Effects of linguistic context on the acceptability of co-speech gestures

We ask whether iconic co-speech gestures are judged as more natural by naive participants when their content is entailed by a preceding context, or repeated in the same utterance, or when they contribute new information (i.e., are nontrivial). Our results show, first, that the acceptability of co-speech gestures is not affected by whether they are entailed by a preceding context (they are not “hard presupposition triggers”). In contrast, our second finding is that gestures are affected by content in the same utterance, such that they are judged more acceptable when they reinforce information already present in the proposition. In addition, gestures varied widely in how acceptable they were judged even in the same information contexts, which we take to be an indication that we are just scratching the surface of a more general question about the felicity of co-speech gestures, of which the current study provides a first experimental foundation.


Introduction
One of the most productive developments of the last several decades of formal semantics/pragmatics research has been increasingly sophisticated models of different kinds of meaning that linguistic content can contribute, whether that content is at-issue or backgrounded, entailed or implicated, or updating or proposing updates to a shared common ground between interlocutors, among other distinctions. A classic three-way divide between entailments, implicatures, and presuppositions (see Chierchia & McConnell-Ginet 2000: Chapter 1 for a brief introduction) has been expanded in a number of ways through more complex distinctions. For example, although presuppositional elements like too, again, etc., often both require particular discourse conditions to be uttered and can "project" through other logical operators so as not to be affected by them, these two properties attributed classically to presuppositions can sometimes be dissociated, which means that attempts to model the contributions of these and other aspects of meaning should be careful to test each property separately.
Recently, this type of formal semantic/pragmatic analysis has been extended beyond language in a narrow sense to co-speech gesture (Ebert & Ebert 2014;Tieu et al. 2017;Esipova 2018;Schlenker 2018). On the face of it, this is a natural extension, given that co-speech gestures are known to be prosodically integrated with spoken language and havebeenarguedtocontributetoaunifiedsemanticcontenttogetherwithspeech/sign (McNeill 1992;Kendon 2004;Goldin-Meadow & Brentari 2017). However, there is some reason for caution about assuming that applications of the same linguistic tests for levels of semantic/pragmatic contribution can be applied wholesale to gestural content. One reason might be that speakers of a language like English may be comfortable making Glossa general linguistics a journal of Zlogar, Christina and Kathryn Davidson. 2018. Effects of linguistic context on the acceptability of co-speech gestures. Glossa: a journal of general linguistics 3(1): 73. 1-28, DOI: https://doi.org/10.5334/gjgl.438 Zlogar and Davidson: Effects of linguistic context on the acceptability of co-speech gestures Art. 73, page 2 of 28 metalinguistic judgments about speech, but less so about gesture, which is almost never a target of explicit instruction and so less frequently considered metalinguistically. Another reason is that gestural content may more often be interpreted in an analog way, potentially leading to more gradient grammaticality and/or truth value judgments. Finally, if there is some agreement among formal analyses of co-speech gestures, it is that they are frequently not-at-issue (Ebert & Ebert 2014;Schlenker 2018), and not-at-issue contentcanvarysignificantlyacrossphenomenaandacrosslanguagesinseveralrespects, including, as we mentioned above, how it projects through various logical operators and whether it imposes any restrictions on the previous discourse. In this paper we focus on this last aspect, by experimentally testing the sensitivity of co-speech gestures to linguistic context, construed broadly as both discourse context and the local context of the simultaneous speech stream. Our hope is that this will contribute an important foundational piece as part of a larger discussion regarding the semantic, pragmatic, and information structural properties of co-speech gestures, and the practical issues involved in creating appropriatecontextsinwhichtotestthemviafieldworkorexperimentation.

