Focus and Intensification in the Semantics of Brow Raise

We argue that in American Sign Language (ASL), Brow Raise has two sorts of functions that can be distinguished by timing: it may serve well-known information-theoretic functions that can, among others, realize focus; but it may also intensify gradable constructions – a far less well-known observation. While Brow Raise on an expression can fulfill both functions, Brow Raise right before an expression preferentially has an information-theoretic function. The main findings are replicated (in an appendix) on some examples from LSF (French Sign Language). Strikingly, these two functions mirror those found for ‘stress’ (= emphasis) by Bergen (2016), who argued for a unified analysis of information-theoretic and of intensificational effects. We sketch a unified analysis within Alternative Semantics, and discuss a further possibility within a simplified version of Bergen’s own theory of ‘noise-reduction’ (Bergen 2016). An extension of our ASL data shows that related generalizations hold when Brow Raise is applied to a highly iconic construction (here involving a helicopter path): depending on timing, Brow Raise may serve to evoke alternatives or to intensify part of the construction.


Goals
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) (1) Stress and focus a. Contrastive focus: I will introduce Mary to you and then I will introduce ANN to you. b. Association with focus: I only introduced ANN to Bill at the party.
→ I didn't introduce someone other than Ann to Bill at the party.
c. Exhaustification: Sam will invite Ann OR Bill. → Sam won't invite them both.

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).
(2) Stress and adjectival strengthening (Bergen 2016) a. Bob is TALL. → Bob is especially tall b. Alice is SMART. → Alice is especially smart c. The watch is EXPENSIVE. → the watch is especially expensive 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 (i) 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 2005and 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).
(ii) By contrast, other researchers take Brow Raise to express certain morphosyntactic or semantic properties.
(a) For Neidle et al. (2000), ASL Brow Raise marks the c-command domain of a morphosyntactic feature.
(c) 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 1 Quer (2016) develops a different theory of Brow Raise for Catalan Sign Language (LSC); for him, Brow Raise "is a portmanteau marker of syntactic integration of the dependent clause into the matrix, potentially layered with other nonmanuals". 2 In Rooth's account (e.g. 1996), cases of contrastive focus as in (i) do involve a dyadic operator, the ~ operator. For instance, in the underlined constituent, ~ introduces a presuppositional requirement that the value of the variable P 2 , coindexed with Canadian farmer, should be part of the focus value of American F farmer (and this condition is satisfied because a Canadian farmer is an X farmer for some alternative X to American). What is not clear to us, however, is in what sense contrastive focus appears here in the restrictor of this dyadic operator.
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.

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.)

The debate about focus and intensification: Bergen's proposal and Wagner's objection 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. (3) Stress and quantifier strengthening (Bergen 2016) a. EVERY girl came to the party. → enlargement of the implicit restriction: every girl within a larger than expected domain came to the part b. NOBODY brought presents. → enlargement of the implicit restriction: nobody within a larger than expected domain brought presents c. SOME of the students passed the test.
→ narrowing of the implicit restriction: some students within a very small domain passed the test  Goodman and Frank 2016;Franke and Jäger 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.

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 3 Bergen (2016) cite the following: (i) Context: Bob is addressing his students before class. He looks at a particular student.
Bob: SOME of you didn't hand me your homework yesterday.
[Understood meaning: The student that Bob is looking at did not hand in his homework yesterday.] 4 There can be 'noise' in any signal, including in writing or in signs.
(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) 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.

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). 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.

