Beyond the Implicit/Explicit Dichotomy: The Pragmatics of Plausible Deniability

In everyday conversation, messages are often communicated indirectly, implicitly. Why do we seem to communicate so inefficiently? How speakers choose to express a message (modulating confidence, using less explicit formulations) has been pro - posed to impact how committed they will appear to be to its content. This commit - ment can be assessed in terms of accountability – is the speaker held accountable for what they communicated? – and deniability – can the speaker plausibly deny they intended to communicate it? We investigated two factors that may influence com - mitment to implicitly conveyed messages. In a preregistered online study, we tested the hypothesis that the degree of meaning strength (strongly or weakly communicat - ed) and the level of meaning used by the speaker (an enrichment or a conversational implicature) modulate accountability and plausible deniability. Our results show that both meaning strength and level of meaning influence speaker accountability and plausible deniability. Participants perceived enrichments to be harder to deny than conversational implicatures, and strongly implied content as more difficult to deny than weakly implied content. Furthermore, participants held the speaker more ac - countable to content conveyed via an enrichment than to content conveyed via an implicature. These results corroborate previously found differences between levels of meaning (enrichment vs. implicature). They also highlight the largely understud - ied role of meaning strength as a cue to speaker commitment in communication.


Introduction
An important challenge in understanding human communication is the question of what processes drive message construction.Why do speakers construct utterances in the way they do?How do they generate utterances to achieve their intended effects?
Recently, speaker commitment emerged as fundamental in answering these questions (Geurts 2019): utterances commit the speaker to the truth of a proposition or to a future course of action (Hamblin 1971;Beyssade and Marandin 2009), but such commitments are only effective if listeners are able to track these commitments and hold speakers accountable to them (e.g., Vullioud et al. 2017; see also Mahr and Csibra 2018, 2020, 2021).
How speakers choose to express their message should impact how committed they are perceived to be -how much others will hold them accountable to what they have expressed and the degree of plausible deniability of their message.Speakers are held accountable for the message they convey and will incur reputational costs if it is found to be unreliable (Boulat and Maillat 2017;Brabanter and Dendale 2008).It is therefore sometimes in their interest if this message is conveyed in such a way that it is plausibly deniable.While the notion of plausible deniability is first a psychological one, which relies on intuitive judgments, several theoretical analyses have now been put forward to account for it (Camp 2018(Camp , 2022;;Dinges and Zakkou 2023;Mazzarella 2021;Pinker 2007;Pinker et al. 2008).Plausible deniability allows speakers to refute having intended a certain message (typically an implicit one), for instance when confronted by the recipient (Brown and Levinson 1987;Lee and Pinker 2010;Pinker 2007;Pinker et al. 2008).By taking a strategic approach to utterance construction, speakers can manipulate the extent to which the audience can hold them accountable for the meaning they have conveyed (Pinker et al. 2008;Soltys et al. 2014).Illustrating this, Lee and Pinker (2010) found that speakers favoured implicit constructions when they were asked how they would attempt to bribe a policeman.The choice to forego an explicit offer in such a scenario is strategic, as speakers can deny their implicit offer and avoid unpleasant and/or awkward social repercussions.Speakers can thus mitigate the risks of a negative outcome, since 'cooperative' recipients can accept implicit offers, while 'antagonistic' recipients would not have enough evidence to confront them.Therefore, how committed speakers are perceived to be is importantly related to plausible deniability.On the one hand, deniability might influence how speakers construct their utterances in strategics situations.On the other hand, plausible deniability might be a function of how strongly a speaker is committed.
However, while multiple factors have been found to influence perceived speaker accountability, much less work has focused on the factors that determine plausible deniability beyond how explicitly or implicitly a message is conveyed.One factor research has focused on is speaker's confidence in expressing a message, which can be marked either linguistically (e.g., 'I guess', 'I'm sure') or non-verbally through posture, gestures, tone of voice or facial expressions.Speaker confidence has been found to impact both the message's credibility -by increasing its chances of being accepted by the interlocutor -and the speaker's accountability -namely the social repercussions if the message is found to be unreliable (Vullioud et al. 2017;Mazzarella et al. 2018).Similarly, claims about the source of one's information ("I saw it" vs. "Somebody told me") have been shown to have an impact on the message's credibility, as well as the speaker's accountability (Mahr and Csibra 2021).
Here we extend this work, by focusing explicitly on two additional pragmatic factors that might not only influence speaker accountability but also plausible deniabil-ity: the level of meaning and its strength.First, speakers can convey messages with different degrees of explicitness, that is, using different levels of meaning: speakers communicate not only the linguistically encoded meaning of their utterances, they can also pragmatically enrich the content of these utterances or implicate propositions in addition to what they explicitly say (Grice 1989).The meaning of the conjunction 'and', for instance, can be pragmatically enriched to 'and then'.An utterance of "they got married and had a child" will then prompt the hearer to believe the two events happened in a certain order.The meaning of an utterance can depart even more from its linguistic form and its explicit content through an implicature, for instance when a child's request for a snack is met with an implicit denial in the form of "dinner will be ready in 10 minutes".
Second, speakers can convey messages with different degrees of manifestnesse.g., a pragmatically inferred part of meaning (be it an enrichment or an implicature) may be more or less strongly communicated.Meaning strength is conceived here as the accessibility of what is communicated; it depends both on how manifest the speaker made their intention to communicate a specific content and how important (or inconsequential) the recovery of this content is for the interpretation of the utterance (Wilson and Sperber 2004).Meaning strength depends on the context of the utterance.For instance, "they got married and had a child" is likely to strongly communicate that the marriage preceded the child's birth in the context of a discussion about the couple's adherence to certain social norms.On the other hand, if the same sentence appears in an exchange about a drop in the couple's social engagements, the temporal reading of and might still be accessible, but is only weakly communicated.Importantly, both the level of meaning and the strength with which a content is expressed may have an impact on how committed a speaker will be perceived to be.
Given that a speaker risks suffering social repercussions when implying something false, would these repercussions be more severe when this content is communicated via a pragmatic enrichment rather than via an implicature?Or would they be worse off if the false content is strongly rather than weakly implicated?Alternatively, would the differences in speaker accountability emerge only when these different types of contents -weakly or strongly implicated or enriched -are denied?Here, we aimed to investigate the influence of the level of meaning and meaning strength on the speaker's accountability, and whether they bring about similar effects on their message's plausible deniability.