Background: Co-speech gestures
The kind of co-speech gestures that have been the focus of recent semantic/pragmatic work and that we will be focusing on in this paper are gestures made simultaneously with speech/sign that enrich utterance meaning by iconically depicting an aspect of the situation or event (Kendon 2004;Goldin-Meadow & Brentari 2017); see (1)(2)(3)(4)(5)(6) for examples. In these and future examples, gestures will be written in all-capital letters, and we will indicate the spoken words that align with the gesture by placing them in square brackets. (3) Ebert & Ebert (2016) One child managed to cut out [a geometrical form]_TRIANGLE.
(6) She [scored]_SHOOT the winning point! All of the co-speech gestures in (1-6) convey some information which the literal speech stream does not. For example, the co-speech gesture PULL-BACK in (1) involves the speakermakingasiftogripandpullbacksomethingflexiblewhichisfixedatthebase, such as a sapling. The iconic information communicated by the gesture but not the spoken wordsisthattheobjectbeingpulledbackisfixedatthebase.Similarly,theSPIRAL-UP gesture in (2) alone conveys the fact that the staircase in question is a spiral staircase, and the gesture TRIANGLE in (3) entails that the geometric shape in question is a triangle. UP in (4) implies that the helping was done by lifting, and LARGE in (5) implies that the bottle was large. Finally, the SHOOT gesture in (6) indicates that the scoring was done by shooting a basketball. Kendon(2004:7)definesagestureasavisibleaction"usedasanutteranceorasapart ofanutterance"withthegoalofcommunicatingsomething.Gesturescanbe classified according to their communicative function, the kind of meaning they express, their co-occurrence with speech, and their degree of conventionality and arbitrariness, among other factors (McNeill 1992;Kendon 2004;McNeill 2005;Abner et al. 2015;among others). Other types of gestures we will not be addressing include emblems (culture-specific gestureswithfixed,arbitrarymeaningsthatcanbeusedwithorwithoutaccompanying speech, such as the "thumbs-up" gesture), pantomimes (sequences of complete gestures that iconically depict scenes and/or events and never co-occur with speech), beats (short and simple non-iconic movements that pattern closely with an utterance's prosodic peaks), and deictics (pointing gestures commonly used with demonstratives and locative adverbs). Iconic co-speech gestures can be distinguished from these other types of gestures by their co-occurrence with speech, their lack of arbitrariness, and their conveyance of meaning through iconicity. However, like other gestures, they are naturally occurring linguistic phenomena that are part of the linguistic system (Kendon 1980;McNeill 1985;1992;Goldin-Meadow & Brentari 2017); they are spontaneously produced by speakers, and are not formally taught to learners.
The modest amount of previous formal semantic/pragmatic work on co-speech gestures has generally focused on inferences related to their not-at-issue-ness (Ebert & Ebert 2016;Tieu et al. 2017;Esipova 2018;Schlenker 2018), as illustrated by (7) where denial of the utterance cannot target the content of the gesture as in (b); instead (7a) can be continued by (b′)or(b″). (7) a. John brought a [bottle of beer]_LARGE. b. …#No, it was small. b′. …Yeah, but it was a small one. b″. …Yeah, and it was huge, you're right!
Of not-at-issue types of meaning, Schlenker (2018) proposes that co-speech gestures are in factatypeofpresupposition,specificallyanassertion-dependentconditionalpresupposition he calls a cosupposition. Based on informal inference judgments, he demonstrates that these cosuppositions exhibit standard presuppositional projection behavior in embedded contexts, except that the inference that projects is conditional. In contrast, Ebert & Ebert (2014; suggest that the way in which co-speech gestures contribute not-at-issue meaning is most analogous to supplements, such as expressives or non-restrictive relative clauses (Potts 2005). It is a subtle distinction: consider the case of non-restrictive relative clauses outlined in Chierchia & McConnell-Ginet (2000), which exhibit projection out of several operators in (9).  b-d) show that the inference survives under negation, in a question, and in a conditional. However, unlike classic presuppositions, in none of (a-d) is it assumed by the speaker that the hearer already knows that Jill lost something, so these inferences havetypicallynotbeenclassifiedaspresuppositionssincetheyimposenorestrictionson the background content. An example of a supplemental analysis of the meaning of a co-speech gesture is given in (10), where Ebert & Ebert (2016) illustrate how the supplemental analysis predicts that the material conveyed by the gesture goes through as an inference in positive contexts (10a) but not in negative contexts (10b). Although both the cosuppositional analysis and the supplement analysis of co-speech gesturestakethemtobenot-at-issue,theymakedifferentpredictionsinseveralrespects,one of which is projection behavior under negation, shown in (10) above. We will focus on one previously unexplored contrast in this paper: the restrictions that the gestures place onthediscourse,eitherinpreviouscontextorinthesamesentence,specificallywhether the gesture is trivial, duplicating content provided elsewhere. Supplements are awkward when trivial: compare (11a), where the supplement is trivial, to (11b), a similar structure but where the supplement contains nontrivial information.
Jill, who frequently travels from Ithaca to New York, likes to travel by train.
Takingasupplementanalysisofco-speechgestureofftheshelf,wewouldexpectdegraded acceptability for co-speech gestures that are trivial, by analogy to speech supplements. The cosuppositional analysis makes a less overt prediction about triviality, but by analogy to presupposition we might in fact expect the reverse direction of acceptability: presuppositions acceptability of co-speech gestures Art. 73,page 5 of 28 are usually expected to be given/trivial, and so the cosuppositional analysis would be consistentwiththefindingthatgesturesaremoreacceptablewhentrivial. Past experimental work on the cosupposition/supplement distinction comes from Tieu etal.(2017),whoreportevidencebasedondifferentpatternsofprojectioninfavorofthe cosuppositional analysis, albeit one with some extra assumptions that need to be made. We note, however, that their work focuses on inferential judgments involving gesture, whilewetakeasourstartingpointthequitedifferenttaskofacceptability judgments of gestures in context. Our motivation for focusing on acceptability is that we begin with the impression that, to the extent that we have acceptability judgments about co-speech gestures, they vary greatly in ways that we cannot predict using current theories of co-speech gesture. This includes examples in existing literature, some of which are entirely natural (e.g., (2)) and others which we found to be less so (e.g., (8d)), and which cannot in our mind yet be entirely explained by processing constraints like complexity, frequency, familiarity, etc. We are therefore interested in asking what kinds of factors contribute to the acceptability of co-speech gestures, so that gesture researchers creating linguistic examples can make more informed choices, including for important patterns like inferential judgments.
To summarize, we are interested in focusing on acceptability given the not-at-issue tendency of co-speech gestures, since dependence on previous context (in particular, being trivial) is unexpected for supplements but a hallmark of one type of presuppositional content(so-called"hardtriggers").Withaneyetowardfieldwork(or,inourcase,work on an understudied phenomenon), Tonhauser et al. (2013) propose a typology for projective content. One of the properties that they note forms a class of projective content is the strong contextual felicity (SCF) condition, which will be the focus of this paper. By directly applying their suggested methodology for investigating expressions that seem to show projective behavior, we hope to better understand how to classify co-speech gestures in English in comparison to other projective spoken language phenomena, and to gain some more empirical evidence to bear on the theoretical analysis of co-speech gesture.

Background: Testing strong contextual felicity
The goal of our study is to essentially test how easily the content of not-at-issue meaning can be accommodated by an interlocutor. In other words, we are interested in asking whether co-speech gestures are more or less acceptable when they duplicate content or are entailed by content in the preceding discourse, or when they contribute new content. That is, are gestures better when they are informative, either with respect to the past context or the utterance that contains them? We will get at the former by testing whether their content must be entailed by the preceding discourse. Tonhauser et al. (2013) refer to this sensitivity to discourse context as strong contextual felicity (SCF);morespecifically, an item is said to be [+SCF] if and only if it is only acceptable in a discourse context that appropriatelyentailsit,wherecontextentailmentisdefinedin(12): (12) Tonhauser et al. (2013: 75-76) a. An m-positive context is one that entails or implies m.
b. An m-neutral context is one that entails or implies neither m nor ¬m. Thenthepropertyofstrongcontextualfelicityisdefinedasfollows: (13) Strong contextual felicity constraint (Tonhauser et al. 2013: 76) If utterance of trigger t of projective content m is acceptable only in an m-positive context, then t imposes a strong contextual felicity constraint with respect to m.
Informally, if some expression can be uttered in a discourse context that neither supports nor denies an inference m, then that expression does not need to be supported by the context, so it is [-SCF] with respect to m. Formally, the following diagnostic can be used to decide on the strong contextual felicity value of an expression: (14) Diagnostic for strong contextual felicity (Tonhauser et al. 2013: 76) Let S be an atomic sentence that contains trigger t of projective content m.
(i) If uttering S is acceptable in an m-neutral context, then trigger t does not impose a strong contextual felicity constraint with respect to m. (ii) If uttering S is unacceptable in an m-neutral context and acceptable in a minimallydifferentm-positive context, then trigger t imposes a strong contextual felicity constraint with respect to m.
Part (ii) of the diagnostic captures the intuition that if an expression is not felicitous in a neutral context, but then is felicitous in a nearly identical context in which the only differenceisthatnowm is entailed by the context, then we can safely conclude that the expression is [+SCF]. Using this diagnostic, we devised an experiment using Amazon Mechanical Turk to test if the semantic content of co-speech gestures is [+SCF] or [-SCF] by constructing various scenarios that permit co-speech gestures and manipulating the context to be either m-neutral or m-positive, where m is the proposition conveying the semantic content of the co-speech gesture.
As an example, consider the English additive particle 'too', which is standardly analyzed as having an existence presupposition of a salient parallel alternative proposition. Our bus driver is eating empanadas, too.
Let m be the proposition that somebody besides the bus driver is eating empanadas. The context in (15a) is m-neutral, because it doesn't specify that anyone else is eating empanadas (Malena is eating a hamburger), or that no one else is eating empanadas. In this context, the sentence with tooisinfelicitous.Theminimallydifferentcontext in (15b), by contrast, is m-positive, since Malena is now said to be eating empanadas, not a hamburger. In this context, the sentence with too is felicitous. Since the same utterance with too is infelicitous in an m-neutral context but felicitous in a minimally differentm-positive context, we conclude by the diagnostic in (14) that too introduces a strong contextual felicity constraint, i.e., too is [+SCF] with respect to the implication m. An example of a projection trigger that does not exhibit a strong contextual felicity constraint is the change-of-state construction stop X.

