1.1 Goals

Bergen (2016) argued that that what he calls ‘stress’ (= emphasis), characterized in English by “increased loudness, duration, and changes to the fundamental frequency”, has two series of effects that are not properly unified in current analyses. One series pertains to the realization of focus, typically analyzed within Alternative Semantics (e.g. Rooth 1996): contrastive focus as in (1)a, association with an overt operator (such as only) as in (1)b, exhaustification (possibly by a covert operator akin to only, Exh) as in (1)c (see Fox and Spector 2018 for the last case).

But Bergen notes that another series of semantics effects is not currently captured within Alternative Semantics. It pertains to the intensification of adjectives, as in (2).

Bergen argues that this is part of a broader pattern in which stress, for pragmatic reasons, serves to strengthen the truth-conditional contribution of a clause. In essence, stress is a costly signal that serves to reduce noise, i.e. the risk that the message will be corrupted during transmission. But due to its cost, stress also signals that the relevant part of the signal carries particular importance, hence a strengthening of its truth conditions.

While the data discussed by Bergen seem clear enough, the claims are controversial: are the phenomena in (2) genuinely related to those in (1)? And if so, are they a challenge to Alternative Semantics? The controversy only deepened when Wagner (2020) noted that in spoken language the unity of focus and intensification is at best partial: focus doesn’t just require accenting the focused element but also deaccenting the unfocused (given) parts, whereas no such requirement holds for intensification. This might suggest that in the end the apparent connection between (1) and (2) is accidental.

Our original goal was to determine whether the cluster of phenomena that Bergen takes to be unified by stress form a natural class relative to other properties in sign language. Specifically, we asked whether eyebrow raising (henceforth Brow Raise) in American Sign Language (ASL), which is known to have among others the functions in (1) (e.g. Schlenker et al. 2016), also has the functions in (2). This was part of a multi-year collaboration between a semanticist and a consultant (and co-author) who is a native signer of ASL, with elicitation methods that have been refined over the years, as discussed below. Due to the complexity of the data, we only focused on ASL versions of (1)a,b and (2). We first obtained a positive result: in our data, Brow Raise can clearly intensify adjectives. But something unexpected happened in the process: the native signer among the authors noticed that the information-theoretic functions in (1)a,b can usually be distinguished by timing from the intensification function in (2)a; while Brow Raise before an expression can serve to mark focus, it has much greater difficulty marking intensification.

Correspondingly, this article has three main goals. First, we establish that Brow Raise in ASL can have an intensification function in addition to its information-theoretic functions; this is to our knowledge a new finding, one that provides a new argument for Bergen’s claim that focus and intensification form a natural class. Second, we show that in most cases the two functions can be distinguished by timing: Brow Raise on an expression can have either function, but Brow Raise before an expression usually only has the information-theoretic function (LSF examples that replicate this generalization are discussed in an appendix). The facts are subtle, however, as an intensification function can to some extent be regained in preposed position if Brow Raise is heightened (= involves higher eyebrow raising).

We then discuss the consequences of our findings for theories of focus and intensification. We first sketch an account within Alternative Semantics: we develop a new account of intensification by focus, but we note that some assumptions are currently ad hoc, and fail to account for the fact that heightened preposed Brow Raise can have an intensificational effect. We then develop an analysis that can more easily accommodate the latter fact within a simplified version of Bergen’s noise-reduction analysis. While it needs auxiliary assumptions to derive the data, these might be rather plausible.

1.2 Brow Raise

But first, what is the semantics of Brow Raise? It is uncontroversial that it can have an information-theoretic role, including to mark focus. But the diversity of its functions has made a unified analysis elusive. Quer (2016) offers a helpful typology of extant approaches (however it must be borne in mind that different authors base their conclusion on different sign languages).

1. The prosodic view takes sign language Brow Raise to correspond to certain prosodic properties in spoken language. In Dachkovsky’s analysis “Brow Raise corresponds to the meaning of the High boundary tone in many spoken languages” (Sandler 2011, following Dachkovsky 2005 and Dachkovsky and Sandler 2009). Functionally, Brow Raise indicates that “the phonological or intonational phrase marked by it is to be followed by another constituent, produced either by the same interlocutor or, in the case of yes/no questions, by another” (Sandler 2011). While the authors base their analysis on data from Israeli Sign Language, Sandler (2011) takes it to extend to the ASL data discussed by Wilbur and Patschke (1998).

2. By contrast, other researchers take Brow Raise to express certain morphosyntactic or semantic properties.

   1. For Neidle et al. (2000), ASL Brow Raise marks the c-command domain of a morphosyntactic feature.

   2. For Wilbur and Patschke (1998), it marks A-bar (= non-argumental) positions associated with [-wh] operators in the syntax.

   3. More recently, Wilbur (2012) takes ASL Brow Raise to mark the restriction of dyadic operators. For her, “dyadic operators apply to various constructions: conditionals, interrogatives, focus structures, relatives, and generics (…). In ASL, the part that restricts subsequent interpretation is marked with br [= Brow Raise]: a conditional clause provides the conditions under which the next clause is likely to hold; without ‘br’, the two clauses are read as conjoined.”¹

Wilbur (2012) takes the stereotypical case of focus to involve association with a particle such as only, as in Rooth’s analysis (e.g. Rooth 1996). Schlenker et al. (2016) discuss ASL and LSF instances of Brow Raise marking exhaustive focus (which can be analyzed in terms of a covert only), but also contrastive focus. Wilbur’s analysis might have to be slightly extended to capture the latter cases.²

On various theories, including Dachkovsky and Sandler’s prosodic view and Wilbur’s dyadic restriction view, it is unsurprising that Brow Raise should have focus-related uses. This function might be cognitively central since it is also found as a co-speech gesture marking focus in spoken language (Dohen and Loevenbruck 2009). On the other hand, the intensification function of Brow Raise has to our knowledge rarely been discussed, and is a central topic of our investigations.