Elicitation methods and limitations
Our ASL data were elicited from Lamberton, who is a native Deaf signer of Deaf, signing parents (theoretical issues were discussed with him after elicitation was complete). We obtained acceptability judgments using the 'playback method', with repeated quantitative acceptability judgments (1-7, with 7 = best) and repeated inferential judgments (on separate days) on videos involving minimal pairs (for earlier uses of the playback method, see for instance Schlenker et al. 2013;Kuhn 2016;Schlenker 2021). Acceptability judgments pertained to entire sentences, but in many cases separate acceptability judgments were also collected on the realization of a word of interest. The goal was to get more fine-grained judgments: a sentence as a whole may seem relatively acceptable even though the non-manual on a word is suboptimal. In such cases, asking for the acceptability of the target word yields more fine-grained contrasts. We indicate clearly at the beginning of each example whether acceptability judgments pertain to the entire sentence or to a word of interest (in the latter case, acceptability judgments for the entire sentence can be found in the Supplementary Materials).
Our method was a more transparent and scripted version of standard elicitation techniques used in linguistics. For accuracy, and in line with recent work that uses similar methods (e.g. Schlenker et al. 2013, and many more recent pieces), acceptability judgments appear as numerical superscripts at the beginning of sentences, thus replacing the symbols *, ??, or ? traditionally used in syntax. This shouldn't suggest that results are experimental in nature: they are not.
When fine-grained inferential contrasts were needed in ASL, we asked for judgments of inferential strength, also on a 7-point scale (with 7 = strongest inference). Quantitatively assessing inferential strength is by now standard in experimental semantics, for reasons discussed for instance in Cremers and Chemla (2017); as they write, graded inferential judgments "may help detect otherwise hidden effects". Quantitative inferential judgments have also proven useful in work on sign language semantics (e.g. Schlenker 2021).
In all cases, only averages of the quantitative scores obtained are provided in the text, with raw scores in parentheses when there was more than a 2-point difference among them. Raw data, including all scores and written inferential judgments (each of which was also redundantly signed on a video), can be found in the Supplementary Materials.
The playback method made it possible to ask the consultants (in ASL and LSF alike) to produce minimal pairs differing primarily by Brow Raise placement. For this reason, the production part was artificial, just as it would be for the creation of experimental stimuli. But the subsequent (and repeated) judgment task (by the same signer) made for minimal comparisons between appropriate and deviant sentences depending on the placement of Brow Raise. Importantly, creating truly minimal pairs with non-manuals is extremely challenging; although our paradigms were minimal with respect to the presence and timing of Brow Raise, they were not as minimal as we initially hoped concerning other non-manuals. As things stand, this is just the best we could do, and more sophisticated methods will probably have to be used to produce even more minimal pairs in the future.

Transcription conventions
ASL data were transcribed by Lamberton himself. In Appendix II, LSF data were initially transcribed by Schlenker for the presence and timing of Brow Raise and Brow Lowering. But for uniformity, Lamberton used the same fine-grained transcription as in ASL for non-manuals and sign modulations. 6 While Lamberton has considerable experience with scientific transcriptions, it should be kept in mind that in the case of manual modulations and non-manuals this is often a particularly difficult task, with judgment calls involved at several junctures.
As is standard, sign language glosses are capitalized. Loci are alphabetically ordered from the dominant to the non-dominant side. IX-i represents a pointing sign toward locus i (usually to realize a pronoun, with IX-1 and IX-2 referring to the speaker and the addressee respectively).
Loci affixed to verbs represent agreement markers; a word signed in locus i is glossed as WORD i .
For reader-friendliness, we follow Schlenker et al. (2016) in using a revised transcription system (the SLASH-notation 7 ) in which sign modulations are indicated by modifying the glosses themselves, while non-manuals appear above the capitalized glosses, with a line indicating their 6 This measure has the advantage of uniformity (these fine-grained properties were transcribed with the same criteria), but it comes with obvious limitations as well: Lamberton is an ASL and International Sign signer, not an LSF signer.
The reader can disregard the fine-grained details found in our LSF transcriptions if they so desire. 7 For more on the SLASH-notation, see: https://sites.google.com/site/linguaeparis/sign_language_slash_notation. longer hold times and speed accelerations were not encoded in this piece because no striking contrasts were initially found; this part of the transcription conventions has correspondingly been bracketed in (6).) In addition, we need a distinction between the case in which Brow Raise appears on a word (the standard case), as in (7)a, or right before a word (cases of interested investigated here), as in (7)b: we distinguish these cases by symbols (^ vs. ^-) and by way of alignment, as shown in (7). Non-manuals were only included in the transcriptions of the emphasized words or in the corresponding controls. Sentences included in the same numbered example were signed and evaluated as part of the same video, and they thus form minimal pairs.
To illustrate, the partial example in (8), extracted from (10) below, involves one word, namely B ILL_b , whose realization changed from example to example (the subscripted locus b reflects the fact that B ILL was signed on the left). The part copied in (8)a indicates that when B ILL_b was realized without emphasis, this word was judged to be degraded, with an average acceptability of 1.3 over 3 iterations of the judgment (on different days). The part copied in (8)b transcribes B ILL_b realized with greater sign amplitude, hence the boldfacing. The sign was accompanied with a forward lean (glossed as /), a head nod (glossed as }), and a heightened Brow Raise (glossed as /\; it would have been ^ for a normal Brow Raise). Acceptability of the word realized in this way was at ceiling, with an average score of 7. The notation (ASL,35,0684;3 judgments) at the end of the example provides the number of judgments obtained, and the reference of the video in which the target sentences were recorded.
The Supplementary Materials can be consulted to obtain full written judgments on that videos (the judgments were also signed, redundantly, on separate videos). To provide maximal access to the data while respecting the consultant's privacy, semi-anonymized ASL videos have been made available below.