How might the Level of Meaning Impact Accountability and Plausible Deniability?
It has recently been proposed that commitment is stronger when meaning is fully linguistically encoded (explicitly communicated) than when it is merely implicated (Morency et al. 2008;Reboul 2017).Indeed, conversational implicatures have been found to foster less accountability than explicit contents, while explicit contents and presuppositions lead to similar levels of accountability (Hall and Mazzarella 2023;Mazzarella et al. 2018).Plausible deniability should be similarly influenced by the degree of explicitness of the conveyed meaning -i.e., by its level of meaning (Brown and Levinson 1987).
Pragmatic inferences are by definition cancellable -i.e., an utterance that implies a proposition p can be followed by the phrase 'but not p' without logical contradiction (Grice 1989;Levinson 2000).However, a proposition may be cancellable without being deniable -or at least, not plausibly so (Pinker et al. 2008): you may be able to logically cancel the non-literal content of your utterance without being in a position to plausibly deny intending it in the first place.If, when asked whether you know about a new policy introduced at a meeting, you answer "I wasn't there" the implication that you did not know is clearly cancellable -there is no logical contradiction between not being present and knowing about something.Yet, it will be hard to deny that you intended to convey your ignorance of the new policy.Pragmatic phenomena can therefore be logically cancelled but whether, and how, they can be plausibly denied is a more complex issue that will depend largely on the properties of the context of utterance (Mazzarella 2021).
Of course, denying that some fully explicit content was intended is difficult -short of lying or claiming a mistake.The phenomenon of plausible deniability primarily applies to contents conveyed via pragmatic inferences, which seem much easier to revoke.Yet, these do not form a homogeneous category: the outcome of a pragmatic inference might be more or less explicit and thus, we believe, more or less plausibly deniable.
Since Grice (1989), most pragmatists consider there to be different types of implicit (i.e., cancellable) contents.Pragmatic enrichments,1 such as the temporal reading of and, go beyond what is linguistically encoded in an utterance, but they are linked to linguistic terms or structures, in the presence of which they will often be derived (e.g., conjunction 'and' enriched to 'and then'; disjunction 'or' enriched to 'not both'; quantifier, 'some' or 'most' enriched to 'not all').In contrast, implicatures 2 , such as the implicit denial for a snack seen above, are entirely context-dependent additional propositions and do not depend on any specific linguistic feature.Their derivation requires taking into account the proposition explicitly expressed, as well as the context of utterance and the speaker's intention (see e.g., Grice 1989; Levinson, 1983;  Sperber and Wilson 1986/95). 3Pragmatic enrichments are considered more closely related than implicatures to the linguistic form and the explicit content of an utterance: some theorists maintain that they are derived automatically, unless blocked by the context (Horn 1989;Levinson 2000), while others argue that, despite being pragmatically inferred, they are part of the explicit content of the utterance ('what is said', in Gricean terms) and contribute to its truth conditions (Carston 2002;Levinson 2000;Récanati 1993Récanati , 2001Récanati , 2004;;Sperber and Wilson 1986/95).Theoretical debates notwithstanding, there is a general sense that pragmatic phenomena might be more or less explicit, with implicatures firmly lodged in the implicit camp and pragmatic enrichments verging toward, or achieving, explicitness (see, for example, Levinson 2000).
A large amount of research focuses on whether participants can distinguish enrichments from explicit content ('what is said' in Gricean terms) to determine whether they contribute to the truth-conditional meaning of the utterance.Enrichments were originally found to be judged as part of 'what is said' (Gibbs and Moise 1997), but the picture subsequently became more complex (Bezuidenhout and Cutting 2002).It seems that participants' intuitions differ depending on the type of pragmatic inference (Doran et al. 2009) and the task used -for instance, the types of enrichments investigated by Doran and colleagues (2012) were neither consistently included nor excluded from 'what is said'.
Relatedly, several recent studies investigated whether interlocutors consider false information conveyed via pragmatic inferences to be an instance of lying.This research on the comprehension of deceitful implicatures and enrichments yields mixed findings (for a study on the production of misleading enrichment and implicature, see Franke et al. 2020).Weissman and Terkourafi (2019) show that participants consistently judged false implicatures to be non-lies, while some types of enrichments (e.g., upper-bounded interpretation of numerals) were more easily considered to be lies when the inferred meaning was false.Hall and Mazzarella (2023) also found that speakers suffered more reputational cost when they communicate false information via enrichments than when they communicated the same information via implicature.Yet, other studies suggest that even false implicatures may be considered eligible to be lies, and sometimes as much so as false enrichments (Antomo et al. 2018;Viebahn et al. 2018;Willemsen & Wiegmann, 2017).Furthermore, Wiegmann (2022) showed that many among the implicatures used by Weissman and Terkourafi (2019) were still considered to be cases of lying (and, thus, the speaker presumably conceived to be committed to the implicated content) provided that the intention to communicate the implicated (and deceptive) content was made salient.
Notwithstanding the fact that there are likely cultural differences in people's intuition of what counts as a lie (e.g., Danziger 2010; Hardin 2010; Hruschka 2020), Reins and Wiegmann (2021) used a variety of particularly relevant measures to investigate the folk notion of lying.Following four scenarios involving a false implicature or enrichment, participants were asked whether they considered them to be lies, among other questions; these were compared to an additional set of measures including (among others) explicit questions about commitment (did the speaker commit themselves to the false enrichment/implicature) and deniability (could the speaker convincingly deny it).Lie responses correlated with those assessing commitment and deniability.Reins and Wiegmann found that false implicatures were mostly judged to be lies.However, attributions of lying, as well as commitment and deniability, were lower for implicatures than for enrichments.In a similar vein, Bonalumi and colleagues (2020) found that people considered unfulfilled promises conveyed via enrichment to have been broken, but not those conveyed via implicature.
Overall, although enrichments are pragmatic inferences -and thus cancellablethey often seem to be perceived as contributing to the utterance's truth-conditions.As a result, they generally appear more difficult to deny than implicatures, which -it is generally agreed -are part of 'what is implicated'.Additionally, as mentioned earlier, implicatures lead to less accountability than the explicit content of an utterance (Hall and Mazzarella 2023;Mazzarella et al. 2018).The two levels of meaning -enrichments and implicatures -should, therefore, modulate both accountability and plausible deniability differently (as suggested by Bonalumi et al. 2020;Reins and Wiegmann 2021;Wiegmann 2022).