1.3 Structure

The rest of this piece is organized as follows. We summarize the debate about Bergen’s proposal in Section 2. Turning to sign language, we introduce our elicitation methods and transcription conventions in Section 3. In Section 4, we show that contrastive focus and association with focus can be marked by Brow Raise on or right before an expression. In Section 5, we show that Brow Raise can also intensify adjectives, but that this requires that it appear on an expression, unless Brow Raise is heightened. An analysis within Alternative Semantics is sketched in Section 6. In Section 7, we present a simplified version of Bergen’s noise-reduction theory: it can immediately account for the dual (focus-related and intensificational) function of Brow Raise, and it can also account for the distinction between Brow Raise on vs. before an expression, but at the cost of additional (if relatively plausible) assumptions. We present an extension of our main generalizations to a highly iconic construction involving a helicopter path in Section 8, before concluding in Section 9. (Appendix I includes technical notes, Appendix II outlines a preliminary replication in LSF, and Appendix III discusses a highly simplified (but still quantitative) version of a noise-based analysis.)

2.1 Bergen’s proposal

In each of the examples in (2) (e.g. Alice is SMART), stress intensifies the adjective and thus strengthens the truth conditions of the clause it appears in. For Bergen (2016), this is part of a broader pattern: even outside of the adjectival domain, stress alone can strengthen truth conditions. A case in point is that of quantifiers, as in (3). Their implicit domain restriction is usually determined by contextual consideration, but stress can modulate the domain restriction, in different directions for different quantifiers: for every and no, the effect is to enlarge the domain; for some, it is to narrow it.

Why should stress have such diverse effects on implicit quantifier domain restrictions? Bergen argues that in each case, stress strengthens the truth conditions. To do so for a clause with a universal positive or negative quantifier (e.g. every girl, nobody), one must enlarge the domain: nobody among Ann, Bill, Carol and Don brought presents is a stronger statement than nobody among Ann, Bill and Don brought presents. By contrast, to strengthen the truth conditions of an existential quantifier (e.g. some of the students), one must narrow the quantifier domain: some of the students among Ann, Bill and Carol passed the test is a stronger statement than some of the students among Ann, Bill, Carol and Don passed the test. In fact, the domain may arguably be restricted to a singleton individual (as in Schwarzschild 2002), hence a quasi-referential reading.³

Bergen (2016) develops a new analysis within the Rational Speech Act model of pragmatics (e.g. Goodman and Frank 2016; Franke and Jäger 2016; and Bergen et al. 2016). His leading idea is that, as in any signal transmission, there is a slight risk of corruption (henceforth ‘noise’⁴), and that the function of stress is to reduce it. He then shows that, in simple cases at least, the phenomena in (1), (2) and (3) can be explained by positing that the speaker uses stress to reduce, at some cost, the risk of corruption of a certain part of a message. Doing so signals that that part carries a particularly important function, and this inference can be exploited for communicative purposes by way of recursive reasoning (the addressee reasons on the speaker’s intentions, the speaker takes into account the addressee’s reasoning, etc); the strengthening effect follows.

2.2 Wagner’s objection

Following Wagner (2020), a reviewer states the following objection.⁵ There are multiple ways to reduce noise, but in English they are insufficient to mark focus unless they are accompanied by a shift in prominence. This shift involves both reducing the non-focused (= given) expression (a reduction marked below with angle brackets <…>) and boosting the focused element by increasing its duration, pitch and intensity (this is marked by capitalization). Consider (4):

As the reviewer notes, “the question in the context requires wants coffee to be metrically less prominent than Ede, as in B1-B3’s responses. (…) We can add to the prominence of Ede by lengthening it absurdly (B2), or repeating it over and over again (B3), but crucially all of these strategies are not sufficient to satisfy the constraint that focus imposes: we also have to reduce ‘wants coffee’, since B4 and B5 sound incoherent”. Things are very different with intensification: lengthening and repetition suffice to mark it in (5)B1-B2, while deaccenting the NP is prohibited (because it is semantically in focus) in (5)B3.

To summarize, the problem is twofold: (i) prominence must be accompanied by deaccenting in the case of focus but not of intensification; (ii) various means of noise reduction (such as repetition) can be used to effect intensification, but not focus.

2.3 Outlook

Taking into account Wagner’s objection, we are led to three main theoretical possibilities, with different expectations for the signed modality, and different challenges.

Option 1: No unification: One possible conclusion is that the project to unify focus and intensification is just wrong-headed: it might be an accident that similar mechanisms (involving pitch, duration and loudness) are sometimes fond in both domains. It might even be that Bergen’s noise-reduction-based analysis is correct for intensification, but not for focus. On this view, we don’t expect that in signs the same means should be employed to mark focus and intensification.

Since by Wagner’s objection unification between focus and intensification cannot be complete, we are left with two ‘partial unification’ views: one within Alternative Semantics, and one within Bergen’s own framework.

Option 2: Partial unification within Alternative Semantics: Focus and intensification could be partly unified along the lines of Alternative Semantics: focus involves both reduction and prominence, as in Wagner’s objection, while intensification just involves prominence. On this view, we could expect sign language to employ in part the same mechanisms to mark focus and intensification. For instance, on the prosodic view, Brow Raise might be expected to be the counterpart of intonational patterns in speech that can mark both focus and intensification. On a theoretical level, the main challenge is to explain how Alternative Semantics can derive intensification (in either modality).

Option 3: Partial Unification within Bergen’s noise-based analysis: Alternatively, one may effect a partial unification within Bergen’s noise-based framework. What focus and intensification have in common is already clear from Bergen’s framework. In sign, mechanisms that can reduce noise (such as increased duration and greater sign amplitude) can be expected to realize both focus and intensification. Brow Raise could play this very role, for instance because it brings attention to a particularly important part of the message. Still, by Wagner’s objection, the challenge would still be to explain how reduction is to be accounted for in the case of focus (but not intensification).

This challenge might not be unsurmountable. Adding emphasis has the benefit of reducing noise but the drawback of being more costly, and it should thus be restricted to the most important parts of a message. By symmetry, deaccenting might have the drawback of increasing noise, but the benefit of decreasing cost, and it should thus be used for the less important parts of a message, notably ones that are given. Developing this view is a separate enterprise, but doing so might help address Wagner’s objection within Bergen’s framework.

