As with exclusive particles in other languages, a sentence with ńkóáá ‘only’ asserts exhaustivity.4 One diagnostic for teasing apart assertions from other inferences is the reason-clause test (Beaver & Clark 2008): the reason for the main clause will be the asserted information in the because-clause. Consider (8) below. As the language consultant states, the reason for repeating the exam is that nobody except Yaw passed, i.e., the exhaustive inference (Grubic & Renans & Duah 2019).

Conversational implicatures are cancellable; thus, if the exhaustive inference in the canonical construction is pragmatic it should be cancellable. Indeed, this is what is found, illustrated in (9)A for object focus (Grubic & Renans & Duah 2019). In this series of sentences, the exhaustive inference from the first sentence—I bought a shirt and nothing else; see (6) above—is cancelled by the second sentence. (Recall that narrow subject focus in the canonical construction is argued to be licensed only in non-exhaustive contexts.)

In contrast to canonical sentences, narrow focus in declarative nà-clefts gives rise to an exhaustive inference that is difficult to cancel. This is illustrated in (10)A, the clefted counterpart to (9)A above. The example below is with object focus, but the same unacceptability is found with subject focus (see, e.g., example (47) in Grubic & Renans & Duah 2019).

Given this unacceptability, Grubic & Renans & Duah (2019: §5.2.2) conclude that exhaustivity in nà-clefts is conventionally-coded as part of the meaning of the cleft structure. In the same vein, Duah (2015), following Boadi (1974), posits that “the focus particle nà can be appropriately identified as an exhaustive focus particle because it occurs only in exhaustive focus environments” (p. 25).

Pfeil & Genzel & Kügler (2015) contradict such a strong claim based on the results of two experimental studies. In their production experiment, native-speaker participants used nà-clefts both in exhaustive and non-exhaustive contexts (albeit in the latter much less frequently). Pfeil & Genzel & Kügler (2015: p. 104) write: “our data suggest that this interpretation of the focus marker [i.e., as an exhaustive focus marker] is too narrow, since the use of [nà] is possible in non-exhaustive contexts as well”. Similarly, Titov (2019) contends that nà-clefts do not semantically encode exhaustivity. Consider, for instance, the second clause in example (11), in which the concessive mmom would be odd if the exhaustivity inference was conventionally-coded in the cleft structure in the first clause: the use of the concessive indicates an interpretation of the first clause that ‘I saw the woman (and possibly someone else)’. Based on this example, among others, Titov argues that “the exhaustive reading is not part of the truth-conditional interpretation of the focus construction [with nà-clefts] and is therefore not obligatory” (2019: p. 16).

The ongoing debate about the source of the exhaustivity inference of clefts, and definite pseudoclefts, is the topic of the following section.

Boadi (1974) claims that definite descriptions with identity statements of the form ‘Nipa no a P ne α’ (‘The person who did P is α’) are the same focus-marking constructions as nà-clefts—namely, na is the basic focus marker from which ne in the pseudocleft is derived. More recently, Ofori (2011) analyzed ne as the basic form of the focus marker, while na is a fusion of the ne focus marker and the relative pronoun a ‘who’. Consider (12), in which ne selects a headless relative clause after NP-deletion of the generic noun phrase onipa ‘person’.

In Ofori’s (2011) approach, the morphonological fusion of the remaining contiguous elements ne + a results in the nà-cleft (cf. Titov 2019: §5, who similarly argues for nà being a fusion of the copula and relative marker, albeit the nà-cleft is not a derived form but is itself a type of pseudocleft equivalent to (12b), an inverse pseudocleft). Although differing in the details, the approaches of Boadi (1974), Ofori (2011), and Titov (2019) share the view that definite pseudoclefts and na-clefts are underlyingly the same; similar claims have been argued in the literature for clefts and pseudoclefts in other languages (among others, Akmajian 1970; Percus 1997; Büring & Križ 2013; Križ 2015; 2017; De Veaugh-Geiss et al. 2018).