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 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').
8 In addition, "forward leans were found in our ASL but not in our LSF data; head nods were found in LSF (and might or might not have been part of 'forward leans' in ASL); and a couple of instances of shoulder raising were found in LSF but not in ASL."

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) (9) (Acceptability of OR) 9 Context: The speaker is an ASL instructor teaching students to sign 3-word sequences.
/\e. 6.7 OR -/} f. 6.3 OR 'You will sign 'A NN AND B ILL ', then 'A NN OR B ILL '. (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 9 There was a numbering error in the raw data, with c, d, e instead of d, e, f appearing in the sentences; this does not seem to have caused confusions since the consultant used all appropriate columns.
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 B ILL_b ) Context: The speaker is trying to teach groups of students to work together.
˄-/} f. 6.3 B ILL_b '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.

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 (11) a. I only introduced ANN to Bill at the party. → I didn't introduce other people than Ann to Bill at the party b. I only introduced Ann to BILL at the party → I didn't introduce Ann to other people than Bill at the party 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) 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) (Acceptability of the last word of the sentence.) 10 We include sentence-final modifiers in (11) because otherwise the last word of the sentence would also be the last word of the VP, and emphasis on it could potentially mark focus on the entire VP (this is due to rules of focus projection: for Selkirk (1995), a focused argument can F-mark its verb, which in turn can F-mark the entire VP). The judgments we report suggest that this potential ambiguity did not extend to our ASL data. 11 We only tested Brow Raise and not Brow Lowering in our ASL data. Brow Lowering should be investigated in this context in the future, as the consultant once noted in relation to (12)b that he "would probably use lowered eyebrows rather than raised eyebrows for this kind of emphasis." ([JL 19.10.03]). 12 Both c. and d. have been transcribed as heightened Brow Raise, but in addition wide open eyes appear in d., which make the Brow Raise appear even stronger. 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) 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 14 The consultant noted that the "function of ONLY not entirely clear in these sentences. Is it "merely" -The only thing the signer is requesting is this. Or is it limiting -The signer wants this and only this to happen. For these sentences, I'll assume the latter." ([JL 19.09.29]) 15 As the consultant noted, a pragmatic step is needed in all these examples: "We understand what signer wants, but for other than what is mentioned, are they neutral or unwanted/disallowed? I tend toward unmentioned = disallowed." ([JL 19.10.05], by email).
(15) Inferential question: same as in (13) The (iii) something else 4 (5, 1, 6) 1.7 1.7 1.7 1.7 1.7 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.

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,  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 16 In addition, one may in some cases use iconic scales to represent degree modifications; see Aristodemo and Geraci (2018).
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 focusrelated 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.

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) 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.