In the rest of this paper, we will discuss three main findings from ASL (with an initial replication in some LSF examples in Appendix II):

1. One and the same formal device, Brow Raise, has focus- and intensification-related uses in ASL, which suggests that Bergen’s unification was not wrong-headed, against Option 1. This leaves Options 2 and 3.

2. But an unexpected finding in view of the current debate is that focus and intensification are distinguished along new lines by the sign language data: focus can be marked by Brow Raise on or before an expression; intensification usually requires Brow Raise on an expression. In Wagner’s data, focus is more demanding than intensification, since the latter allows for diverse means of emphasis (including repetition), and does not involve deaccenting. In our sign language data, intensification is more demanding, since it requires Brow Raise on rather than before the target expression.

3. On a theoretical level, we will sketch ways to develop Options 2 and 3. Within Alternative Semantics, we will posit an operator (‘noteworthiness’) which is trivialized in standard focus-related cases but strengthens the truth conditions in intensificational cases. Within (a simplified version of) Bergen’s theory, we will show that some (arguably plausible) assumptions about the relative cost and noise-reducing behavior of different versions of Brow Raise can account for the data.

4.1 Movement vs. prosody in ASL focus marking

How is focus marked in ASL? Wilbur (1999) establishes that “the primary indicator of stress marking is the significant increase in peak velocity of prominent signs”, and that as in English “a single prominence is assigned to the right-most lexical item in the phrase”, but that unlike in English prominence cannot be moved, with the result that focus is preferably realized by movement (as in other languages that Vallduví 1991 calls [-plastic], such as Catalan). Still, there are cases in which the focused elements remain in situ (some appear in Wilbur and Patschke 1998 and Lillo-Martin and Quadros 2008).

Schlenker et al. (2016) investigated ASL and LSF examples in which movement is inapplicable, and showed that prominence and non-manuals alone can realize two types of focus: contrastive, and exhaustive (yielding readings akin to those obtained with a covert only). As they concluded, “increased amplitude, speed acceleration, longer hold times, and raised eyebrows were found in ASL and LSF alike (very systematically for raised eyebrows and forward leans/head nods)”.⁸ But since they were interested in the clusters of properties that can realize focus, they did not tease apart the specific role of Brow Raise. This is what we attempt to do in the rest of this piece, by investigating paradigms that only differ, to the extent possible, with respect to Brow Raise, both on and before a word (producing truly minimal pairs is very difficult, hence our rider ‘to the extent possible’).

4.2 Contrastive focus

We start by modifying two paradigms from Schlenker et al. (2016) in order to assess whether contrastive focus can be marked by way of Brow Raise not just on a word, but also before a word. We asked for acceptability judgments both for the target sentence as a whole, and for the target word (whose realization changes from sentence to sentence). The latter judgments were more informative, which is unsurprising in view of the relative subtlety of prosodic/non-manual cues, as they could easily get drowned by other properties of the sentence. We thus focus on acceptability of the target word.

Example (9), modified from Schlenker et al. 2016, contrasts the words A_{NN_a} AND B_{ILL_b} in the first clause with the words A_{NN_a} OR B_{ILL_b} in the second.

(9)	(Acceptability of OR)9
	Context: The speaker is an ASL instructor teaching students to sign 3-word sequences.
	IX-2 WILL SIGN ‘ANN_a AND BILL_b’, FINISH ‘ANN_a ____ BILL_b’
	a.	3.7 OR	(2, 4, 5)
	b.
	c.
	d.
	e.
	f.
		‘You will sign ‘ANN AND BILL’, then ‘ANN OR BILL’. (ASL, 35, 0694; 3 judgments)
		Anonymized video: https://youtu.be/S2XMpFlClbE

Due to the contrast with AND, OR is degraded when it appears without emphasis, as in (9)a. With diverse means of emphasis including Brow Raise, as in (9)b, the word is acceptable. It continues to be acceptable when just greater amplitude and forward lean are used, as in (9)c. Crucially, Brow Raise alone can be used as well, and this is the case whether it appears on the word, as in (9)d, or right before, as in (9)e (unsurprisingly, preposed Brow Raise combined with further means of emphasis is also acceptable, as seen in (9)f). It should be noted that the Brow Raise found in (9)d,e was transcribed as ‘heightened’, although our intention was to have even more minimal pairs with the same level of Brow Raise across sentences.

The paradigm in (7) is slightly less telling because the preposed version of Brow Raise co-occurred with greater manual amplitude. With this limitation, the findings are compatible with those in (9). The paradigm uses five letters of the manual alphabet to stand for five proper names (a standard device in ASL): A for Ann, B for Bill, etc. The name for B_ILL contrasted with C_HARLES.

(10)	(Acceptability of BILL_b)
	Context: The speaker is trying to teach groups of students to work together.
	TODAY IX-1 SEVERAL MEETING-rep FIRST MEETING ANN_a CHARLES_b EDITH_c DENIS_d, FINISH ANN_a _____ EDITH_c DENIS_d
	a.	1.3 BILL_b
	b.
	c.
	d.
	e.
	f.
	‘Today I have several meetings. My first meeting is with Ann, Charles, Edith and Denis, then [I meet] with Ann, Bill, Edith and Denis.’
	(ASL, 35, 0684; 3 judgments)
	Anonymized video: https://youtu.be/gLrLI-LsFDQ

In (10)a, not marking contrastive focus in a clearly contrastive environment is dispreferred. A cluster of focus-marking strategies including Brow Raise is used in (10)b, with ceiling acceptability. (10)c uses the same marking strategies but without Brow Raise, with less acceptable results. (10)d uses Brow Raise on B_ILL, with a head nod (which wasn’t intended). (10)e has Brow Raise right before B_ILL, and as mentioned an (unintended) increase in manual amplitude. The result is acceptable, and likely due to Brow Raise rather than to greater amplitude, since the latter gave rise to decreased acceptability in (10)c. (10)f has a cluster of focus-marking properties on B_ILL, and also preposed Brow Raise, again with high acceptability.