With respect to their meaning, I will discuss two broad camps in the theoretical literature which take clefts and definite pseudoclefts to be semantically identical. I will refer to these two camps as (A) the SEMANTIC DEFINITE and (B) the DISCOURSE PRAGMATIC accounts. The term SEMANTIC DEFINITE subsumes a diverse group of theoretical analyses which conventionally-code exhaustivity as part of the meaning of definite pseudoclefts and clefts. For instance, in Percus 1997 it-clefts are syntactically derived from an underlying definite description with identity statement. In a nutshell, the derivation is as follows: from the definite pseudocleft ‘the one(s) who ate the beans is Kodwo’, the relative clause is extraposed into clause-final position, and after applying a spell out rule for the definite, the pronoun it appears clause-initially, resulting in ‘it t_i is Kodwo [who ate the beans]_i’. In this approach, the exhaustive inference in clefts is the maximality5 presupposition of the definite description plus identificational semantics. As Percus (1997: p. 333) writes: “[clefts and definite pseudoclefts] are identical in their properties, and any account that applies to one should apply to the other”.

On the other hand, Büring & Križ (2013) propose that clefts and definite pseudoclefts encode exhaustivity as a homogeneity presupposition (cf. Schwarzschild 1996; Löbner 2000; Gajewski 2005). However, Križ (2017) later clarifies: “[Büring & Križ] speak of homogeneity as a presupposition […] though with some reluctance, as they all but say explicitly that they do so merely for lack of alternatives and do not want to strongly commit to a particular status of the neither-truth-nor-falsity that is observed with definite descriptions and cleft sentences, as long as it is the same in both cases” (p. 18). In Križ’s (2017) revised account, clefts and pseudoclefts are taken to be identity statements between individuals: one individual is provided by the cleft pivot and the other by the cleft predicate turned into a number-neutral definite description, illustrated in (13). When exhaustivity is violated the cleft/pseudocleft sentences suffer from a truth-value gap, referred to as homogeneity (see Križ 2019 for an overview to homogeneity; see also Renans & De Veaugh-Geiss 2019 for further discussion of Križ 2017).

A crucial aspect shared by the SEMANTIC DEFINITE accounts is that exhaustivity is semantically encoded in both sentence types, and thus the inference is predicted to arise across speakers and contexts.

The DISCOURSE PRAGMATIC approaches include both the focal-exclusion analysis in Titov 2019 as well as the anaphoricity-driven analysis in Pollard & Yasavul 2016 and De Veaugh-Geiss et al. 2018, among others. For the focal-exclusion approach, Titov (2019) proposes that nà-clefts are an inverse pseudocleft in which an exhaustive interpretation is “favored but not obligatory”, and when there is an available contrastive interpretation the exhaustive interpretation “can be dropped” (p. 17). Specifically, in this approach clefts/pseudoclefts are focus-marking devices which quantify over a discourse-salient set of alternatives,6 and exhaustivity is just one of the ways to do so. Thus, exhaustivity may or may not arise depending on context. For example, the semantics of the example sentence ‘It is Kodwo who ate the beans’ with a contrastive and exhaustive interpretation is shown below, in which the background and set of alternatives to the focus are represented in (14) and the two interpretations are shown in (15) (Titov 2013).

The interpretation obtained depends on how many of the alternatives are considered in context and rejected: for a contrastive interpretation, at least one member of the alternative set is considered, and in all worlds within the speaker’s beliefs,7 this member is rejected as a candidate for fulfilling the proposition, shown in (15a); by contrast, for an exhaustive interpretation all of the focal alternatives are rejected, shown in (15b).