(16)
Adapted from Tonhauser et al. (2013: 80) [Context: Laura, who doesn't live with her parents, visits them and asks them to sit down with her because she wants to tell them something:] I've stopped eating gluten.
Let m be the proposition that Laura used to eat gluten. The context in (16) is neutral with respect to m since Laura's parents are not asserted or implied to know about Laura's gluten consumption or lack thereof. Because the utterance is felicitous in the m-neutral context, we conclude that stop does not impose a strong contextual felicity constraint, i.e., is [-SCF] with respect to the implication m.
Recall that we are interested in whether iconic co-speech gestures are better when they are informative, meaning either with respect to the past context or the utterance that contains them. We will address the second of these issues by adding an additional dimension to the SCF diagnostic, which is whether the semantic content of the gesture is duplicated in the same proposition. This is especially expected to bear on the analysis of co-speech gestures as supplements, which predicts that triviality/duplication should result in lower acceptability of co-speech gestures. Our hypotheses are as follows: •Hypothesisregardingstrong contextual felicity: A large category of expressions carrying not-at-issue content require that content to be entailed by the preceding context. We ask whether co-speech gestures have the same requirement. •Hypothesisregardingmatchingspeech cue: One hypothesized analysis of gestures is as supplements (Ebert & Ebert 2014), which are infelicitous when trivial. We ask how matching content in the speech stream affects felicity of co-speech gestures, with the expectation that it should decrease grammaticality under the supplement account.
We describe the methods and procedures of our experiment, including the implementation of both of these factors, in the next section.

Participants
Participants were 198 adults recruited through Amazon Mechanical Turk, restricted to the United States region. All participants self-identified as native speakers of English. Participants were compensated monetarily for their participation in the questionnaire via Amazon payments of $2. Experimental protocols were approved by the Harvard University Institutional Review Board under approval number IRB16-1331.

Procedure
The questionnaire was created using the Qualtrics Survey Software platform. Amazon Mechanical Turk workers were directed to a Qualtrics link in order to complete the survey. The questionnaire took approximately 10-20 minutes to complete. Participants completed the survey on their own time and on a device of their choosing after receiving a link to the survey; they were instructed at the start to make sure to use a device with a large enough screen to play videos and with working speakers/headphones. The experimental task instructions given at the start of the survey were as follows: If you choose to be in the study, you will complete a questionnaire. This questionnaire will help us learn more about co-speech gestures in English. You will be asked to watch short video clips and judge the naturalness of English sentences, and you may find all of them completely natural, all of them not completely natural, or a combination: some completely natural and some not completely natural.
The term co-speech gesture was not defined and was mentioned nowhere else in the instructions.Wealsochosenottodefinethetermnatural, in order to not prejudice the participants toward judging only the spoken words or only the gestures. The experimental design (discussed in detail below) was between-subjects, ensuring that each participant was shown either only videos with co-speech gestures or only videos without gestures, so as to help the gestures seem as natural as possible (since participants who saw gestures saw gestures in every trial). We worried that the participants viewing all no-gesture trials might feel uncomfortable rating every trial as "completely natural", which was the expected rating for non-gesture videos since all of the stimuli were designed to be felicitous English sentences. To counteract this possibility, we included and highlighted the bolded portion of the above instructions so that participants would know that this wasapossibleoutcomeandthattheydidnotneedtoartificiallyratesometrialslower than others just for the sake of variety in their responses. (We will see in Experiment 2, Section 3, that the resulting pattern of judgments remained even after adding infelicitous non-gesture trials.) For each of the 19 trials of the experiment, the participant was presented with the same instructions, namely to read the short context paragraph and then click "play" to view the following video. The context paragraphs were one-to two-sentence paragraphs describing a conversation between "Eliza", the speaker in the video, and another named interlocutor. Each video featured the same speaker, a female native English speaker in her early twentieswhowasidentifiedas"Eliza"fromthecontextparagraph,sayingasentenceor two that continued the discourse started in the written context paragraph.
The embedded videos were hosted through YouTube and participants could replay the video if they wished, although no mention of the possibility of replaying videos appeared in the instructions. We did not collect data on the frequency of participants replaying videos.
Beneath the video, participants were prompted to make a binary naturalness judgment in response to the following prompt: PleaseratehownaturalyoufindEliza'sresponseinthevideo.
Participants were forced to press either the completely natural button or the not completely naturalbuttontomoveontothenexttrial.WespecificallychosetodescribeEliza's utterance (speech and gesture) in the video as a response because this speech word seemed to best encompass both her spoken words and her gestures. Other alternatives such as utterance, statement, performance, etc. we deemed to be either too technical or to implicitly bias the participants towards judging only the spoken words or only the gestural production. However, the term response implies that Eliza is part of a dialogue; hence we intentionally wrote each pre-video context paragraph as a dialogue, either implicit or explicit, between Eliza and another named interlocutor.
Each participant was presented with three "attention check" trials randomly interspersed between the experimental trials. These attention checks consisted of a context paragraph, written in the same manner as the experimental contexts, and a video in which Eliza informs the participant that this is an attention check and that they should press a particular response and move on to the next trial. One of the attention checks instructed the participant to choose "completely natural"; the other two instructed them to choose "notcompletelynatural".Theseattentioncheckswereusedtofilteroutresponsesfrom participantswhowerenotwatchingornotpayingsufficientattentiontothevideos.

Stimuli
For each trial of the survey, participants saw a screen like that shown in Figure 1. At the top of the screen were instructions to read the context paragraph and then view the embedded video; below the video was the linguistic naturalness judgment question, along with the two options completely natural and not completely natural. Participants were forced to choose one or the other in order to proceed to the next trial.
Example (17) is one of the experimental scenarios seen by participants. The topic of the scenario is that Eliza and a friend are discussing a co-worker's wealth and jewelry. The participant would see either (i) or (ii) as the written context paragraph at the top of the page, and then watch a video with Eliza uttering one of (a)-(d). Utterances (a) and (b) contain co-speech gestures, while (c) and (d) do not. The gesture EARRING conveys the information that the type of diamond jewelry Alicia was wearing was earrings; this information is expressed under Proposition m in the example below.   In the appendices, we list the inference licensed by the co-speech gesture in each scenario explicitly as a proposition, so that it is clear what proposition m the m-positive context is supposed to entail/imply, in the Tonhauser et al. (2013) terminology.
In choosing co-speech gestures for the experiment, we avoided gestures that have conventionalized or codified meanings, such as a "thumbs-up" gesture, as these fall under the category of "emblems" and do not need to be accompanied by speech/sign to convey meaning (Kendon 2004). We also chose not to include pointing gestures, as these presumably intersect non-trivially with the semantics of deictic expressions (e.g., see the treatment in Lascarides & Stone 2009). The choice of gesture target (i.e., the NP or VP semantically modifiedbythegesture)turnedouttobeasimportantasthechoiceofgestureindesigning the stimuli; in order for a co-speech gesture to contribute non-trivially to the truth conditionsofanutterance,thegesturetargetneedstobesemanticallyunderspecifiedinsome way. Modeling our examples after those discussed in Ebert & Ebert (2016) and Schlenker (2018),wechosegesturetargetsthatareunderspecifiedinmannerwhenthetargetisa VP, or in adjectival content when the target is an NP; hence the co-speech gestures in our experimentfunctionsemanticallyaseithermanneradverbialsoradjectivalmodifiers. Figure 2 shows screencaps (captured "mid-action") of six of the co-speech gestures appearing in the videos shown to participants who were assigned to the "gesture-is-present" condition. These six co-speech gestures correspond to Eliza's video utterances like the following:  For a full listing of the written and spoken experimental stimuli for Experiment 1, see Appendix A. Appendix B provides screencaps for all 16 co-speech gestures appearing in the videos.