The conclusion as this point is that contrastive focus preferentially involves Brow Raise (and can involve further means of emphasis as well), but that Brow Raise can be realized on or just before the focused word, with little difference. Future work should seek to produce even more minimal pairs to further buttress these conclusions.

4.3 Association with ONLY

Some particles, such as only in English, associate with focus and yield different truth conditions depending on which item is focused, as in (11). This makes it possible to test the effect of focus marking by way of inferential rather than acceptability judgments.¹⁰

The paradigm in (12) tests the inferential effect of Brow Raise appearing on or right before the last word of the sentence, the pronoun IX-b. The advantage of investigating the last word is to avoid ambiguities that arise when Brow Raise precedes a multi-word sequence: it may become unclear whether Brow Raise modifies just the following word or a longer sequence. (12)a is a control with no emphasis, while (12)b involves multiple means of emphasis: greater sign amplitude, a forward lean, a head nod, and Brow Raise. All other examples involve only Brow Raise, on or before the pronoun, and in two versions: normal Brow Raise, heightened Brow Raise (with higher eyebrows).¹¹ We intended the production of (12)c to involve normal Brow Raise and (12)d to involve heightened Brow Raise, but both turned out to be transcribed as heightened. Preposed Brow Raise was of normal size in (12)e and heightened in (12)f, and (unintentionally) accompanied with a head nod in (12)d.¹²

(12)	(Acceptability of the last word of the sentence.)
	YESTERDAY IX-1 1-MEET JOHNa MARYb. IX-1 ONLY PERMIT IX-a a-HELP-b ____ .
	a.	7 IX-b
	b.
	c.
	d.
	e.
	f.	strong
		‘Yesterday John and Mary. I only allow him to help her / HER.’ (ASL, 35, 1518; 3 judgments)
		Anonymized video: https://youtu.be/OT8eOJU0KWg

Inferential effects were assessed by way of the difference between the target sentences, with emphasis on the last word, and (12)a, where no word was emphasized. The effect of focus on the last word was expected to only disallow one alternative, namely that John help someone other than Mary (since the pronoun referring to Mary was emphasized). This was indeed found in (12)b-f.¹³ In (12)a, the absence of emphasis made it underspecified what ONLY associated with. In view of the consultant’s responses, it seemed to associate with the entire proposition, thus disallowing all conceivable alternative propositions, namely (i) that someone other than John help Mary, (ii) that John help someone other than Mary, (iii) something else, which the consultant took to be that Mary help John.

Importantly, in all cases, inferential effects are broadly indicative of association of the final pronoun with ONLY: Brow Raise right before the final word seems to work like Brow Raise on the final word, though possibly less clearly. There was no clear difference between normal and heightened Brow Raise. A limitation of this paradigm (and of the next one) is that we can’t exclude the possibility that the head nod was crucial to mark focus in the case of preposed Brow Raise in (12)e.

A related pattern can be seen in (14). As before, the target inference is that the signer disallows that John helps someone other than Mary.¹⁴ All the examples with emphasis, in (14)b-f, give rise to the inference that the signer disallows John from helping someone other than Mary, and doesn’t disallow anything else (among the options offered). Without emphasis, as in (14)a, ONLY seems to associate with the entire embedded proposition, hence all conceivable propositions are disallowed. Here too, we can’t exclude the possibility that a head nod plays a role in focus marking in (14)e,f.¹⁵

(14)	(Acceptability of the last word of the sentence)
	YESTERDAY IX-1 1-MEET JOHNa MARYb. IX-1 ONLY WANT IX-a a-HELP-b ____.
	a.	7 IX-b
	b.
	c.		normal
	d.		strong
	e.		normal
	f.		strong
		‘Yesterday I met John and Mary. I only want him to help her / HER.’ (ASL, 35, 1476; 3 judgments)
		Anonymized video: https://youtu.be/Ar-7mmkWLPY

Importantly, there seems to be little difference between Brow Raise on or before an expression: all signal, to some extent at least, focus on the relevant word.

In sum, in our data, Brow Raise can mark focus on an expression, both in the case of contrastive focus and association with ONLY. There seems to be little difference between Brow Raise on a word and Brow Raise right before it. But a limitation is due to the fact that our paradigms are not entirely minimal due to the presence of head nods that may mark focus in tandem with preposed Brow Raise, in particular. As we will now see, when it comes to intensification, timing seems to matter more.

5.1 Diversity of intensification strategies

As we will now see, Brow Raise also has intensification functions. But it should be kept in mind that there are diverse modulations that can help realize intensification in sign language.¹⁶ Summarizing earlier literature, Aonuki (2019) mentions that intensification in ASL has been described as involving “longer duration of an initial hold and presence of a (longer) final hold, enlargement or addition of a movement path, and nonmanual components (Klima & Bellugi 1979; Padden 1988; Brentari 1998; Sandler & Lillo-Martin 2006; Wilbur, Malaia, & Shay 2012)”. Concerning non-manuals, Wilbur et al. 2012 tangentially discuss “frown on face” and “head tilt away from neutral”, but not Brow Raise.

In a production study with a non-native fluent signer of ASL, Aonuki (to appear) finds “statistical support for longer duration of initial and final holds as well as enlargement of path movement under intensification”. Concerning non-manuals, she found that “intensified signs show increased involvement of head or torso movements aligned with the manual movement in rhythm or direction”, but she did not investigate other non-manuals.

Displaying an intensification function of Brow Raise is thus of interest in its own right, since it has not been well documented in the earlier literature. As mentioned in the introduction, it is also an important theoretical question to determine (i) whether it should be unified with focus-related uses, and if so (ii) how. In addition, we will now see that the relevant data raise a new puzzle because in this case the two realizations of Brow Raise mostly part company: Brow Raise on a word can have the intensification function, whereas this seems more difficult for Brow Raise before a word. Importantly, in view of our data, we cannot claim that the effect is categorical. Rather, Brow Raise before a word might be a less effective means of intensification than Brow Raise on a word, and this can be compensated for (to some extent at least) by using heightened Brow Raise in a preposed position.