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.  (17)) One infers that a. b. c. d. e.
(i) John is taller than Peter 1 1 1 1 1 (ii) Peter is taller than John 1 4 6 2.7 4 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. (ii) between 1 and 2-miles 7 3.7 2 5.7 3.7 (iii) > 2 miles 1 1 1 1 1 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) 18 Since the first inferential judgment task on this question was binary (yes/no) rather than quantitative, we only provide information about the last three judgment tasks, which involved quantitative ratings instead. This also applies to acceptability judgments: for uniformity, we only use the last 3 judgments provided.
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) Here too, we only provide information about the last three judgment tasks, which involved quantitative judgments, leaving aside inferential and acceptability judgments given in the first judgment task (because its inferential component was based on a yes/no question).
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.

Interim summary and initial LSF replication
The generalizations obtained are stated in (28).
(28) Summary of the generalizations a. Existence of intensification-related Brow Raise: In our ASL data, Brow Raise can intensify a gradable construction. b. Distinction between Brow Raise on vs. before a word: (i) Brow Raise on a word can either mark standard focus (contrastive focus, association with focus) or intensification. (ii-1) Normal Brow Raise before a word can mark standard focus (contrastive focus and, to some extent, association with focus), but not intensification. (ii-2) In several ASL cases ((22)e, (24)e, (26)e), heightened Brow Raise in a preposed position can (unlike normal Brow Raise) mark intensification.
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).