Design
Each participant saw 19 trials total: 16 experimental trials and 3 attention check trials. Each experimental trial (scenario) came in one of 8 types, depending on (i) whether or not there was a co-speech gesture in the video (the GestureCue condition); (ii) whether or not there was a speech cue in the video, i.e., a linguistic expression verbally expressing the content of the gesture (the SpeechCue condition); and (iii) whether the video was presented with a neutral context paragraph or a positive context paragraph (the Context condition),accordingtotheTonhauseretal. (2013)definitions;seeTable1foralistofall eight trial types. We discuss the three experimental factors in more detail below. At the start of each survey, the participant was randomly assigned to either the [GestureCue = yes] group or the [GestureCue = no] group. The sixteen scenarios were then presented in a randomized order (with the three attention checks randomly interspersed). For each scenario, a 2 × 2 Latin square design was used which crossed the two factors Context and SpeechCue. Each participant saw a trial for every scenario.
The GestureCue condition. The GestureCue condition encodes the presence ("yes") or absence ("no") of a co-speech gesture in the video utterance. As described above, this condition was manipulated between subjects; each participant saw either only videos with co-speech gestures or only videos without co-speech gestures. This design was chosen so as to help the gestures seem as natural as possible and to elicit more subtle felicity judgments, since there seemed to us to be a very real possibility that participants would rate any video with a gesture as worse than a video without one (as indeed turned out to be the case).
Within a scenario and given identical SpeechCue values, the corresponding videos with and without co-speech gestures were identical; that is, the words spoken by Eliza were exactly the same and were delivered, as nearly as possible, with the same intonation.
In trials with co-speech gestures, one factor that was not systematically controlled for waswhetherthegesturemodified(i.e.,whetherthegesturetarget was) a verb or a noun.  In (19a), the gesture target performed is a verb, while in (19b) the gesture target is the NP a dog. Out of the 16 total experimental scenarios, 13 had gestures modifying VPs, while only 3 had gestures modifying NPs, and one of these three needed to be excluded from analysis due to an accidental name mismatch between the contexts and the videos (Scenario 11). We discuss the results of a follow-up analysis on the data based on this division (noun/verb) in Section 2.3. The SpeechCue condition. The SpeechCue condition encodes the presence ("yes") or absence ("no") of a spoken expression in the video that (approximately 1 ) duplicates the same semantic content as the corresponding co-speech gesture for that scenario. We refer to this spoken linguistic expression as a speech cue. Consider the following pairs of target utterances (20) and (21)  In (20b) the speech cue basketball indicates that the sporting event described is a basketball game, and the co-speech gesture SHOOT depicts the act of shooting a basketball; hence both contribute the semantic information that the sport in question is basketball (and so the co-speech gesture is trivial in (20b)). Similarly, in (21b) the speech cue big indicates that Sandy's dog is a big dog, and the co-speech gesture BIG manually depicts the same information (and is hence trivial). Although the speech cues duplicate the semantic content of the designated co-speech gesture for a given scenario, in our stimuli a speech cue can and does appear in trial types for which [GestureCue= no], i.e., in video utterances that do not have a gesture. In these trial types, the speech cue is exactly the same as that which appears in the utterance that has the co-speech gesture for that scenario.
The timing of the SpeechCue with respect to its (roughly) equivalent co-speech gesture varied across scenarios. In some scenarios, the speech cue phrase occurred before the gesture target (22); in others, it was contained within or was the entire gesture target phrase (23); and in still others it occurred after the gesture target (24). (As before, in the followingexamplesthespeechcuesareboldedforidentificationpurposes.) In (22b), the bolded speech cue and took turns with the telescope conveys that the looking up was done with a telescope, just as the gesture TELESCOPE does, and it occurs linearly before the gesture target looking up. In (23b), on the other hand, the bolded speech cue down occurs within the gesture target verb phrase run down. Finally, in (24b), the bolded speech cue on his watch occurs immediately after the gesture target and, like the gesture WRISTWATCH, conveys that Alex checked the time using his wristwatch. As discussed above, the SpeechCue condition was manipulated within subjects and crossed with Context in a 2 × 2 Latin square design.
The Context condition. The Context condition encodes whether the written paragraph shown to participants before the video entails or implies the content of the cospeech gesture (a positive context), or whether it neither entails/implies the content of the co-speech gesture, nor entails/implies its negation (a neutral context). The "positive" and "neutral" terminology follows the naming conventions for m-neutral and m-positive contexts in Tonhauser et al. (2013), where here m is the semantic proposition expressingtheinformationconveyedbytheco-speechgesture.Theeffectistomanipulatethe informativity/triviality of gestural content. An example can be seen in (25) (25a), while participants assigned [Context= positive] were shown the context paragraph in (25b). As seen in the sample target utterance (25c), the co-speech gesture for this scenario is SHOOT, which conveys that the scoring event was done by shooting a basketball. The "neutral" context (a) does not specify what type of sporting event is being discussed; hence it entails/implies neither SHOOT nor ¬SHOOT, meeting the criteria of being an m-neutral context. By contrast, the "positive" context (b) contains the information that the athlete in question is a basketball player; this entails that were this athlete to score in a game, she would do so by shooting a basketball. This is exactly the content of the gesture SHOOT, so (b) entails the content of the co-speech gesture and meets the criteria of being an m-positive context. Notice that the positive and neutral context paragraphs in (25) are extremely similar; theydifferonlyinthereplacementofthephraseathlete with basketball player. In general wekepttheneutral/positivecontextpairsasminimallydifferentaspossible,onlymaking those changes from the neutral to the positive that were necessary to entail or imply the proposition expressed by the co-speech gesture. This follows Tonhauser et al.'s (2013) recipe to have an m-positivecontextbeminimallydifferentfromanm-neutral context, in order to tell if m does indeed require the support of the context to be used felicitously.
The Context condition was manipulated within subjects, and, as discussed above, was crossed with SpeechCue in a 2 × 2 Latin square design.