5.2 Initial paradigms with Brow Raise

We first sought to assess how Brow Raise on its own compares to other properties that can help mark focus, as in the paradigm in (16). Throughout, we translate intensified adjectives using capitals in the English version, since the adjective with emphasis allows for the intensified reading; the reader may read these with an explicit modifier (e.g. very tall) if they prefer.¹⁷

(16)	(Acceptability of the second word of the sentence.)
	PETER _____. JOHN TALL17.
	a.	7 TALL
	b.
	c.
	d.
	e.
	f.
		‘Peter is TALL. John is tall.’ (ASL, 35, 1512; 3 judgments)

Starting from a neutral realization of TALL in (16)a, we added in (16)b a normal emphasis effected by various manual and non-manual means, including Brow Raise. This yielded a clear intensificational effect, diagnosed by way of inferential judgments: in (16)b but not in (16)a, an inference was obtained to the effect that Peter is taller than John. Removing Brow Raise while keeping all other means of emphasis preserved the semantic effect, as seen in (16)c. In (16)d, only Brow Raise was used to emphasize the predicate, with a possibly weakened but still clear intensificational effect (Brow Raise was unintentionally realized in its heightened form). Importantly, Brow Raise before the word did not yield clear intensification, as in (16)e. Comparable judgments were obtained when the order of the predicates was reversed, as in the paradigm in (18) (here too, preposed Brow Raise in (18)e was smaller than Brow on TALL in (16)d).

(18)	(Acceptability of the last word of the sentence)
	JOHN TALL. PETER _____.
	a.	7 TALL
	b.
	c.
	d.
	e.
	f.
		‘John is tall. Peter is tall / TALL.’ (ASL, 35, 1508; 3 judgments)
		Anonymized video: https://youtu.be/vHEZGTBG9K8

Two possible conclusions could be drawn as this point. One is that Brow Raise before an expression just cannot intensify it. An alternative is that it can, but that the realization we picked was insufficiently strong. We will now see that more minimal paradigms provide a partial argument for the latter possibility.

5.3 Comparing normal and heightened Brow Raise

The paradigm in (20) assesses the effect on intensificational readings of two parameters: the size of Brow Raise (normal or heightened), and its timing (on or right before an expression). There are two main results: (i) heightened Brow Raise marks intensification better than normal Brow Raise; (ii) the intensificational effect is reduced when Brow Raise occurs before than on a word. This is diagnosed by the strength of the inference that Peter is taller than John.

(20)	(Acceptability of the second word of the sentence)
	PETER ____. JOHN TALL.
	a.	7 TALL
	b.
	c.
	d.
	e.
		‘Peter is tall / TALL. John is tall.’ (ASL, 35, 1504; 3 judgments)
		Anonymized video: https://youtu.be/-fRd_wSaRvg

In our initial paradigm in (20), the intensified word comes first. Partly similar effects are obtained when it comes last, as in (22): normal Brow Raise on but not before TALL leads to intensification. A bit more clearly than in (20), a heightened Brow Raise before the word does give rise to an intensification-like effect, albeit a reduced one. Brow Raise before TALL fails to yield any clear intensification.

(22)	(Acceptability of the last word of the sentence)
	JOHN TALL. PETER ____.
	a.	7 TALL
	b.
	c.
	d.
	e.
		‘John is tall. Peter is tall / TALL.’ (ASL, 35, 1500; 3 judgments)
		Anonymized video: https://youtu.be/h3ZfTA57tYQ

In (24), we perform similar tests with the ASL word NEAR, assessing whether it means near or very near depending on whether it is intensified.

(24)	(Acceptability of the last word of the sentence)18
	IX-1 WANT XI-2 DRIVE ____.
	a.	7 NEAR
	b.
	c.
	d.
	e.
		‘I want you to drive near / NEAR.’ (ASL, 35, 1254; 3+1 judgments)
		Anonymized video: https://youtu.be/5Y8tHF9vWLY

To facilitate inferences, the written questions explicitly suggested that ‘near’ counts as 2 miles or less, ‘very near’ counts as 1 mile or less, which made it possible to ask by way of multiple choice questions which distances are desired: (i) ≤1 mile (ii) between 1 and 2 miles (iii) >2 miles. Contrasts were found: without emphasis, as in (24)a, NEAR allows for options (i) and (ii) (but not (iii)). With normal or heightened Brow Raise on NEAR, as in (24)b,c, option (ii) becomes less acceptable, indicating a ‘very near’ interpretation. With normal Brow Raise before NEAR, as in (24)d, option (ii) becomes more acceptable again, which is indicative of the possibility of a ‘near’ interpretation. The effect is less clear with heightened Brow Raise before the modified word, as in (24)e: it seems to be somewhat compatible with an intensificational effect.

Similar results were found with SHORT in (26), where heightened but not normal Brow Raise yields intensification when it appears before the adjective. We must note that our paradigms were not, despite our best efforts, entirely minimal, since a head nod occurred in (24)d,e and (26)d,e (the fact that we didn’t obtain intensification suggests that, in this paradigm at least, a head nod can’t have this function).

(26)	(Acceptability of the last word of the sentence)19
	IX-1 WANT POSS-2 LECTURE ____.
	a.	7 SHORT
	b.
	c.
	d.
	e.
		‘I want your lecture to be short / SHORT.’ (ASL, 35, 1256; 3+1 judgments)
		Anonymized video: https://youtu.be/xPU5CdqXCqw

In sum, Brow Raise on a gradable expression can serve to intensify it. The intensificational effect is reduced or removed when Brow Raise occurs before an expression. For normal Brow Raise, intensification seems to disappear when the non-manual occurs before the word, but for heightened Brow Raise, a reduced intensificational effect may still be found.

5.4 Interim summary and initial LSF replication

The generalizations obtained are stated in (28).