For the second account in the discourse pragmatic camp, Pollard & Yasavul (2016), De Veaugh-Geiss et al. (2018), Destruel & De Veaugh-Geiss (2018; 2019), and Zimmermann et al. (2020) posit that clefts and definite pseudoclefts8 obtain an exhaustive or a non-exhaustive interpretation through the resolution of the anaphoric existence presupposition encoded in both sentence types (see Delin 1992 for anaphoricity in clefts; see also Horn 1981; 2014, who similarly derives exhaustivity from the cleft existential). Specifically, the exhaustive interpretation is derived from the interaction of the existential with wh-questions: a wh-question introduces a maximal discourse referent x with respect to the background property P (Hamblin 1973), and the anaphoric it-cleft picks up this maximal discourse referent as its discourse antecedent, illustrated in (16).

By contrast, the non-exhaustive interpretation is obtained by resolving the existential to a non-maximal discourse antecedent, illustrated in (17). In this example, the cleft specifies an underspecified discourse referent (i.e., the indefinite a gas station). In contrast to Pollard & Yasavul (2016), who take (17) to lack a corresponding question, De Veaugh-Geiss et al. (2018) model such cases as giving rise to a potential question, shown in parentheses (see Onea 2013; 2016).9

Under this approach (non-)exhaustivity arises via the anaphoricity of clefts and pseudoclefts, and not from contrastive or exhaustive exclusion. Nevertheless, what the two approaches in the DISCOURSE PRAGMATIC group share is that clefts and pseudoclefts may give rise to either an exhaustive or a non-exhaustive interpretation.

For the two Akan versions of the experiments: In Experiment I (verifier) 29 participants (male: 9, female: 20; mean age: 22.48, age range: 18–32), and in Experiment II (falsifier) 29 participants (male: 9, female: 20; mean age: 21.34, age range: 18–25) were tested; note that the participants in Experiment I were distinct from the participants in Experiment II.13 Participants, mostly undergraduate and graduate students, were recruited at the University of Ghana at Legon in February 2017 over a period of two weeks. Participants were compensated 10 Ghanian cedis for their participation. For the two German versions of the experiments the data set includes 32 participants in Experiment I (verifier) and 32 participants in Experiment II (falsifier); again, the participants in each experiment were distinct from one another.

All materials, including the instructions and target/filler items, were constructed by the author together with several Akan native-speaker students at the Linguistics Department at the University of Ghana at Legon. For a presentation of the target stimuli, including further details about the structure of the sentences used in the study, see Document 2 of the supplementary materials.

There were four sentence types with exhaustive inferences tested: two control conditions and two target conditions. The control conditions included (a) sentences with the exclusive particle ńkóáá ‘only’, illustrated in (18a), and (b) non-cleft canonical sentences, illustrated in (18b). The target conditions included (c) definite pseudocleft constructions, illustrated in (18c), and (d) nà-clefts, illustrated in (18d). Half of the trials were in past tense and half were in present tense. Note that for the auditory stimuli, in order to ensure that focus was on the intended constituent, e.g., on the object Anan in (18), the native-speaker who recorded the stimuli read all sentences as an answer to a narrow-focus wh-question in English, e.g., Who did Yaa kick out? (cf. Matthewson 2004). The manipulation of the grammatical argument involved having the focused entity in brackets—one of four fictional roommates—be either the subject or object, which was balanced across trials. Importantly, by having four fictional roommates identified by name with no further specification, the focal alternatives were unordered with respect to one another and the exhaustification domain was held constant. (Materials for the German version of the experiments were directly comparable in form though differing in the lexicalizations and, importantly, the grammatical argument manipulation; see De Veaugh-Geiss et al. 2018 for a description of the German stimuli).

For the filler trials there were four sentence types: (i) sentences with the universal quantifier obiara ‘everyone’, as in (19); (ii) sentences with the verum expression ɛyɛ nokware ‘it’s true that’, as in (20); (iii) sentences with a plural conjunction, as in (21); and (iv) sentences starting with nnipa a ɔmo nnuru mmiɛnsa ‘fewer than three people’, as in (22). Half were in past tense and half in present tense, and all items had a subject/object alternation for the relevant manipulation balanced across trials. The filler trials had three crucial characteristics: (i) the number of expected ‘true’ vs. ‘not true’ judgments was balanced across the trials so that the experiment was not biased toward one or the other extreme; (ii) in order to use all four ‘boxes’ throughout the experiment in the incremental-information paradigm (see below for the procedure), the filler trials varied in terms of the number of ‘roommates’ participants had to uncover in order to make a judgment; and (iii) the filler trials differed from the target trials in terms of when a judgment was expected to be made.