Results
Out of 198 participants, 5 participants' responses were excluded due to those participants failing at least one of the three attention checks. The results discussed below are for responses from the remaining 193 participants.
Recall that the experimental design included eight trial types resulting from all possible combinations of the experimental conditions GestureCue, SpeechCue, and Context. Table 2 reports the mean acceptance rates, standard deviations, and standard errors across the eight trial types, and Figure 3 shows mean acceptance rates for each trial type with standard error bars. Descriptively, we see an interesting pattern in which the presence of a co-speech gesture decreases acceptability (as indicated by the values of M for trial  types 5-8), although the presence of a matching speech cue with the gesture somewhat mitigatesthiseffect(asindicatedbythevaluesofMfortrialtypes7and8). With respect to the experimental conditions GestureCue, SpeechCue, and Context, trends were as follows. On average, trials with gestures (trial types 5-8) were rejected more often than trials without gestures (trial types 1-4) (with gesture: M = 0.65; without gesture: M = 0.77). Trials shown with a neutral context (1, 3, 5, and 7) were rejected at approximately the same rate as trials shown with a positive context (2, 4, 6, and 8) (neutral: M = 0.72; positive: M = 0.70). Finally, trials with a speech cue (3, 4, 7, and 8) were rejected on average at approximately the same rate as trials without a speech cue (1, 2, 5, and 6) (with speech cue: M = 0.73; without speech cue: M = 0.70). Table 3 gives a breakdown of ratings by scenario. Scenario 11 trials were excluded from analysis because of an accidental name mismatch between the written contexts and the speech in the video. Means for the remaining 15 scenarios ranged from 0.57 (Scenario 1) to 0.82 (Scenario 5), with SDs ranging from 0.38 to 0.50.
Analyses of subjects' judgment responses were conducted using the R programming language(version3.2.3)(RCoreTeam2016)tobuildgeneralizedlinearmixedeffects models (Baayen et al. 2008), using the function glmer from the lme4 package (Bates et al. 2015). In the model with the most data variation coverage (determined by ANOVA testing), the three independent factors were GestureCue (no/yes), SpeechCue (no/ yes), and Context (neutral/positive); the binary naturalness judgment (coded as 1 = "ompletely natural" and 0 = "not completely natural") was the dependent variable, and scenarionumberandparticipantIDwerecodedasrandomeffects.

Discussion
The main experimental question of this study was how contextual support (within a discourseorthesameutterance)influencesthefelicityofco-speechgestures.Thefirstfactor we tested was whether co-speech gestures need to be entailed by their preceding discourse context to be used felicitously. In the terminology of Tonhauser et al. (2013), we wantedtofindoutifco-speechgesturesare[+strongcontextualfelicity(SCF)]or[-SCF]. Our experimental results indicate that manipulating the discourse context from being m-neutral to m-positive (where m is the proposition representing the semantic content of theco-speechgesture)hadnosignificanteffectonparticipants'acceptanceratesofstimuli items. Since participants were equally likely to judge an utterance as completely natural with or without the positive entailment of the content of the co-speech gesture, and assuming that participants were judging the video with the context paragraph in mind, we can tentatively conclude that co-speech gestures are [-SCF]. In other words, co-speech gestures can either be easily accommodated or need no contextual entailment to be used felicitously. This is in clear contrast to other projective content like the English additive particle too, a so-called "hard" presupposition trigger (Abrusán 2016); as we discussed in example (15) in Section 1.2, too is [+SCF] with respect to its implication of the existence ofasalientparallelalternativepropositioninthediscoursecontext.Thedifferingbehavior of too and co-speech gestures with respect to the content of the contexts they appear in supports the claims that the former is [+SCF] (Tonhauser et al. 2013) and the latter is[-SCF].Insum,ourexperimenthasshownthatco-speechgesturescannotbeclassified as "hard" presupposition triggers (assuming participants did indeed read and include the context paragraphs in their linguistic judgments, which concern we will address with Experiment 2 in Section 3). ThesignificantmaineffectofGestureCue in the data indicates that the presence of aco-speechgestureinatrialingeneralhadanegativeeffectontheratingofthevideo. Intriguingly, this negative effect was mitigated when there was a speech cue present along with the gesture in the trial. One way to interpret this is that gestures are used most felicitously when they are semantically duplicating information already present in thespeech/signstream.Thisredundancypreferenceclearlypragmaticallydifferentiates co-speech gestures from well-studied non-gestural supplemental material like appositives; appositives are not felicitous when they convey the same information as the main assertion (Potts 2005), as can be seen in (26): (26) Adapted from Ebert & Ebert (2016) Paul, [the best horse riding instructor in the world], moved to Stuttgart recently (#and is the best horse riding instructor in the world).
The content of the appositive NP in (26), shown in brackets, cannot be reiterated as part of the foreground asserted content. However, as we see from the experimental results, partial and even complete redundancy is completely acceptable with co-speech gestures; (27) is an example of a trial from the experiment with both a co-speech gesture and a speech cue present (Scenario 3, Appendix A).
(27) Sandy just got [a big dog]_BIG yesterday, and I hear it's quite the handful!
Here the gesture BIG is arguably contributing very similar content to the speech cue big. ThesignificantinteractionbetweenGestureCue and SpeechCue indicates that speech cueshadadifferenteffectonjudgmentsdependingonwhetherornottherewasagesture; namely, trials with gestures had a higher average acceptance rate with a speech cue than without, while trials without gestures had a lower average acceptance rate with speech cues than without. Presumably this has something to do with pragmatic calculations about the amount of information present in the utterance and any corresponding implications the hearer (our participants) might have drawn. Clearly, at this point our results raise more questions than answers, especially regarding whether the same pattern wouldemergewithdifferentkindsofco-speechgestures.
Since there was such wide variation in ratings across scenarios, we did several follow-up analyses (which were not planned before the experiment was run) of scenario types to see howpropertiesthatvariedbyscenarioaffectedjudgments.Wefocusedonthreequestions: (i)whetherthegesturesemanticallymodifiedanounorverb;(ii)whetherthespeechcue that duplicated the gesture's content came temporally before, during, or after the co-speech gesture; and (iii) whether the belief state of the addressee, given the context paragraph, affectedjudgments.Forthefirstquestion,wefoundthat,overall,co-speechgesturesthat appeared in scenarios where they were modifying nouns were more acceptable than those modifying verbs ( Next, speech cues that occurred after their corresponding gesture were generally less acceptable than those that occurred with or before the gesture (   Thedifferencesbetweenplacementofspeechcues(before,during,andafterthe gesture) mayinitiallyappeartobeintriguing,butcriticallytherewasnodifferencebetweenthese timing conditions for speech cues in trials where the speech cue was present versus those where it was absent. Using the glmer function in R, we constructed a generalized linear mixedeffectsmodel(fitbyMaximumLikelihood)onthesubsetofthedatawhereagesture was present [GestureCue= yes], with subject ID and scenario number as random effects,theparticipant'snaturalnessjudgment(Response) as the dependent variable, and SpeechCue (yes/no) and SpeechCueTiming (before/during/after) as the independent variables. Neither the interaction between the presence of a speech cue and the speech cue coming after the gesture, nor the interaction between the presence of a speech cue and the speech cue coming beforethegesture,wassignificant(p > 0.1 in both cases). Thissuggeststhatthedifferenceinratingsbetweenthedifferingspeechcuepositionsis an artifact of the large variation in trial types and not in the end about the speech cues themselves.
Anotherfactoronemightsuspectofinfluencingacceptabilityjudgmentsbyparticipants is the belief state of the addressee in the "dialogue" between Eliza and her interlocutor described in the context paragraphs. Does the addressee need to know/believe/be able to infer the content of the gesture proposition in order for the experimental participant to judge Eliza's use of the gesture felicitous? 2 We conducted a follow-up analysis on the data, classifying scenarios (yes/no) according to whether the addressee of the dialogue knows or could infer the content of the proposition in question based on the information provided by the "positive" context. We constructed two separate generalized linear mixed effectsmodels,oneonthe"yes"subsetofthedata(wheretheaddresseeknows/caninfer the semantic content of the gesture based on the positive context), and the other on the remaining "no" subset of the data, with Response as the dependent variable, SpeechCue, GestureCue, and Context as the independent variables, and subject ID and scenario numbercodedasrandomeffects.NeithermodelshowedasignificanteffectofContext on Response(p > 0.1). From this we conclude that the belief state of the addressee is notasignificantfactorinacceptabilityjudgmentsofutteranceswithco-speechgestures based on prior discourse contexts.
In this experiment, there were several methodological issues which may have had an unintendedeffectandrequirefollow-upstudies.Forone,wetoldparticipantsthatthey were going to be asked to rate English sentences as completely natural or not completely natural;however,wedidnotexplainordefinetheconceptoflinguisticnaturalness.This mayinfacthaveresultedinparticipantsperformingdifferentratingtasksfromeachother duetointerpreting"naturalness"indifferentways.Somerespondents,forexample,may have been rating the "acting" performance of the speaker in the videos, rather than rating the felicity of the utterance (speech + gesture) alone. One way to address this might be to provide a simple, non-technical explanation of linguistic naturalness in the survey instructions so as to better communicate to participants what we as researchers are asking them to do. However, at this stage we are still unsure what exactly this would look like, and how one could dissociate performance factors from gesture with a prompt.
A more worrying methodological issue is that from Experiment 1, it is impossible to tell if participants were actually taking the time to read the written context paragraphs and if the contexts factored into their judgments of the video utterances. In fact this is related to our previous concern, because participants might rate the delivery (rather than the linguistic naturalness of the utterance) precisely because they weren't taking context into account. The attention checks built into the experiment could only detect if a participant was not watching or paying proper attention to the videos. Without knowing more about the participants' behavior with respect to the written contexts, we cannot fully conclude whether or not co-speech gestures need to be entailed by the discourse context. We address this concern in a follow-up experiment, Experiment 2, in the next section.

