (63) tells us more about what the speaker expects or desires than it tells us about the speaker’s reasoning. Hence, attitude reports like (60)–(62) more closely resemble (53) [They ??(must) prefer white wine by now] than they do (54) [They ??(probably) live in Mountain View by now], while attitude reports like (63) more closely resemble (54) than they do (53).
Given these observations, we can rephrase the puzzle as follows: what allows us to analyze (59) and (63) on a par with epistemic modals, but not (60)–(62)? In particular, why would hope (but not say/tell/think) allow for an analysis in which the speaker came to know about the wine preference by indirect means, leading the hearer to deduce that there was a change of state (the wine preference) prior to the point at which the attitude report was uttered? We leave this question open for further research, noting some recent work that may help to solve the puzzle, e.g. Anand & Hacquard Reference Anand, Hacquard, Crnic and Sauerland2014, which posits various discourse constraints imposed by attitude verbs and Klecha Reference Klecha2016, which motivates a modal semantics for attitudes in which verbs like hope are distinguished from say/think.
4 Conclusion
We have motivated a change-of-state schema for BTA sentences by appealing to a theory of contextual operators, which we made formally precise, using a Neo-Davidsonian event semantics. Key to the analysis was the idea that BTA sentences require the onset of a resultant state to overlap a time that precedes the time described by the adverb. This analysis allowed us to identify the pragmatic factors that yield the inferential construal of present-tense BTA reports. Subsequently, we built on an analysis of epistemic modals by von Fintel & Gillies (Reference von Fintel and Gillies2010) and Mandelkern (Reference Mandelkern and Truswell2016) to hypothesize the manner in which the BTA change schema is instantiated in intensional contexts and discussed the relationship between intensional and evidential contexts. We assumed that an assertion must 
$\unicode[STIX]{x03C6}$ requires information that supports the speaker’s evidence for 
$\unicode[STIX]{x03C6}$ and proposed that the speaker’s receipt of this evidence is understood as an event, thereby facilitating the accommodation of the event required by BTA schema. Other epistemic-stance indicators, such as probably, differ from must in that their interpretive contributions alleviate the need to accommodate an event required by the BTA. They do so by identifying this event with the source of indirect evidence from which the speaker draws her assertion.
The analysis offered here differs from prior analyses that view the connection between evidential and modal implications of aspectual constructions through a diachronic lens, as primarily a grammaticalization problem. We treat it as an inferencing problem and a semantic-constraint-satisfaction problem. We see the fusing of aspectual and epistemic implications in BTA sentences, and in particular present-tense sentences, as the product of a reconciliation procedure in which a knowledge state correlates with a resultant state. By highlighting the role of state assertions in triggering acts of pragmatic reasoning, this case study also illustrates the need for an aspectual ontology that includes events, states and times, echoing the view of Parsons Reference Parsons1990, Altshuler Reference Altshuler2016 and Altshuler et al. Reference Altshuler, Parsons and Schwarzschild2019. We found that the BTA could not be analyzed purely in terms of times, and in this respect, the aspectual analysis offered here goes beyond time.