How might Meaning Strength Impact Accountability and Plausible Deniability?
Another factor that can be linked to both plausible deniability and accountability is the degree of manifestness of what is communicated, i.e., its strength4 .A pragmatically inferred part of meaning (be it an enrichment or an implicature) can be more or less strongly communicated; this will depend on how manifest the speaker made their intention to communicate it (Wilson and Sperber 2002), as well as how essential the pragmatic content is to understand the overall communicative act.First, a strongly pragmatically inferred content (enrichment or implicature) is a proposition the speaker intends to communicate, and they will therefore make this intention clear to their interlocutor, whereas their intention to communicate weaker contents is hazier and, as a result, less manifest to their interlocutor.Second, a strong implicature or enrichment is generally crucial to make the speaker's utterance relevant in context, while the recovery of a weak one might be optional.Both aspects point towards strongly pragmatically inferred parts of meaning as being more accessible for the hearer than weaker ones.
Imagine two young parents arriving at home after braving a downpour and commenting on how they never want to leave the comfort of their living-room again.If one of them exclaims: "We're out of milk!" the implicature that someone must go out to get milk for the child is strongly communicated.Indeed, it is difficult to see how the utterance would be relevant in this context if the implicature was not intended.On the other hand, other (weaker) implicatures might have been intended, or note.g., "our child drinks more milk than she used to" or "you forgot to put milk on the grocery list again"5 .
As Mazzarella (2021) notes, the strength of an implicit meaning will affect who endorses responsibility for the pragmatic inference.In the case of a strong implicature or enrichment, the speaker bears more responsibility since they make their intention to communicate it clearly manifest.Inversely, in the case of a weak implicature or enrichment the responsibility of deriving it lies mostly with the hearer (Sperber and Wilson 2006).This, in turn, should involve consequences for how accountable the speaker will be perceived to be: the stronger the implicature or enrichment, the more committed to it the speaker should appear (see also Boulat and Maillat 2023).Plausible deniability should be equally affected by meaning strength.Since the derivation of a strong implicature or enrichment is paramount to understanding the utterance, there is little room left in these cases for an alternative interpretation.Any attempt of denial would, thus, be less plausible, since there is only a narrow range of possibilities to re-construct the context -and thus providing an alternative, non-committal, interpretation of the utterance (Mazzarella 2021).On the other hand, weak implicatures and enrichments offer the speaker exactly this range of possibilities, suggesting that meaning strength is inversely connected to plausible deniability.
The hypotheses that stronger implicatures and enrichments should be more accessible than weaker ones, but also more committal, are mostly borne out by the handful of studies investigating meaning strength.Nicolle and Clark (1999) first found that strong implicatures prompted participants to select the implied meaning conveyed by the utterance as the best reflection of 'what [it] said'.In contrast, with weaker implicatures, participants were more likely to select the minimal proposition of the utterance as representative of the explicit content ('what is said').Consistent with the hypothesis that meaning strength (modulated by relevance) influences accountability and plausible deniability, Bonalumi and colleagues (2020) found that the same explicit broken promise produced different social repercussions for the speaker depending on whether the recipient was known to rely on the promise made by the speaker.Finally, Sternau et al. (2015) investigated the deniability of enrichments, as well as weak and strong implicatures using an explicit question about deniability (akin to Reis & Wiegmann, 2021).Although their findings rely on participants' a priori intuitions, rather than actual attempts of denial, they indicated that enrichments are perceived as less deniable than implicatures, and strong implicatures less so than weak ones.
Taken together, these results suggest that strong implicatures are more easily included into the explicit content, have higher impact on accountability and might be harder to deny compared to weaker ones.Note that since meaning strength is a feature of enrichments and implicatures alike (Clark 2013), it should modulate commitment and plausible deniability for both phenomena (Mazzarella 2021;and Sternau et al. 2017 both also make this prediction for plausible deniability).