As we show in Appendix II, we replicated similar contrasts pertaining to generalizations (28)a,b(i)–(iia) in several LSF paradigms (but without being in a position to make claims about the generality of this phenomenon).

7.1 A simplified version of Bergen’s analysis

We start by summarizing a simplified Bergenian analysis of two cases: exhaustification as in (1)c, and adjectival strengthening as in (2)a.

Consider the case of Sam will invite Ann OR Bill. Bergen’s goal is to derive the exclusive (exhaustive) reading by pragmatic means, without positing an exhaustivity operator in the syntax. Bergen’s starting point is that there is always a small risk of signal corruption, whereby or could be misheard as and (the probability may be very small). One can decrease this risk by stressing the word, yielding a benefit, which we will call b. But this comes at a slight cost, which we will call c. If the speaker is entirely rational (which isn’t the case in Bergen’s actual analysis), it’s only worth reducing the risk of corruption if the benefit derived in so doing is greater than the cost, i.e. if b > c. Now we consider two situations:

• Situation 1: the speaker knows that Sam will invite one of {Ann, Bill} but not both.

• Situation 2: the speaker doesn’t know whether Sam will invite just one or both of {Ann, Bill}.

It is clear that the speaker will consider the risk of misperception of or as and as being worse in Situation 1, where it provides clearly incorrect information, than in Situation 2, where it might provide correct information. Thus the use of stress will tend to be associated with Situation 1 and for this reason it will come with an exclusive inference akin to exhaustification (whereby p or q is strengthened to p or q but not both). The addressee who takes this into account will thus increase her belief (i.e. her probability) that or was used exclusively. And the speaker who takes into account the addressee’s behavior may thus use stress to signal exhaustification. Formalizing this reasoning requires a detailed analysis within the Rational Speech Act model, as developed by Bergen.

The reasoning is rather similar with adjectival strengthening. Following the literature, Bergen assumes that tall and short come with contextually determined thresholds, so that Bob is tall is deemed true just in case his height is above the height threshold θ_tall, and Bob is short is true just in case his height is below a threshold θ_short. The values of θ_tall and θ_short are not known with certainty, but not anything goes: it is very likely that 1m90 counts as being above the ‘tallness’ threshold θ_tall, while 1m75 might or might not be above the threshold. Similarly, 1m60 is very likely to count as being below the ‘shortness’ threshold θ_short, whereas 1m75 might or might not be below that threshold. Here too, there is a risk that tall might be misperceived as short, but the risk can be mitigated, with a benefit b, in case the speaker stresses the word, at a cost c – which is worth doing if b > c. We consider the sentence Bob is tall, and we consider once again two situations:

• Situation 1: the speaker knows that Bob is very tall, e.g. 1m90.

• Situation 2: the speaker knows that Bob is just tall, e.g. 1m75.

In Situation 1, if tall gets misperceived as short, the addressee will almost certainly form incorrect beliefs, as the threshold for short is unlikely to classify 1m90 as short. In Situation 2, the risk that the addressee forms incorrect beliefs is a bit smaller, because there is a greater chance that the threshold for short classifies 1m75 as short. For instance, Bob might count as tall if his height is ≥ 1m70, while he might count as short if his height is ≤ 1m75, and the overlap would ensure that if tall is misheard as short, no incorrect beliefs are formed in this case.

As a result, the speaker will tend to use stress more in Situation 1 than in Situation 2. The addressee that takes into account the speaker’s behavior will thus tend to associate stress on tall with ‘very tall’ situations. And the speaker S who takes into account this behavior on the addressee’s part will be able to signal that S has in mind a ‘very tall’ situation by stressing the adjective. Here too, the details, which are complex, are worked out in Bergen 2016.

7.2 Brow Raise and noise reduction

Bergen (2016) notes that “there are three main acoustic changes associated with prosodic stress: increased loudness, duration, and changes to the fundamental frequency (Breen et al. 2010). An utterance that is louder and longer is less likely to get swamped by sounds in the environment, while changes in pitch will focus the addressee’s attention on the utterance.”

In line with these two types of noise reduction (increasing signal clarity and focusing the addressee’s attention), the role of Brow Raise may be viewed in two ways. As noted in Section 1.2, Sandler (2011) argues (following Dachkovsky) that Brow Raise has the same semantic function as “the High boundary tone in many spoken languages” (Sandler 2011; Dachkovsky 2005; Dachkovsky and Sandler 2009), which in turn might be consonant with Bergen’s discussion of the salience-related effect of higher pitch.²³ Independently, one could postulate that Brow Raise might be a signal that one’s eyes need to be widened, which in turn has been shown to enhance stimulus detection (Lee et al. 2014): this might lie at the source of the signal that the relevant part of the message is particularly important. In this way, Brow Raise might reduce noise by focusing the addressee’s attention on a particular part of the message.

The noise-reduction analysis can be further strengthened by noting that, in our data, Brow Raise is part of a cluster of properties that includes several other manual or non-manual modifications such as forward lean, greater sign amplitude, and head nod, as discussed above. This can be seen in two ways. First, when the consultant was asked to realize emphasis on a word with all available means, these did not just include Brow Raise, and the result was at least as acceptable as with Brow Raise alone, as can be seen for focus in (10)b, (9)b, (12)b, (14)b, and for intensification in (16)b and (18)b. In particular, the latter two cases involved the following form, with not just heightened Brow Raise, but also a forward lean, a head nod and increased amplitude.

(37)

Second, using these other means to the exclusion of Brow Raise sometimes lead to acceptable results as well: this was the case for focus in (9)c (whereas for reasons we don’t understand (10)c was more degraded) and for intensification in (16)c and (18)c. And just as in Bergen’s description of the English acoustic facts, some of these means (such as greater sign amplitude) can be taken to help with sign perception, while as mentioned Brow Raise might indicate that the addressee should pay special attention to a certain part of the message. Head nods might fall in the latter category as well, while forward leans might fall in the first category if one thinks that by moving closer to the addressee one is making the sign easier to perceive.