Experiment 2: Context follow-up
In order to address the methodological concern that participants were not reading the context paragraphs and/or not taking them into consideration in their rating of the videos, we conducted a follow-up study on MTurk in which participants were shown contexts that were pragmatically infelicitous with the video utterance, in addition to the usual neutral and positive contexts. The prediction was that if participants were truly reading the contexts and considering them when rating the videos, then the trials with infelicitous contextswouldbeacceptedatasignificantlylowerrate.Thispredictionwasindeedborneout.

Participants
Participants were 90 adults recruited through Amazon Mechanical Turk, restricted to the UnitedStatesregion.Allparticipantsself-identifiedasnativespeakersofEnglish.Participants were compensated monetarily for their participation in the questionnaire via Amazon payments of $2. Experimental protocols were approved by the Harvard University Institutional Review Board under approval number IRB16-1331.

Procedure
The questionnaire was created using the Qualtrics Survey Software platform. Amazon MTurk workers were directed to a Qualtrics link in order to complete the survey. The questionnaire took approximately 10-20 minutes to complete. Participants completed the survey on their own time and on a device of their choosing after receiving a link to the survey; they were instructed at the start to make sure to use a device with a large enough screen to play videos and with working speakers/headphones. The experimental task instructions given at the start of the survey were the same as for Experiment 1 (see Section 2.1.2).
For each trial of the experiment, the participant was presented with the same instructions, namely to read the short context paragraph and then click "play" to view the following video. The video stimuli used were a subset of the video stimuli from Experiment 1. The embedded videos were again hosted through YouTube. OnesignificantdifferencebetweenExperiment1andthisfollow-upexperimentwasthe judgment task instructions shown to participants. In this study, beneath the video, participants were shown the following prompt: PleaseratehownaturalyoufindEliza'sresponseinthevideo,giventhecontext paragraph: Participants again had to press either the completely natural button or the not completely natural button to move on to the next trial. The addition of the words …given the context paragraph to the prompt was intended to signal to participants that they should rate the video utterance in the context of the written paragraph (our concern from Experiment 1).
As in Experiment 1, each participant was presented with three "attention check" trials randomly interspersed between the experimental trials. As before, these attention checkswereusedtofilteroutresponsesfromparticipantswhowerenotpayingsufficient attention to the videos.

Stimuli
The stimuli used for this follow-up study were all re-used from Experiment 1, except for thenewcontextparagraphsofthe"infelicitous"flavor(seebelow).
As an example, we return to the "jewelry scenario" in (28) (compare to example (17) from Experiment 1). In this new experiment, the participants saw one of three possible context variants (i, ii, or iii) as a written paragraph at the top of the page. Below this they saw the embedded video, which either contained a co-speech gesture (28a) or did not (28b). Finally, below the video were the judgment task instructions and the completely natural and not completely natural buttons. Infelicity was designed not to be egregious but frequently involved, e.g., a switch in names, as in (28iii) below. All of the stimuli used in Experiment 2 can be found in Appendix C.
(28) Jewelry scenario, Experiment 2 (Scenario 9, Appendix C) (i) Neutral context: Eliza and Nina are gossiping about their coworker Alicia, and Nina says that she thinks Alicia has a lot of money. Eliza agrees and says: (ii) Positive context: Eliza and Nina are gossiping about their coworker Alicia, and Nina says that she thinks Alicia has a lot of money based on her new pair of earrings. Eliza agrees and says: (iii) Infelicitous context: Eliza and Alicia are gossiping about their coworker Nina, and Alicia says that she thinks Nina has a lot of money. Eliza agrees and says: a. Alicia was wearing real diamond [jewelry]_EARRING at work this morning. b. Alicia was wearing real diamond earrings at work this morning.
Note that in this study, the experimental condition SpeechCuemanipulated in Experiment 1 was eliminated since we only wanted to focus on the relationship between the context paragraphs and the rating of the video utterance. For the [GestureCue= yes] condition, we chose to re-use the "gesture-only" videos from Experiment 1, i.e., those that didn't have a supporting speech cue, as in (28a). By contrast, for the [GestureCue= no] condition, we picked the "speech cue-only" videos that did contain a speech cue, as in (28b). 3 This ensures that, for a given scenario, each member of the pair of videos (e.g., (28a,b)) conveys (roughly) the same overall semantic content, without duplication (again with the caveat that the two are not strictly equivalent, given that the gesture is iconic and interpreted in an analog way).