The Present Study
A message can be conveyed both with different degrees of manifestness, i.e., more or less strongly, and with different degrees of explicitness, i.e., graded levels of meaning (see Fig. 1).As reviewed above, both factors might affect the extent to which a speaker is committed to the content of her utterance, and consequently how easily that commitment is deniable.Here, to further understand the attribution of commitment (and how speakers strategically attempt to avoid it), we aimed to directly test the effects of meaning strength and level of meaning on deniability.Specifically, we sought to test the following hypotheses: 1. Strongly implicated contents should lead to higher accountability and be more difficult to deny than weakly implicated contents.2. Enrichments should lead to higher accountability, and be more difficult to deny, than implicatures.
We tested these hypotheses in an online experiment.The experiment itself -the Commitment Experiment -was preceded by a Norming Study to ensure participants interpreted the materials with the pragmatic inferences and drew comparable intended meanings in each experimental condition.Participants were presented with written scenarios in which speakers used different levels of meaning (Enrichments or Implicatures) with different strengths (Weak or Strong) to make a commitment.
Meaning strength depended on how manifest the implied content was in the scenario.Implicatures were always determined by the interaction between the utterance and the specific context, while enrichments were of four types: temporal conjunction enrichment ('and' meaning 'and then'), the enrichment of the conditional ('if') to a biconditional ('if and only if'), as well as the scalar inferences linked to the quantifier Fig. 1 The degree of explicitness (x-axis) interacts with the degree of manifestness (y-axis): fully linguistically encoded contents, as well as enrichments and implicatures, can be more or less strongly/ weakly communicated 'some' ('not all') and to disjunction ('or' meaning 'not both'; for discussion of these phenomena see for instance, Levinson 2000;Carston 2002;Noveck 2004).We chose four different types of enrichments to make sure our findings could generalise to enrichments as a category and were not limited to a single phenomenon.We took care to pick phenomena generally agreed to be enrichments across theoretical frameworks -i.e., all of the phenomena we chose are considered as enrichments or as generalised conversational implicatures (GCIs) by authors such as relevance theorists (Sperber and Wilson 1986/95;Carston 2002;Noveck and Sperber 2007), Récanati (2004), and by neo-Griceans (such as Levinson 2000).These authors agree that these pragmatic phenomena differ from (particularised) implicatures and may (unlike implicatures) contribute to the truth-conditions we intuitively assign to the utterances in which they appear.
In the Norming Study, we measured whether participants inferred the expected enriched/implicated meaning by asking them whether the speaker intended it, as well as their level of confidence about their answer.The Commitment Experiment itself was conducted to test our main hypotheses that more strongly implicated contents, on the one hand, and enrichments, on the other, lead to higher accountability and are harder to deny than weaker implicated contents and implicatures, respectively.Participants were presented with scenarios (selected from those tested in the norming study) in which speakers later broke their implied commitment.Following previous studies investigating speaker commitment (Mazzarella et al. 2018;Bonalumi et al. 2020; Yuan and Lyu 2022), we used two indirect measures to assess whether the speaker was held accountable for breaking their commitment: asking participants whether the speaker was blameworthy (which relates to partner control attitudes, i.e., judgements aimed to manipulates partners' behaviours so to disincentivise these behaviours in the future) and trustworthy (which relates to partner choice attitudes, i.e., judgements indicating one's willingness to avoid the interaction with that partner in the future).Previous results suggest that trustworthiness and blameworthiness judgments tend to mirror each other (although the former seem to be more influenced by pragmatic factors than the latter, as shown by Mazzarella et al. 2018).We, therefore, predicted that these two measures would provide similar results: a speaker judged more blameworthy would be deemed less trustworthy, and vice versa.Additionally, the influence of the level of meaning and of meaning strength on denial was also assessed.There is always a risk that participants' a priori intuitions on something like deniability (as measured by Reins andWiegmann 2021 andSternau et al. 2015) would be coloured by pre-assumptions or other kind of judgements about deniability-hypothetical considerations may generate additional inferences that colour participant answers and may not accurately reflect acceptance of an actual denial.We therefore favoured a more direct approach to establish whether an implied content is perceived as plausibly deniable or not: we compared participants' judgments following the broken commitment with, and without, denial.A decrease of accountability following denial would indicate the plausible deniability of the implied content; if speakers making an implied commitment are held less accountable when it is denied compared to when it is not denied, it is fair to conclude that the implied commitment was (to some extent) deniable.We predicted that the impact of meaning strength and of the level of meaning on plausible deniability would mirror their impact on accountability.