Despite these arguments for the noise-reduction analysis, Bergen’s view is faced with two challenges. First, Wagner’s objection shows that focus involves prominence shift but intensification does not: for spoken language at least, a component must be added to Bergen’s analysis to account for deaccenting. Second, Bergen’s unitary analysis must explain why focus but (usually) not intensification is compatible with Brow Raise before the target expression.

7.3 Sketch of a noise-based account

Without providing a full account, we will sketch a general direction, mentioned by Leon Bergen (p.c.). The main ideas are as follows.

1. Brow Raise before an expression is a less efficient way of reducing noise than Brow Raise on an expression. Why this is would need to be determined, but we can note that Brow Raise before an expression is plausibly much shorter than Brow Raise on an expression, simply because in the latter case it must span the duration of at least one word.²⁴

2. Brow Raise before an expression is less costly than Brow Raise on an expression. Here too, one might invoke shorter duration to justify the difference (this is in part speculative since duration isn’t the only thing that enters into cost).

3. Under certain conditions, (i) and (ii) balance each other out and one can thus optionally use Brow Raise on or before an expression; this is the case of focus-related uses.

4. When the benefit of reducing noise is greater, Brow Raise on an expression wins out; this is the case of intensificational uses.

5. When the benefit of reducing noise is too low, it does not outweigh the cost of using Brow Raise, and no Brow Raise is used; this is the case for expressions that neither involve focus nor intensification.

To make things concrete, we will consider a single sentence, PETER TALL, which could be used in three kinds of situations depending on the Question under Discussion (QUD) and the speaker’s state of knowledge.

Intensificational situation: The QUD is {PETER TALL, PETER SHORT}, and the speaker knows that Peter is very tall.

Focus situation: The QUD is {PETER TALL, PETER SHORT}, and the speaker has no knowledge about how tall Peter is (but knows that Peter is tall).

Unmarked situation: The QUD is {PETER TALL, PETER SHORT, PETER FRENCH}, and the speaker has no knowledge about how tall Peter is (but knows that Peter is tall).

In each case, we need to compute the trade-off between the cost and the benefit of reducing noise. Here we assume for simplicity, that perception errors transform one element of the QUD into another (in other words, misperception is constrained by knowledge of the QUD). We can then order the cases of misperception as follows:

Strong error: The worst case of misperception arises in the intensificational situation. If PETER TALL is perceived as PETER SHORT, and the speaker knows that Peter is very tall, the information conveyed will most likely mislead the addressee about the state of the world.

Medium error: A less severe case of misperception arises in the focus situation: if PETER TALL is misperceived as PETER SHORT, but the speaker doesn’t know how tall Peter is, the information will probably but not necessarily contradict the state of the world. There is a situation in which the threshold for TALL is ≥ 1m70, the threshold for SHORT is ≤ 1m75, and Peter’s actual height ranges from 1m70 to 1m75. In this case, misperceiving TALL as SHORT won’t be as catastrophic as in the intensificational situation.

Weak error: Still less severe is the case of misperception that arises in the unmarked situation. Here two things could happen when PETER TALL is misperceived: it could be misperceived as PETER SHORT (say half the time), or as PETER FRENCH (half the time as well). In the first case, we get the same result as in the focus situation: the message conveyed will probably but not necessarily mislead about the state of the world. In the second case, the message conveyed is orthogonal to what the speaker intended, and thus it may or may not mislead about the state of the world. Since misleading is in this case less likely than in the case in which TALL was turned into SHORT, this is overall a less severe case of misperception that in the focus situation.

Still to make things concrete, we’ll assign numbers to these situations, assuming that the benefit is 3 if information is transmitted without error, and less than 3 if a perception error arises:

2 in situation of weak error, 1 in situations of medium error, and 0 in situations of strong error, as summarized in (38) (in a ‘real’ Rational Speech Act model, these values would be derived from the effect of different forms on the addressee’s beliefs).

We further need to specify how the chance of an error is affected by means of noise-reduction, here Brow Raise. We will see that with the assumptions in (39) we derive the desired results, namely that Brow Raise on an expression will be used in intensificational situations, Brow Raise on or before an expression will be used in focus situations, and no Brow Raise will be used in neutral situations (see Appendix III for a more general treatment).

These assumptions can be described as follows. Brow Raise on an expression is most efficient in reducing the risk of misperception – for simplicity, we take it to reduce the risk to 0. Next, Brow Raise before an expression leaves a 20% risk of misperception, followed by the absence of Brow Raise, yielding a 40% risk of error (we assign these probabilities for simplicity; real values are undoubtedly far smaller). The ordering by cost is the opposite: using no Brow Raise is free, Brow Raise before an expression has a cost of .3, Brow Raise on a word has a cost of .7. As mentioned, the differences in cost and efficiency might be justified on the basis of duration, although this is currently speculative.

We now need to compute the costs and benefits of TALL, ^TALL and ^-TALL. It will help to introduce some notations to refer to the cost of an expression e (= c(e)), to the probability it will be incorrectly perceived (= p(e)), and to the benefit obtained if the target expression is correctly perceived in a situation s (= b⁺(s)), as well as the benefit obtained if the target expressions is incorrectly perceived in s (= b^-(s)). These notations are summarized in (40). (We write b⁺(s) and b^-(s) rather than b⁺(e, s) and b^-(e, s) because the benefits are the same for TALL, ^-TALL, ^TALL, and thus do not depend on the expression e. The reason is that the three expressions have the same literal meaning, and thus the only thing that matters for the benefit they yield is whether or not they are correctly perceived. What differs across the three expressions is their cost, and the probability that they are incorrectly perceived.)

Now a signer that must choose an expression within the set {TALL, ^-TALL, ^TALL} has to balance the expected benefits and costs. The expected benefit of using an expression e in situation s is just the sum of the benefit obtained if e is correctly perceived and of the benefit obtained if e is incorrectly perceived, weighted by the relevant probabilities. The cost is just the cost of the expression, and the expected utility U(e, s) is the difference between the expected benefit and the cost. This is expressed in (41), where the third line is obtained by using the fact that in all cases b⁺(s), the benefit obtained if the expression is correctly perceived, is of 3 (as specified in the second column of (38)).