Design
Exactly as in Experiment 1, each participant saw 19 trials total: 16 experimental trials and 3 attention check trials. There were six distinct trial types, depending on (i) whether or not there was a co-speech gesture in the video (the GestureCue condition); and (ii) whether the video was presented with a "neutral" context paragraph, a "positive" context paragraph, or an "infelicitous" context paragraph (the Context condition) (Table 4). We discuss the two experimental conditions in more detail below.
At the start of each survey, the participant was randomly assigned to either the [GestureCue = yes] group or the [GestureCue = no] group. The sixteen scenarios were then presented in a randomized order (with the three attention checks randomly interspersed), and for each scenario the participant was randomly assigned one of the three Context condition values. Each participant saw a trial for every scenario.
The GestureCue condition. As in Experiment 1, the GestureCue condition encodes the presence ("yes") or absence ("no") of a co-speech gesture in the video utterance. This condition was manipulated between subjects, for the same reasons discussed in Section 2.1.4 above for Experiment 1; thus each participant saw either only videos with co-speech gestures or only videos without co-speech gestures.
The Context condition. The Context condition was manipulated within subjects and encodes whether the written paragraph shown to participants before the video either (i) neither entails/implies the content of the co-speech gesture, nor entails/implies its negation (a neutral context), (ii) entails/implies the content of the gesture (a positive context), or (iii) is written so that the video utterance is a pragmatically infelicitous continuation of the context paragraph (an infelicitous context). Example (29) (29b), and participants assigned [Context= infelicitous] were shown (29c). As seen in the sample target utterance (29d), the co-speech gesture for this scenario is TYPE, which conveys that the essay-writing event was done by typing on a computer keyboard (as opposed to, e.g., with a paper and pencil). The "neutral" context (a) does not specify anything about Jamie's actions other than her location in the library; hence it entails/implies neither TYPE nor ¬TYPE, meeting the criteria of being an m-neutral context. By contrast, the "positive" context (b) contains the information that Julia is on her computer; this naturally implies that if she is writing an essay, she is doing so on her computer, so TYPE is implied and this is an m-positive context. Finally, the "infelicitous" context (c) is logically incompatible with the target utterance because in the context, Eliza doesn't see Julia in the library, but then in the video utterance she asserts that she saw Julia in the library. We would expect participants shown this infelicitous context to rate the video as not completely natural, with or without a co-speech gesture. As we mentioned above, another technique we used to create the infelicitous contexts was to swap the names of Eliza's interlocutor and the person under discussion in the video; this can be seen, for instance, in Scenarios 8, 9, and 10 in Appendix C. This was in anefforttokeeptheinfelicitouscontextparagraphsasminimallydifferentfromtheneutral contexts as possible, just as we strove to make neutral and positive contexts minimally different.

Results
Out of 90 participants, 2 participants' responses were excluded due to those participants failing at least one of the three attention checks. The results discussed below are for responses from the remaining 88 participants. Table 5 reports the mean acceptance rates, standard deviations, and standard errors across trial types, and Figure 6 shows mean acceptance rates for each trial type with standard error bars.
Trends across the experimental conditions GestureCue and Context were as follows. On average, trials with gestures (trial types 4-6) were rejected slightly more often than trials without gestures (trial types 1-3) (with gesture: M = 0.62; without gesture:  Note that neutral and positive context trials were rejected at roughly the same rate. Table 6 gives a breakdown of ratings by scenario. Means for scenarios across trials with infelicitous contexts ranged from 0.23 (Scenario 12) to 0.66 (Scenario 2), with SDs ranging from 0.43 to 0.51. Means for scenarios across trials with either neutral or positive contexts, by contrast, ranged from 0.67 (Scenario 16) to 0.93 (Scenario 5), with SDs ranging from 0.25 to 0.49.
Analyses of participants' judgment responses were conducted using the R programminglanguagetobuildgeneralizedlinearmixedeffectsmodelsusingthefunctionglmer. In the model with the most data variation coverage (determined by ANOVA testing), the independent factors in the model were GestureCue (no/yes) and Context (neutral/positive/infelicitous); Response (1/0) was the dependent variable, and scenario numberandparticipantIDwerecodedasrandomeffects.
Unlike the results from Experiment 1, GestureCuewasnotasignificantmaineffect (p > 0.1).WediscusspossiblereasonsforthisdifferenceinSection3.3.Therewereno significantinteractionsbetweenfactors. We also analyzed the subset of participant responses for which the context presented was either "neutral" or "positive", thereby excluding the data from "infelicitous" Context trials. Again we used R and the the function glmer to build a generalized linear mixed effectsmodel,withindependentfactorsGestureCue and Context, dependent variable Response, and random effects of scenario number and participant ID. Results of the modelindicatenosignificantmaineffectofeitherGestureCue or Context, nor a significantinteractionbetweenthetwofactors(p > 0.1). This supports the conclusion from thefullmodelreportedabovethattherewasnosignificantdifferenceinacceptancerates between trials with neutral contexts and those with positive contexts.