Norming Study
The Norming Study focused on the derivation of the appropriate pragmatic meanings, conveyed either by enrichments or by implicatures in different contexts.The results of this study were then used to make informed decisions about which scenarios to use in the main experiment.Participants were not presented with any breach of the implied commitment, since this might have confounded participants' responses to the implicature question.

Participants
We recruited 150 participants (105 females, M age = 33.23)through Prolific Academic (Palan and Schitter 2018).Eligibility criteria for participation in the study were age (20 to 70) and first language (English).We excluded participants if their completion time diverged by more than three standard deviations from the mean (M = 379.86s, SD = 375.6 s; N = 2), or if they provided wrong answers to the comprehension question (N = 29).Participants provided informed consent before taking part in the experiment and were paid £0.84 for their time.

Materials
We created 21 scenarios, each with the following structure: • Context describing the situation in which the utterance occurs -manipulated so to create Weak and Strong conditions; • Dialogue containing the speaker's implied commitment to accomplish a specific task.The commitment was conveyed either via Enrichment or Implicature (see Table 1).
All the scenarios are available at https://osf.io/2fu93/files/osfstorage.We modulated meaning strength through changes in the scenario context resulting in an increase or decrease of the relevance of the speaker's utterance.This change in relevance should affect the accessibility of the implied commitment.For instance, in the scenario mentioned in Table 1, the change in context would concern the number of customers waiting to be served.As Elliot utters, "I'll finish this cocktail and change the keg," in a weak context where few customers are waiting, the order in which he does so should be less relevant than in the context in which there are numerous customers to serve.Although the implicature would be drawn in both contexts, in the latter, stronger context, Sophie would understand Elliot's utterance as more pointedly ordered, thus resulting in a more accessible and stronger implicature.
The level of meaning was examined using 8 scenarios conveying commitment via an implicature and 13 scenarios conveying commitment via an enrichment.Four types of enrichments were used: two types of scalar implicatures -one linked to the quantifier 'some' ('some', but 'not all'), the other to the connective 'or' (but 'not both') -as well as the temporal enrichment of the connective 'and' (to 'and then') and conditional perfection, where 'only if' is derived from 'if' (see Table 2 for examples).

Procedure and Design
The Norming Study used a mixed factorial 2 ('strength' as between-subjects factor: Strong vs. Weak) x 2 ('level of meaning' as within-subject factor: Enrichment vs. Implicature) design.Participants were randomly presented with four enrichments and two implicatures and saw all of them either in a strong or in a weak version.After reading each scenario, participants answered a comprehension question about the scenario content.Participants were then reminded of the speaker's utterance containing the implicit commitment, and were asked to answer an Implicature question and a Confidence Rating question, as illustrated below: • Implicature Question Do you understand Elliot [speaker] to have meant that he will finish making the drink first, and then change the keg [implied commitment]?
(Yes/No/I don't know) • Confidence Rating How confident are you in your answer?Rate your confidence from 0 to 5, with 0 being 'not at all' and 5 being 'completely'.
(6-point Likert scale) Sophie and Elliot are colleagues and both work in a bar as bartenders.There is no more craft beer on tap and Sophie and Elliot have to change the keg.It is a Saturday night and there are a lot of impatient customers.Sophie: There's no more craft beer on tap.Elliot: I'll finish making this cocktail and change the keg.