Each condition had 8 lexicalizations, 4 with subject focus and 4 with object focus. There were 32 items in the target/control trials and 32 items in the filler trials, for 64 trials in total.

The experiments used a sentence-picture verification task in an incremental information-retrieval paradigm (Conroy 2008; Franke & Schlotterbeck & Augurzky 2016). The procedure was identical to that described in De Veaugh-Geiss et al. 2018; 2017 (German; see §3) as well as in Destruel & De Veaugh-Geiss 2019 (French; see §3) and Zimmermann et al. 2020 (English and Hungarian; see §3); however, the exploratory analysis presented here differs from those studies.

In the instructions, participants were introduced to four fictional roommates, and participants were told that these four roommates will undertake various activities together. At the start of each trial, a computer screen showing four covered boxes was presented while the stimulus played in the participants’ headphones. The screen looked as in the left image in Figure 1. After hearing the auditory stimulus, participants were asked to uncover as many boxes as necessary to decide if the sentence they heard was nokware ‘true’ or ɛnyɛ nokware ‘not true’. Each box contained a photo of one of the roommates14 and a written first person statement about which activity this roommate did, as in the right image in Figure 1. The experimental software was programmed in Python (PSFL: GNU/Linux v.3.4.2) using the PyGame module (LGPL: v.1.9.2a0, Shinners 2011), which allowed full control over the experimental set-up. Both experiments began with three practice trials using stimuli that were unrelated to the experimental materials.

For 23 participants (Experiment I) and 22 participants (Experiment II) out of the total 29 participants per experiment, the boxes were uncovered by moving the cursor over them with the mouse, and after entering a box the cursor could not exit for at least 2000 ms in order to disincentivize unnecessary uncovering of the remaining boxes. When the cursor eventually left a box, the text inside disappeared. Participants were free to choose which box they uncovered next, but they did not know that their choice had no influence on the order of information they received—the order was pre-determined by the experimental software. Participants were instructed to press one of two designated keys on the keyboard for either ‘true or ‘not true’ once they had enough information to make a decision. Once a judgment was made the boxes onscreen were recovered and the next item played in their headphones.

For the final 6 participants in Experiment I and 7 participants in Experiment II the procedure was slightly different. Anticipating the discussion to come, almost all of the participants had behaved unexpectedly in the CANONICAL and EXCLUSIVE control conditions: namely, a response strategy was employed of first uncovering all boxes before making a truth-value judgment regardless of the information presented on screen. Thus, to further disincentivize an uncover-first-judge-later strategy, for these 13 participants the controls were changed to be keyboard-driven (i.e., the space bar was used to uncover boxes) and, crucially, the delay between uncovering was increased to 5000 ms. This increased delay doubled the total running time of the experiment. Although the extended delay influenced to a slight degree when participants made a judgment, many participants still uncovered all boxes before making a decision; furthermore, and most importantly in light of the final judgments made, the reasons for further uncovering remain unclear.

The participants in the Akan version of the experiments generally exhibited an uncover-first-judge-later response strategy, which in this section I will explore in detail. First, I take a look at the results for the control conditions at Box 2, in which either the canonical meaning was verified (Experiment I) or the exhaustivity inference falsified (Experiment II). In these early manipulations, the German and Akan data appear to differ. After this I present a different way of looking at the data—taking into account both the early and late manipulations together—which in fact suggests participants were engaged in the task. Following this, I present the linking hypotheses and research questions for the post hoc exploratory analysis.