An analysis within Alternative Semantics
To derive the data within Alternative Semantics, we adopt Rooth's (1996) semantics for focus, and we assume that Brow Raise forces the appearance of F-marking (which generates alternatives) on the expression it modifies. But in order for Brow Raise to have an intensificational reading as well, we need to add something to Alternative Semantics. We propose to posit that Brow Raise makes a semantic contribution of its own, which we call 'noteworthiness'. The semantics is set up in such a way that this 'noteworthiness' contribution will make itself felt with gradable constructions, but will usually be vacuous in other cases.
(29) Main assumptions a. Brow Raise before an expression exclusively (or preferentially) F-marks the entire expression it modifies. b. Brow Raise before a gradable expression can either (i) F-mark the entire expression, or just (ii) its degree variable. c. Brow Raise makes a semantic contribution of its own, indicating that the asserted clause is 'noteworthy' relative to its set of alternatives. We define 'noteworthy' as: 'not entailed by most of its alternatives' To avoid writing formulas on two lines simultaneously, we will write ^E for Brow Raise on an expression E, and ^-E for Brow Raise before an expression E.
The key assumptions are in (29)b,c. Per (29)b, a sign language expression such as PETER ^TALL, with Brow Raise on (rather than before) TALL, can receive an analysis of the form Peter is (at least) d F -tall, with focus marking on the degree argument. Per (29)c, Brow Raise introduces a noteworthiness requirement. When the F-marked expression is not a member of a neo-Gricean scale, the noteworthiness requirement will usually be vacuously satisfied and the net effect will reduce to focus marking. When a degree variable is F-marked, the requirement won't be trivial: for Peter is (at least) d F -tall, the noteworthiness requirement is that the clause should not be entailed by most of its degree alternatives, and hence Peter's degree of height should lie within the upper part of the scale, hence the intensificational effect observed. 20 We turn to a more precise definition of our focus-related notations. (30) Rooth (1996), as sets of semantic objects. D is the set of entities, Deg is a (contextually specified) finite set of degrees, Property is a (contextual specified) finite set of properties (of type <s, <e, t>>). d. As is standard, if s is an assignment function, s[d→d*] is the function that is identical to s, with the possible exception that it assigns d* to the variable d (in the discussion below, d will be a degree variable). e. We write as tall' and Peter' the semantic values of TALL and PETER respectively, and adopt related conventions for other expressions.
In our general theoretical machinery, we adopt a standard rule of extensional function application whereby if F is a functor and A is its argument, ⟦F A⟧ s, w, o = ⟦F⟧ s, w, o (⟦A⟧ s, w, o ). Focus semantic values are defined by the procedure specified in (31), from Rooth (1996).
(31) a. The focus semantic value of a focused phrase of semantic type t is the set of possible denotations of type t. b. The focus semantic value of a non-focused lexical item is the unit set of its ordinary semantic value. 20 We take the noteworthiness requirement to be associated with further means of emphasis as well, since in our data manual intensification gives rise to semantic effects. Brow Raise is special and theoretically informative because it can both co-occur with an expression and precede it.
c. Let a be a non-focused complex phrase with component phrases a 1 , …, a k and let F be the semantic rule for a, e.g. function application. The focus semantic value of a is the set things obtainable as F(x 1 , … x k ), where x 1 Î ⟦a 1 ⟧ f and … and x k Î ⟦a k ⟧ f . (33)a explicates that a proposition is noteworthy just in case most of its alternatives don't entail it. (33)b,c introduce standard assumptions about gradable adjectives: tall is gradable and comes with a degree argument, while French, which isn't gradable, doesn't have a degree argument.
(33)d makes the simplifying assumption that there is a finite number of degrees (so we can easily define what it means for something to hold of 'most' of them).
(33) a. If p is a proposition and ∏ is a finite set of propositions, noteworthy(p, ∏) iff (= if and only if) most members of ∏ fail to entail p. b. TALL is represented as d-TALL, with a degree variable d as argument. It has the lexical entry: ⟦TALL⟧ s, w, o = ld lx x is at least d-tall in w = ld lx tall'(w)(d)(x). c. FRENCH does not take a degree variable as an argument, and it has the lexical entry: ⟦FRENCH⟧ s, w, o = lx x is French in w = lx french'(w)(x) d. Simplifying assumption: we assume that the set of degrees is finite (to avoid comparing the size of infinite sets).
Let us now see how this analysis derives the intensified reading of ^TALL, with Brow Raise on the predicate. This makes two patterns of F-marking possible: on the entire predicate, or on its 21 In our computations below, we take -to be semantically vacuous (it just marks that Brow Raise is before an expression, which in turn has consequences for F-marking possibilities, hence an indirect effect on interpretation). degree variable. We consider the latter option first. The outcome will be that Peter is tall to a degree d* which is above d half , the middle of the scale of degrees.
Let us start with (a sketch of) the computation of the ordinary value and of the focus value of d F -TALL. It will be useful to make separate assumptions about the computation of the focus value of d F -TALL, as in (34)b (these values will be relativized to a world parameter s in the ensuing computations).
We assume that the degree variable of TALL is existentially closed as in the LF in (35)a, whose truth conditions are sketched in (35)b, and made more precise in Note 1 of Appendix I; the result is that Peter's degree of height should be above the middle of the scale.
iff for some degree d*, Peter is tall to degree d*, and this is noteworthy relative to (degree-) alternatives to this proposition, iff for some degree d*, Peter is tall to degree d*, and most (degree-) alternatives to this proposition do not entail it, iff for some degree d*, Peter is tall to degree d* and d* is above most degrees of height.
It is clear that the analysis could be tweaked by changing the meaning of noteworthy: if one requires that a proposition is noteworthy relative to a set of propositions just in case it is entailed by less than 10% of them (rather than less than 50% of them, as in our definition), the intensificational effect will be strengthened (as d* will have to be within the top 10% of degrees).
We now consider the case in which ^ triggers F-marking on the entire expression it associates with -which is the only (or preferred) possibility when Brow Raise precedes an expression. The outcome will be that the noteworthiness requirement is typically trivialized because most of the alternative propositions do not stand in an entailment relation anyway. The derivation is sketched in (36) and made more precise in Note 2 of Appendix I. Since the noteworthiness requirement is trivialized in this case, if F-marking must be justified by something, we will presumably end up with whatever informational effects are produced by focus in standard cases, and in particular F-marking may be justified by a contrast, or by association with an operator. Importantly, the present analysis predicts a categorical distinction between Brow Raise before vs.
on an adjective: only the latter should yield an intensificational reading. This is not quite correct, since in our data heightened Brow Raise can sometimes yield an intensificational reading. As things stand, this is a limitation of our analysis (see also Note 3 of Appendix I).
In sum, we can capture our main data within Alternative Semantics, but we must stipulate that Brow Raise doesn't just serve, in these cases at least, to F-mark expressions, but that it also makes a semantic contribution of its own ('noteworthiness'). The repercussions of these assumptions would need to be assessed in greater detail. In addition, our analysis does not capture the fact that preposed Brow Raise can to some extent fulfill an intensification function if it is heightened.