Implicature condition Weak condition
Strong condition Scott and Samy meet every week to watch the new episode of their favourite TV show together.This week, Samy can't make it.When this happens, the one who can't make it usually catches up on the missed episode before the next one the following week.
Scott and Samy meet every week to watch the new episode of their favourite TV show together.This week, Samy can't make it.It is the first time it happens and Samy is upset he can't make it.
Samy: I won't be able to come over to watch the show with you this week.I have an urgent deadline.Scott: It's ok, there's a new movie I've been meaning to see.

Results and Discussion
We took the answers 'No', and 'I don't know' to the implicature question as indicating that the implied meaning had not been inferred by participants, while 'Yes' answers were interpreted to indicate that the implicature had been drawn.To get a measure of how reliably participants inferred the implied meaning, we converted participants' responses to the implicature and confidence questions into a unified 'inference score' by multiplying participants' confidence responses by -1 when participants failed to draw the correct inference and by + 1 when they succeeded (for a similar approach, see Starmans and Friedman 2012).
Based on this measure, we selected the four implicature scenarios with the highest scores in both strong and weak contexts.The same process was applied for the enrichments (on 'and', 'or', 'some' and 'if'), we chose the scenario with the highest inference score.However, in the case of 'or' enrichments, we found the scenario with the highest inference score to be flawed: the inference giving rise to the exclusive meaning was a product of world knowledge rather than of the utterance in context.Therefore, the enrichment with the second-highest inference score in this category was selected instead.Across all selected scenarios, 95.79% of participants drew the correct pragmatic inference and the average inferences score was 4.21 out of 5.

Commitment Experiment
The Commitment Experiment was designed to test our main hypothesis that meaning strength and level of meaning modulate both the extent to which a speaker is held accountable for their implied commitment and the extent to which a speaker can plausibly deny such a commitment.We predicted that contents conveyed via enrichment would lead to higher accountability ratings and would be less easily deniable than contents conveyed via implicature.We also predicted that strongly conveyed contents would lead to higher accountability ratings and would be less easily deniable than weakly conveyed contents.
We measured perceived accountability through two test questions: one asking how blameworthy the speaker is (blame question), the other asking how much participants would trust the speaker in the future (mistrust question).The blame question measured commitment attribution via blameworthiness; the mistrust question measured whether participants would draw any inference about the speaker's dispositions (resulting from the breach of the commitment) which may be relevant to future interactions.While accountability was measured using direct questions, to assess the effect of plausible deniability we introduced an additional between-subjects factor: the denial of the implied commitment.If the accountability ratings of an implied commitment are lower when it is denied than when it is not, then the implied commitment was (at least to some extent) deniable.

Methods
The study was pre-registered on OSF.io, with the sample size, planned analyses and participant exclusion criteria specified.The pre-registration document is available at https://osf.io/nkv63/.Some of the analyses presented in the paper deviate from the pre-registered ones in view of comments received during reviewing processes and conference presentations.

Participants
A power analysis conducted with G*Power 3.1 (Faul et al. 2009) revealed that, assuming a small to medium effect size (F = 0.175), a sample size of 400 participants would convey a statistical power of 0.89.Consequently, we recruited 400 participants (297 females, M age = 35.39)through Prolific, with age (between 20 and 70) and first language (English) as eligibility criteria.Participants provided informed consent and were compensated with £0.09.Participants were exposed to only one story, and each experimental session lasted few minutes (an average of 112s to place a response).Data was discarded for participants who took too much or too little time to complete the study (three standard deviations from the mean; N = 7) or failed the comprehension question (N = 6), totalling 13 excluded participants.The final analysis thus included 387 participants.

Materials
The commitment experiment used the eight scenarios selected based on the results of the Norming Experiment.In four scenarios the commitment was conveyed through an implicature and in four others the commitment was conveyed through an enrichment, one in each category: quantifier 'some', connectives 'or' and 'and', conditional 'if' (see, Table 2).
In contrast to the Norming Experiment, the commitment experiment included an additional between-subjects factor: 'denial'.In the Denial Present condition, the breach of the commitment was followed by the speaker's denial of the implied content, when confronted by the recipient.The denial always appeared in the following form: "I didn't say I would [implied commitment].I said I would [as explicitly stated]".