For the analysis in Section 3.2, I will focus on the two critical combinations which are identical in informational import when looking at the unordered combinations of early and late information, namely [+VER, –EXH] and [+FAL, +CAN]—i.e., when the canonical meaning holds but exhaustivity is violated. When analyzing the final truth-value judgments, there are only two response choices, ‘true’ and ‘not true’.

The research questions I address in this paper are presented in Q1–Q3 below.

Similar to the semantic-pragmatic division found in the theoretical literature on English it-clefts (see De Veaugh-Geiss et al. 2018: §2.1 for an overview), it has been claimed both (i) that exhaustivity in clefts in Akan is conventionally-coded and thus obligatory (e.g., Grubic & Renans & Duah 2019); and (ii) that exhaustivity is just one of the interpretive options for the nà-cleft structure and thus not obligatory (Titov 2019). Indeed, it is theoretically possible that German and Akan encode exhaustivity in clefts/pseudoclefts differently: e.g., exhaustivity in German es-clefts is a discourse pragmatic phenomenon (see, e.g., De Veaugh-Geiss et al. 2018), while Akan nà-clefts encode exhaustivity as part of their conventional meaning. In fact, Grubic & Renans & Duah (2019) argue for such cross-linguistic variation in cleft exhaustivity for Akan/Ga (Kwa) vs. Ngamo (West Chadic). In the former exhaustivity is claimed to be a conventionally-coded inference, whereas in the latter it is a pragmatic one (cf. clefts in St’át’imcets and Nłeʔkepmxcín, which are also claimed to lack a ‘semantic’ exhaustivity inference; see Davis & Matthewson & Shank 2004; Koch & Zimmermann 2010). Similar cross-linguistic variation is also claimed for the existence presupposition of clefts. For instance, Davis & Matthewson & Shank 2004, Koch & Zimmermann 2010, and Grubic & Renans & Duah 2019 argue that clefts in St’át’imcets, Nłeʔkepmxcín, and Ngamo lack an existential inference; by contrast, clefts in German, Akan, English, etc. are all claimed to encode existence as a presupposition.

Assuming clefts and pseudoclefts in Akan are underlyingly the same, the two are predicted to exhibit parallel exhaustivity effects. Thus, the first question is as follows:

As a secondary investigation, I entertained the idea that exhaustivity in object nà-clefts may differ from subject nà-clefts since for subject focus the cleft is the default structure, whereas for object focus use of the cleft flouts the maxim of manner (e.g., “be brief (avoid unnecessary prolixity)”); by contrast, there is no reason to expect that definite pseudoclefts in Akan will differ across grammatical arguments. Thus:

Finally, given the by-participant results reported in De Veaugh-Geiss et al. 2018, another question that is of interest here is as follows:

I refer to the above early/late combinations as ‘critical’ since it is in these combinations that a difference between sentence types in terms of exhaustivity may emerge. I will start with the control conditions, which are plotted in the right graphs in Figure 3 (on page 16). In Akan, the EXCLUSIVE condition elicited few ‘true’ judgments when exhaustivity was falsified (<9%), and a similar pattern was found in German, although participants there made close to zero ‘true’ judgments (<1%). A brief note on these results: It is, perhaps, not unexpected that the data for exclusives in German show floor effects, whereas in Akan there is more noise. Recall that Akan participants employed an uncover-first-judge-later response strategy. This strategy will increase the demands of the task as more information must be stored in memory over a longer period of time; by contrast, German participants immediately stopped uncovering at the box with the falsifier. Nevertheless, the general response pattern for exclusives is as expected in both languages. Moreover, for the canonical sentences, the opposite pattern was found, also as expected (Akan: 64%–88%; German: 77%–82% ‘true’ judgments). As for the primary conditions of interest, in Akan the DEFINITE PSEUDOCLEFT elicited, on average, low mid-range ‘true’ responses (35%–45%), and in German a similar pattern was found (42%–48%). Moreover, results for clefts were comparable across languages: Akan nà-CLEFTS and German es-CLEFTS elicited ‘true’ responses almost half of the time (39%–47%), similar to their definite pseudocleft counterparts. See Table 2 for an overview of the descriptive results for all sentence types.