An analysis in terms of noise-reduction
Bergen (2016)  in (2). The fact that Brow Raise has the focus-related functions in (1) and can also strengthen adjectives provides an additional argument for Bergen's view that these should be treated as a partly unified phenomenon (we write 'partly unified' to take into account Wagner's objection: Bergen's theory needs to be supplemented with a mechanism to explain why prominence must shift in focus-related cases but not in intensification). While we argued in the previous section that the Brow Raise data can be analyzed within Alternative Semantics, this was at the cost of positing a new operator ('noteworthiness') associated with Brow Raise.
While our first finding -Brow Raise can have focus-related and intensificational uses alike -strengthens Bergen's argument, the contrast between Brow Raise on vs. before an expression requires a detailed discussion. A full model lies beyond the scope of this paper, but we will develop a simplified version of Bergen's analysis, and show that with some auxiliary hypotheses (which are arguably plausible) the data can be derived. We discuss a concrete case in this section, referring the reader to Appendix III for a slightly more general treatment. Importantly, we develop the analysis with full rather than bounded rationality, which greatly simplifies computations (Bergen uses bounded rationality instead).

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 q tall , and Bob is short is true just in case his height is below a threshold q short . The values of q tall and q short are not known with certainty, but not anything goes: it is very likely that 1m90 counts as being above the 'tallness' threshold q tall , while 1m75 might or might not be above the threshold. Similarly, 1m60 is very likely to count as being below the 'shortness' threshold q 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. Bergen (2016) notes that "there are three main acoustic changes associated with prosodic stress:

Brow Raise and noise reduction
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.
23 Since tones cannot be realized before a word whereas Brow Raise can, the latter makes it possible to test options that are probably not afforded by high boundary tones.
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) /}/\ TALL 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.

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.
(i) 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 24 To give an example, in (12)c,d, where Brow Raise appears on a pronoun, duration was of approximately .8s and 1s. By contrast, in (12)e,f, where Brow Raise appears right before the pronoun, duration was of approximately .2s and .3s.
(ii) 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).
(iii) 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.
(iv) When the benefit of reducing noise is greater, Brow Raise on an expression wins out; this is the case of intensificational uses.
(v) 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)  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).
(39) Assumptions about the cost and effect of noise-reduction 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 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)  - 3-c 2 = 3-.7 = 2.3 TALL 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.