Results
All analyses reported here were performed using R version 3.4.1 (R Core Team 2020), RStudio (RStudio Team 2020).To test our hypotheses, we computed separate multiple linear regression models for each of our dependent variables (blame and mistrust ratings) (see e.g., Norman 2010, The unstandardized results of this approach are summarized in Table 4; standardized coefficients are reported in the text below. Across participants and conditions, blame and mistrust responses were significantly correlated (r = .62,p < .001).Nonetheless, these two measures were not equally sensitive to our experimental manipulations: our analysis only explained a significant amount of variance for blame ratings.For mistrust ratings, however, the same model did not explain a statistically significant proportion of variance (p = .283).Therefore, we did not interpret the effects of our manipulation on this variable and only report the results of our regression analysis for blame ratings here.Figure 2 illustrates the distribution of blame ratings across experimental conditions.

Sophie and Elliot are colleagues and both work in a bar as bartenders.
There is no more craft beer on tap and Sophie and Elliot have to change the keg.It is a Saturday night and there are a lot of impatient customers.

Implied commitment (either Enrichment or Implicature)
Sophie: There's no more craft beer on tap.Elliot: I'll finish making this cocktail and change the keg.

Breach of implied commitment
Elliot leaves the cocktail he was making and goes to change the keg.The customer whose cocktail it was complains to Sophie.Sophie is unhappy about this.