For the statistical analysis of the data, two binomial mixed logistic regression models in a Bayesian framework were fitted; see, e.g., Kruschke & Liddell 2018 and Vasishth et al. 2018 for a general introduction to Bayesian modelling. The statistics software R (v. 3.6.3, GPL-2 | GPL-3; R Core Team 2019) with the brms package (v. 2.13.0, GPL >= 3; Bürkner 2017; 2018) was used, which provides an interface to fit Bayesian models using Stan (New BSD License; Stan Development Team 2018). There were 122 participants in the analysis (Akan: 29 participants * 2 experiments; German: 32 participants * 2 experiments), with a total of 4 judgments per participant for each of the 4 sentence types when looking at the critical combinations of early and late manipulations, for a total of 1,952 data points (122 * 4 * 4). Model 1 compares the main effects of ST (Sentence Type, 4 levels: EXCLUSIVE, CANONICAL, DEF. PSE., CLEFT) and LANG (Language, 2 levels: AKAN, GERMAN) as well as their interaction (ST:LANG). Model 2 was fit to the subset of data for Akan to explore the effects of ST (Sentence Type, 2 levels: DEF. PSE., CLEFT) and ARG (Argument, 2 levels: SUBJECT, OBJECT) as well as their interaction (ST:ARG).

For the comparisons in the models, contrast matrices were defined following Schad et al. 2020; see Document 1 of the supplementary materials. For Model 1, the sentence type (within-participant, within-item factor) comparisons were coded using centered treatment contrasts, with clefts as the baseline: ST1 compared the cleft condition to the exclusive condition; ST2 compared the cleft condition to the canonical condition; and finally, ST3 compared the cleft condition to the definite pseudocleft condition. For the factor LANG (between-participant, between-item), sum contrasts were used.17 For Model 2, which looked at the effect of grammatical argument (a within-participant, between-item factor), only the Akan data for the definite pseudocleft and cleft conditions were of interest. The ARG and ST comparisons had sum contrasts. For the random-effects structures, varying intercepts as well as varying slopes for the within-participant and within-item manipulations were used. Moreover, regularizing priors were defined in order to downweight extreme values and obtain stable inferences (Vasishth et al. 2018).18 In Document 1 of the supplementary materials, see Section 2 “Data analysis” for the specification of the models reported here.

From the models I will report the posterior distribution of the parameters of interest and the 95% credible intervals (CrI)—i.e., given the data and model, the interval containing the 95% most credible values of the parameter. In cases when the credible interval of the estimates overlaps with zero, this will be taken as evidence of uncertainty about the effect, since it is possible that the effect is either zero (no effect) or has the wrong sign (e.g., the effect is in fact positive despite the posterior mean having a negative value). By contrast, when the credible interval does not overlap with zero, this will be interpreted as evidence of an effect.

As can be seen in the left plot in Figure 4, in Model 1 for all primary comparisons of interest there is no evidence of an effect: when comparing definite pseudoclefts and clefts in the ST3 comparison ( β^ \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document} = –0.12, CrI: [–0.60, 0.33]) and the interaction of ST3:LANG ( β^ \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document} = 0.06, CrI: [–0.84, 0.95]), all credible intervals overlap with zero to a considerable degree. By contrast, there is robust evidence of a negative effect for the ST1 comparison ( β^ \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document} = –4.55, CrI: [–6.15, –3.23]), with the exclusive control condition more likely to be judged ‘false’ when compared to the cleft condition; moreover, there is robust evidence of a positive effect for the ST2 comparison ( β^ \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document} = 3.55, CrI: [2.60, 4.64]), with the canonical control condition more likely to be judged ‘true’ when compared to clefts. Both of these results are as expected. What is unexpected, though, is the robust evidence of an interaction of ST1:LANG ( β^ \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document} = 3.06, CrI: [1.13, 5.14]), with exclusives in Akan more likely than exclusives in German to be judged ‘true’ despite the violation context, contrary to expectations. However, as discussed previously, the uncover-first-judge-later strategy of the Akan participants will arguably increase the cognitive load of the task; moreover, the noisier data for Akan (7%–9% ‘true’ judgments for exclusives) and the near floor results in German (<1% ‘true’ judgments for exclusives) would likely make any statistical comparison between the two languages robust.