To illustrate, consider the expected utility when one uses ^-TALL (= Brow Raise before the word) in a situation of medium error (= a focus situation). Per (38)-(39), the probability of misperception is p(e) =.2, and the benefit when there is a misperception is b^-(s) = 1 (otherwise the benefit is 3). The cost of using this expression is c(e) = .3. So the expected utility is:

Similarly, if one uses ^TALL (= Brow Raise on the word) in the same situation, the benefits remain the same, but the probability of error and the cost change: the probability of error goes down to 0, while the cost goes up to .7. In this very special case, we obtain the same expected utility as for ^-TALL, which derives an optionality in this case, as shown in (43) (the second line is obtained by noting that the probability of error p(e) is now set to 0).

The expected utilities with the values in (38)–(39) are computed in (44), with maxima boldfaced in each column.

As desired, in a situation of strong error (i.e. an intensificational situation), Brow Raise on the expression maximizes utility: the utility obtained with ^TALL, 2.3, is higher than the utility that would be obtained with ^-TALL (= 2.1) or TALL (= 1.8). In a situation of medium error (i.e. a focus situation), Brow Raise on and before an expression are equal winners: both yield utility 2.3, which is higher than the utility obtained without Brow Raise (= 2.2). Finally, in an unmarked situation, maximal utility is obtained by not using Brow Raise at all: this yields utility 2.6, whereas ^-TALL and ^TALL yield utilities 2.5 and 2.3 respectively. While this just describes the speaker’s association between situations and signals, the addressee who takes into account the speaker’s reasoning will come to the same associations.

These results amount to an existence proof that, in a highly simplified framework, the desired results can be derived. Furthermore, the auxiliary hypotheses needed are not outlandish: positing that Brow Raise before an expression is both less costly and less efficient (to reduce noise) than Brow Raise on an expression makes some sense, especially because of its smaller duration.

There are many open questions in this analysis, as is explained in Appendix III, but it could prove fruitful in the future. Importantly, Bergen’s theory might be better positioned than our alternative-based analysis to explain why heightened Brow Raise can often intensify adjectives when it is preposed. The reason is that heightened Brow Raise might, at a cost, increase the benefit of the preposed version of Brow Raise, thus making its behavior closer to that of Brow Raise on an expression.²⁵

Addressing these fine-grained questions will require a detailed quantitative investigation that is beyond the scope of this paper.

9.1 Results and limitations

It goes without saying that our generalizations should be tested with further ASL consultants (our LSF data reported in Appendix II are particularly preliminary, since we just argue that there are some cases that replicate our main ASL generalizations); further examples should be investigated, especially in cases in which our paradigms were not as minimal as we had hoped. Still, we have arguably obtained the following results.

1. Brow Raise doesn’t just have information-theoretic uses in ASL (and LSF); in our data, it can also serve to intensify gradable constructions.

2. This can be seen as an argument for the claim in Bergen (2016) that focus and intensification have some properties in common. Bergen wanted to derive them from the same mechanism entirely; but in view of Wagner’s objection, partial unification is probably the best we can achieve, as a mechanism must be added to Bergen’s analysis to account for deaccenting (which arises with focus but not intensification).

3. While Brow Raise on an expression is ambiguous, normal Brow Raise before an expression lacks the intensificational reading. But heightened Brow Raise gives rise to some intensificational reading when it comes before an expression.

4. An analysis can be developed within Alternative Semantics on the assumption that (i) Brow Raise on an expression (but not before one) can focus-mark a degree variable, and (ii) Brow Raise makes a semantic contribution of its own (‘noteworthiness’). But our analysis requires positing a new operator, and doesn’t account for the possible fact that heightened Brow Raise can marginally have intensificational uses.

5. An alternative can be developed within the noise-reduction-based analysis of Bergen (2016). Within a highly simplified framework, relatively plausible assumptions about the cost and efficiency (in terms of noise reduction) of Brow Raise can derive the desired results.

6. In our ASL data, the dual functions of Brow Raise can be found in highly iconic classifier constructions, and Brow Raise can focus or intensify a subpart of an iconic representation.

9.2 Future directions

Besides being tested with further consultants, our investigation ought to be extended to further cases of emphasis-based intensification discussed by Bergen (2016), notably exhaustification as in (1)c and effects on quantifier domain restriction as in (3).

On a theoretical level, both analytical directions considered in this piece are highly simplified. The operator we posited within alternative-semantics would need to be refined and independently motivated. As for the noise-reduction analysis, it would need to be developed within Bergen’s Rational Speech Act model (which countenances bounded rationality), rather than in the model with perfect rationality we posited for reasons of simplicity.³⁰

Several important extensions could be considered in the future.

1. Eyebrow raising is known to mark focus in spoken language (Dohen and Loevenbruck 2009). Can it have intensificational uses as well? We conjecture that it can, at least when it appears on a pro-speech gesture, as in (51): our impression is that the second gesture, with eyebrow raising, lends itself to a meaning akin to ‘very big’, even when the manual gesture is kept constant.

(51)	John is but Peter is .

One would need a detailed investigation of the focus- and intensification-related uses of Brow Raise on pro-speech gestures (i.e. on gestures that fully replace some words). For highly relevant work, we refer the reader to the study of intensificational and mirative uses of an ‘eyes-wide-open’ facial expression, glossed as OO, in Esipova 2019a (esp. (4.28b)), Esipova 2019b (esp. (22b)), and Esipova 2021 (esp. (35)).

2. Is there a broader generalization to the effect that intensificational emphasis must be realized on an expression whereas informational focus can be realized before one? One could explore the behavior of pauses to mark an expression as focused, as in (52).

The question is twofold: (i) can association with focus and contrastive focus be realized in this way? (ii) can intensificational uses be produced with gradable constructions? While (i) requires more work, our impression is that (ii) should receive a negative answer: we believe that an intensificational reading of the second adjective is extremely difficult in (53)b, unlike (53)a.

Here too, the data will require a separate study.