Discussion
Sincethetrialswithinfelicitouscontextswereratedsignificantlylowerthanothertrials, this follow-up study is encouraging, suggesting that participants were reading the context paragraphs and, just as importantly, taking them into account when rating the video utterances. Similarly to Experiment 1, in this follow-up study there was no significant difference in ratings between trials with neutral contexts and trials with positive contexts.Takentogether,wecanconcludemoreconfidentlythatco-speechgesturesarenot sensitive to entailment/implication by the discourse context, and hence are [-SCF] in the Tonhauser et al. (2013) terminology.
The factor GestureCuewasnotasignificantmaineffectinExperiment2.Wesuspect thatthisislikelyduetotheoverwhelmingeffectofcontextinExperiment2withtheintroduction of infelicitous trials, minimizing the variability available among felicitous trials. To investigate this further, we compared the means for the same trials across both experiments (the two trial types [SpeechCue= yes, GestureCue= no] and [SpeechCue= no, GestureCue= yes]), and found that the range of means for Experiment 1 is 0.60-0.77 (mean SD 0.46), compared to the more compressed range of means in Experiment 2 of 0.70-0.82 (mean SD 0.43). In other words, the same trials in Experiment 2 had higher and more compressed ratings for positive and neutral contexts than those trials did in Experiment 1, which we attribute to the addition of infelicitous contexts in Experiment 2. We therefore suspect that this compression of contexts of interest (felicitous trials) may have contributed to the lack of effect for GestureCue in Experiment 2 compared to Experiment 1.
In Section 3.1.4, we noted that many of the infelicitous contexts for this experiment were created by simply swapping the names of the addressee and the person being talked about intheneutralandpositivecontexts.Onemightwonderifparticipantswerepayingsufficient attention to these "name-swap"-type infelicitous contexts to detect the cause of infelicity,andiftheywerenot,whetherthisartificiallyraisedtheratingsofthosetrials.Totest this, we coded the scenarios for Experiment 2 according to whether their corresponding infelicitous contexts were made bad by swapping names ("name-swap") or by some other mechanism ("other"), such as introducing a contradiction between the context paragraph and the video utterance (e.g., the infelicitous context of Scenario 5, Appendix C). We constructedageneralizedlinearmixedeffectsmodelonthedatafromjustthosetrialswhere the participant saw an infelicitous context (condition [Context= infel]), with Response as the dependent variable, type of infelicity (name-swap/other) and GestureCue as the independentvariables,andsubjectIDandscenarioasrandomeffects.Therewasnomain effectoftypeofinfelicityonacceptancerates,norasignificantinteractioneffectbetween type of infelicity and GestureCue (p > 0.1 in both cases). We interpret these results asindicatingthatparticipantsdidnotbehavedifferentlywhenpresentedwitha"nameswap" infelicitous context than they did with other types of infelicitous contexts, and so thecauseofinfelicitydidnothaveanoveralleffectonfelicityjudgments.
As in Experiment 1, we wanted to check whether the belief state of the addressee in the "dialogue" between Eliza and her interlocutor described in the context paragraphs influenced participants' judgments. We conducted another follow-up analysis on the Experiment 2 data, using the same classification of scenarios (yes/no) according to whether the addressee of the dialogue knows or could infer the content of the proposition in question based on the information provided by the "positive" context. We constructed twoseparategeneralizedlinearmixedeffectmodels,oneonthe"yes"subsetofthedata (where the addressee knows/can infer the semantic content of the gesture based on the positive context), and the other on the remaining "no" subset of the data, with Response as the dependent variable, GestureCue and Context as the independent variables, and subject ID and scenario number coded as random effects. Just as in the Experiment 1 analysis,neithermodelshowedasignificanteffectofContext on Response (p > 0.1 in both cases). From this we once again conclude that the belief state of the addressee is not asignificantfactorinacceptabilityjudgmentsofutteranceswithco-speechgesturesbased on prior discourse contexts.
Overall, Experiment 2 lends support to our experimental methodology, providing encouraging evidence that participants judged the overall effect of context plus video when providing their ratings, although the addition of the infelicitous contexts meant thatmoresubtledifferencesbetweengenerallyfelicitoustrialsinsomecasesdisappeared. Together, we suggest that Experiments 1 and 2 provide a more clear overall picture of the empirical landscape for co-speech gesture pragmatics.

Directions for future research
By directly controlling whether the content of co-speech gestures is duplicated in the preceding context and/or the same utterance, the two experiments we report in this paper show how the acceptability of co-speech gestures may be affected by linguistic context.Wehopethatthiscanbeafirststepforfuturestudies,and,insomecases,provide a foundation for interpreting results found in the few already existing studies on the semantics/pragmatics of co-speech gesture.
Through the notion of triviality, we connect to the existing literature on the way that gestures contribute content, which has been the focus of previous discussion of co-speech gestures as either "supplemental" (Ebert & Ebert 2014; or as "cosuppositional" (Schlenker 2018). Under a supplemental analysis, it is quite surprising that speech cues aid the acceptability of gestures, given that supplements are typically less acceptable if they are trivial. On the cosuppositional side, we have shown that co-speech gestures are not "hard" presupposition triggers since they need not be entailed by preceding context; however, many presuppositions are known to be easily accommodated, which could account for their acceptable nature in our study. Under this view, it remains a question why a positive preceding context doesn't also provide the same kind of content support (and our second experiment suggests that it is not due to participants' ignoring written context). Altogether, given the improvement of gestures with matching speech cues, our data are much harder to reconcile with the supplemental theory.
One further remaining question raised by these studies has to do with the choice of gesture targets in the development of the stimuli, discussed above in the Methods section(2.1.3)ofExperiment1.Recallthatwechosesemanticallyunderspecifiedpredicates so that the corresponding co-speech gestures would non-trivially contribute to the truthconditionsoftheutterances.Someunderspecifiedpredicatesseemtohaveapreferred "default" manner or adjectival property that is assumed in the absence of further modification(eitherbyspeechcueorgesturecue).Ebert&Ebert (2016)lookatsome examples of these default interpretations for NPs in German, referring to the phenomena as the "typicality of a gesture for an NP concept". A particularly interesting example they describe involves the NP Fenster 'window'andthetwodifferentshapeproperties of either square or circular; they assume the square option to be the more typically expected shape for windows. For an example from our experimental stimuli, consider the VP writing an essay: Scenario 5 (Appendix A) I saw Julia over in the library [writing an essay]_TYPE -it looks like she's a little preoccupied right now.
In this scenario we chose the gesture TYPE, indicating that the writing was done on a computer as opposed to by hand with pen and paper. In the current decade, it would be a very natural inference to make that writing an essay means writing (typing) on a computer; anyone visiting a college campus these days will see ample evidence of this preferred mode of writing essays. Returning to the experiment, in Scenario 5 trials such as (30) we chose the gesture option with the "default" or more expected interpretation of TYPE instead of a more uncommon co-speech gesture indicating writing with a pen and paper, call it WRITE-WITH-PEN. An important question is whether this choice of gesture has a significanteffectonutteranceratingsandwhetheritinteractsinasignificantwaywith the presence of a speech cue in an utterance. The supplement analysis of co-speech gesture,althoughgenerallynotsupportedbyourfindings,wouldpredictthatlesstrivial,less expected gestures (given speech cues) would be improved, and this does match our intuitions about examples like (2)  Given that the prototypical staircase is not a spiral staircase, the gesture content is unexpected and hence informative. An experiment could be designed with gestures varying along the dimension of unexpectedness, given context and speech cue.

Summary
The primary goal of these experiments was to diagnose the behavior of co-speech gestures in contexts that do and do not entail/imply their semantic contents, thereby gaining a better understanding of when and how co-speech gestures can be felicitously used in conversation. We implemented this question formally using the strong contextual felicity diagnostic proposed in Tonhauser et al. (2013), and by varying whether similar information was contained in accompanying speech cues. The results of our experiments show that co-speech gestures do not need to be entailed/implied by their preceding discourse context; hence co-speech gestures are [-SCF] and cannot be considered "hard" (i.e., unaccommodatable) presupposition triggers. We also saw that speech cues, or speech expressions that (approximately) duplicate the semantic content of a co-speech gesture, hadasignificantinteractionwiththepresenceorabsenceofagestureinthetrials.We take this to be an indication that there are other restrictions on the felicitous use of co-speech gestures that we do not yet know about and that involve when and how the gestures can contribute "extra" semantic content to the utterance meaning. We speculate that this may vary depending on the type of content conveyed in the gestures, for example whether they represent size-and-shape or manner information, and whether they modify nouns or verbs, among other potentially relevant dimensions. We hope that the data