Extension: focus and intensification in an ASL iconic construction
We briefly extend our findings to constructions that are highly iconic. We consider a classifier predicate representing a helicopter movement, and show that Brow Raise on a part of the movement can have intensificational uses, but Brow Raise before doesn't lend itself to such an interpretation.
We start from the iconic description of a helicopter movement with a helicopter-denoting classifier predicate, represented in its neutral form in (45). Classifier predicates are conventional words whose position or movement can iconically represent that of the denoted object (e.g. Emmorey and Herzig 2003;Zucchi 2011;Davidson 2015). In other words, the lexical form is conventional, but its position or movement is not and yields precise iconic information about the position or movement of the denoted object. 26 In our paradigm, the expression is first introduced in its neutral form, glossed as HELICOPTER, with a nominal use ('your helicopter'), before appearing as a verbal classifier predicate to represent the helicopter movement, glossed as HELICOPTER-FLY. by way of its four corners as a low _a high-stationary _b high-stationary _b low ; but it should be remembered that this is a continuous movement. The helicopter path is represented by four pictures in (47). The paradigm is then constructed by adding Brow Raise either on or before one of the two circling, stationary parts glossed as a high-stationary and b high-stationary . Acceptability judgments pertained to the entire sentence, and inferential judgments, which were subtle, were answered in words rather than by way of multiple choice questions (we write 3/4 judgments, 4/4 judgments… when an inference was obtained in 3 out of 4 judgment tasks, in 4 out 4 judgment tasks, etc).
circle [after take-off] F and before landing.' → the signer doesn't want the helicopter to circle right after take-off (4/4 judgments) → circling before landing might/would be allowed (3/4 judgments) }/\ b. 7 HELICOPTER-FLY_a low _a high-stationary _b high-stationary _b low . circle for longer than normal after take-off and circle before landing.' → the signer doesn't want the helicopter to circle for longer than normal after take-off (4/4 judgments, but in 2/4 judgments with an additional specification: when leaving for another location / if landing is then preceded by circling) → limited circling after take-off is permitted (4/4 judgments) c. 7 HELICOPTER-FLY_a low _a high-stationary _b high-stationary _b low .
circle after take-off and circle for longer than normal before landing.' → the signer doesn't want the helicopter to circle right after take-off and then circle for longer than normal before landing (4/4 judgments) Second, this intensificational reading disappears when Brow Raise is brief and precedes the 'high stationary parts', as in as in (46)a (= Brow Raise right before a high-stationary ) and (46) d (= Brow Raise right before b high-stationary ). In (46)a, we just obtain a reading on which, in the relevant circumstances, circling after take-off is disallowed, with an implication that circling before landing might be allowed. Everything happens as if the particular sequence displayed is disallowed, but with an implicature that an identical sequence without circling after takeoff (but with circling before landing) would be allowed. This can be explained if the iconic sign with Brow Raise evokes alternatives obtained by replacing the focused part with some salient expressions, as shown in (48). It is then implicated that although the path as shown is disallowed, an alternative to it displayed by a member of that set is allowed, hence the result.
(48) Formal alternatives to a low ^-[a high-stationary ] b high-stationary b low Alt(a low ^-[a high-stationary ] b high-stationary b low ) = {a low π b high-stationary b low : π an alternative to a high-stationary } For reasons we do not understand, the inferences obtained are more complex in (46)d, but there too it is clear that the 'longer than normal' reading obtained in (46)c does not arise.
If the iconic path of the helicopter is considered as one sign, these results show that focus and intensification can apply at the sublexical level. For focus, this point was made about spoken language by Artstein (2004) in connection with sentences such as (49).
(49) John only brought home a stalagMITE from the cave. the alternatives Robin isn't BIG and Robin isn't TALL are understood to be denied, hence the inference that Robin is big or tall, as the case may be. Here too, a theory of iconic alternatives is crucial. 29

As
Finally, Brow Raise co-occurring with the 'circling' parts of the path might be an instance of a sublexical intensification, which should be of interest in its own right.

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 29 Schlenker (2019) speculates on a more subtle point: the more complex gestures VERY-BIG and VERY-TALL seem to evoke, even in the absence of context, the sub-gestures BIG and TALL, but the converse might not hold. If so, this argues for the extension to the iconic case of an asymmetry derived by Katzir (2007): more complex expressions automatically evoke less complex ones, but not the other way around. This asymmetry is illustrated in (i), where the more complex expression drink a lot evokes the less complex expression drink (hence the implicature in (ib), but not conversely (hence the absence of an implicature in (ia)).
(i) a. I drank.
≠> I didn't drink a lot b. I didn't drink a lot.
→ I drank 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.

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 .
30 One might also try to treat intensificational Brow Raise on an expression as a marker sui generis, e.g. as an iconic modulation (see Schlenker 2018). But this view would fail to explain (i) why intensificational Brow Raise is part of the same cluster of properties that mark focus constructions, and (ii) why heightened Brow Raise before an expression can to some extent fulfill an intensificational function.

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-wideopen' 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).
(52) I only introduced Ann to… Bill. →? I didn't introduce other people than Ann to Bill 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.
(53) a. John is tall, but Peter is TALL. b. #John is tall, but Peter is… tall.
Here too, the data will require a separate study.