General Discussion
As anyone who follows daily politics knows, in order to avoid accountability people are often tempted to exploit plausible deniability: whenever a commitment is broken (a promise is not lived up to, or an assertion is found to be false), one might try to limit social repercussions by denying having committed to it in the first place.In order to refute a commitment one might deny the alleged meaning of the original utterance ('I didn't say that…') or appeal to an alternative meaning ('I meant that…') (Boogaart et al. 2020).Pinker and colleagues have argued that speakers in certain circumstances capitalise on these options when they generate their messages (Pinker et al. 2008;Lee and Pinker 2010).In this study, we investigated what factors influence plausible deniability.What determines whether a speaker can get out of conversational commitments by denying they intended the alleged meaning of their utterance?If a commitment is plausibly deniable the costs the speaker incurs following its breach will be mitigated after denial.However, the implicit/explicit dichotomy is not the only factor at play.Our design therefore explored the impact of two factors: the degree of explicitness (the level of meaning) of what is communicated and its strength.
Our findings indicate that both meaning strength and level of meaning influence plausible deniability: in the presence of a denial, participants judged the speaker to be less blameworthy when the implied content was weakly conveyed (but not when it was strongly conveyed), or when this content was an implicature (but not an enrichment).In view of the results of the norming study it is unlikely that these observations could be attributed to participants failing to draw the intended implicatures from our materials.
As predicted, our results show that denial works better in weak contexts than in strong contexts: weak contents showed higher deniability (i.e., they were associated with lower blame ratings after denial) than strong contents, for which blame rates remained unaffected by denial.This is one of the key findings of our study.The fact that weakly conveyed contents are easier to deny is consistent with Nicolle and Clark (1999), who found that strongly conveyed meanings (in contrast to weakly conveyed ones) are frequently associated with 'what is said'.Our results also reinforce the conclusions of Sternau et al. (2015): when explicitly asked, their participants found implicatures more deniable than enrichments, and weak implicatures more deniable than strong implicatures.They are also consistent with the considerations by Dinges and Zakkou (2023), who argue that deniability is an epistemic feature preventing an audience to reason or form knowledge about what was communicated.Together, these findings confirm that, as argued by Mazzarella (2021), meaning strength exerts a considerable influence on plausible deniability.
Importantly, the current study also shows that levels of meaning modulate plausible deniability.Implicatures appeared to be more easily deniable (with blame rates lower after denial) than enrichments (blame rates were unaffected by denial).This is reminiscent of Reins and Wiegmann (2021), who found a similar pattern relying on participants' a priori intuitions about denial.Our findings also echo those of Hall and Mazzarella (2023) who found participants would trust more a speaker uttering a false enrichment than one conveying a false implicature.We used four different types of enrichments -conjunction enrichment, conditional perfection, as well as scalar inferences linked to the quantifier some, and to disjunction; our results are therefore not reduceable to a single pragmatic phenomenon, instead they can be, to some extent, generalised to enrichments in general (see also, Hall and Mazzarella 2023, for how different types of enrichments might affect speaker accountability).One caveat worth noting, however, is that -since scenarios were not matched for content -we cannot currently rule out that the effect of levels of meaning was driven to some extent by differences in content.
These findings are also consistent with the contextualist claim that enrichments can be included into the truth-conditions of the utterance (i.e., 'what is said') (Récanati 1993(Récanati , 2001(Récanati , 2004;;Carston 2002;Sperber and Wilson 1986/95).If enrichments affect the truth-conditional content of the utterance and are perceived as being part of 'what is said', then they should, ceteris paribus, be harder to deny.Our results are thus in line with the those of Doran et al. (2012) indicating that, contrary to implicatures, enrichments are sometimes included in 'what is said'; Weissman and Terkourafi (2018), who show that false enrichments are considered lies, while false implicatures are not (see below for further discussion); as well as Bonalumi et al. (2020), who highlight that unfulfilled enriched promises are considered de facto broken promises, while unfulfilled implicated promises are not.
We collected two measures of accountability: a blameworthiness judgment and an untrustworthiness judgment.While the two judgments were correlated, we found no evidence that mistrust judgments were affected by our experimental manipulations.One possible reason for this discrepancy might be that the mistrust question was always presented after the blame question.It may be that some participants, after having simulated a partner-control strategy (i.e., blaming the speaker for falsely implying something), perceived an additional partner-choice strategy (i.e., mistrusting the speaker) as redundant or excessively severe (see Noë and Hammerstein 1994).It may also be the case that blameworthiness is more severely impacted by pragmatic factors than trustworthiness.It could also be that the different utterances presented in the stimuli were themselves carrying disparate illocutionary force, causing an array of other expectations that were instead (partially) satisfied.There would then be no reason left to consider the speaker untrustworthy, despite still being blameworthy for the misleading utterance.Finally, it may be that the phrasing of the mistrust question was confusing for the participants -leading them to interpret it as a trust question.
Interestingly, some very recent studies have linked the concept of lying to commitment (Reins and Wiegmann 2021;Wiegmann et al. 2021).Specifically, they argue that participants' intuitive understanding of lying does not only encompass intentionally false assertions (part of 'what is said'), but also false implicatures to which the speaker seems committed (against traditional views, which restrict lying to what is explicitly asserted, see, e.g., Carson 2006Carson , 2010;;Saul 2012;Stokke 2018). 6Claims concerning the nature of lying and whether it should include misleading implicit communication are beyond the scope of our work.Nevertheless, our findings have interesting consequences for views which equate lying with intentionally communicated misleading content, including implicit content -as long as the speaker appears sufficiently committed to it.If commitment is central to an analysis of lying, it is essential to investigate markers of commitment.From this perspective, the present study precisely highlights two factors routinely used to modulate commitment: the speaker's choice of level of meaning and the strength of the implicit content.Indeed, the difference we find between enrichments and implicatures, both in terms of accountability and of deniability, echoes the results of Reins and Wiegmann (2021).Even more crucially, our findings emphasize the role of meaning strength in how committed the speaker appears to be to a given implicit content: meaning strength seems to play a crucial role in shaping our intuitions about commitment.If speaker commitment is the key to the hearer's perception of truth and lying -and their related social consequences -it is critical to further investigate the role of meaning strength.
When speakers aim to limit their commitment and the social consequences of communicating potentially unwelcome or unreliable messages, one good strategy is to increase the room for plausible deniability (Lee and Pinker 2010;Pinker 2007;Pinker et al. 2008).The results presented here provide clear evidence of the effective impact of a denial on speaker's accountability.Our findings suggest that accountability can only be mitigated by denial when certain pragmatic factors are in place: despite being logically cancellable, not all contents conveyed implicitly by the speaker can be plausibly denied.This will depend on the degree of explicitness and the strength with which the message is communicated.Only when these are properly aligned can the speakers optimally minimise the social consequences of an unreliable message.Strategic communication is a complex phenomenon that goes beyond the implicit/explicit dichotomy.

Table 1
Examples of scenarios in the four conditionsEnrichment condition Weak conditionStrong condition Sophie and Elliot are colleagues and both work in a bar as bartenders.There is no more craft beer on tap and Sophie and Elliot have to change the keg.It is a Tuesday night and there are very few customers.

Table 2
Examples of different types of enrichment used in the norming study and in the commitment experiment

Table 3
Scenario structure and measures used in the commitment experiment with example (of the Strong + Enrichment + Denial Present conditions) Sophie: You said you would finish making the cocktail before changing the keg!Elliot: I didn't say that I would do that first.I said I'd finish making the cocktail and change the keg.
Violin plots of distributions of blame ratings across meaning strengths, presence of denial, and levels of meaning.Denial was associated with lower blame ratings in Weak conditions and when meaning was conveyed via Implicature 95% CI [-0.86, -0.08]; t(381) = -2.39,p=.017)andasignificant interaction effect between 'level of meaning' (Implicature) and 'denial' (Present) (ß = -0.53,95%CI[-0.92, -0.15]; t(381) = -2.70,p=.007).Standardized parameters were obtained by fitting the model on a standardized version of the dataset.These results suggest that, denial was effective at reducing blame rates in Weak and in Implicature conditions while having no effect in Strong and Enrichment conditions (see Fig.2).