To investigate exhaustivity effects across grammatical arguments (subjects vs. objects), Model 2 was fit to a subset of data: the definite pseudocleft and cleft conditions in Akan. As can be seen in the right plot in Figure 4, for the primary comparisons of interest there is no evidence of a main effect of argument (ARG β^ \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document} = –0.07, CrI: [–0.73, 0.57]); nor is there evidence for an interaction of grammatical argument with sentence type (ST:ARG β^ \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \hat \beta \] \end{document} = 0.50, CrI: [–0.72, 1.79]). In short, from this model there is no indication that clefted object focus differs from either clefted subject focus or their definite pseudocleft counterparts.

As seen in Table 2, clefts and definite pseudoclefts in Akan and German elicited on average intermediate response patterns; however, De Veaugh-Geiss et al. (2018) report for German that the intermediate response pattern was not due to individual participants responding at chance levels with a normal distribution around the mean; rather, participants fell into two main clusters, i.e., those who largely judged the sentences as ‘true’ (non-exhaustive responders) or as ‘false’ (exhaustive responders).

As can be seen in the plots in Figure 5 for the data in both languages, Akan participants similarly exhibit a multimodal distribution. In the left plot one finds the counts of participants given the number of ‘true’ judgments made. Each participant had the possibility of making up to four judgments in the critical manipulations: when participants made 0/4 judgments, they are counted up in the leftmost bar, and so on for 1/4 judgments, etc. Plotted in this way, the majority of participants in most conditions in both languages either made 0/4 ‘true’ judgments (exhaustive responders) or 4/4 ‘true’ judgments (non-exhaustive responders), with fewer participants in between (although the shape of the definite pseudocleft condition in Akan is slightly different, with a peak at the left and perhaps two smaller peaks in the middle and right). In the right plot, the correlation between sentence types is shown: the y-axis shows the counts for clefts and the x-axis the counts for definite pseudoclefts, going from 0 to 4, and each point (jittered) represents an individual participant. The circles (Akan) and triangles (German) in the upper right corner show the participants who judged clefts and definite pseudoclefts as ‘true’ 4/4 times (non-exhaustive responders), while those in the bottom left corner show participants who judged the sentence types as ‘true’ 0/4 times (exhaustive responders). The two lines show the positive correlation between the two sentence types.

In order to obtain participant-specific inferences and correlations in sentence type judgments from the statistical model reported in Section 3.2.2, Model 1 was refit as a zero-intercept model and the distribution of participant estimates was inspected. In particular, I aim to see whether—despite few data points per individual and shrinkage in the mixed-effects model (i.e., strength borrowed from the intermediate response at the population level, making extreme values less likely)—most participants are still expected to have largely positive/negative responses, or whether a mid-range response pattern is instead predicted from the model. Samples from the posterior distribution were obtained, and the by-participant samples were converted into the probability scale for the plots here; see Section 2.3 “By-participant responses” in Document 1 of the supplementary materals for details about this model.

Figure 6 (German) and Figure 7 (Akan) show the model estimates for the mean proportion of ‘true’ responses per participant plus 95% credible intervals—with solid lines indicating that the credible intervals do not cross chance (0.5) and dashed lines indicating that they do. Participants along the y-axis are ordered by the predicted means (x-axis) of the cleft condition, and the plots are cut into tertiles by two vertical lines in each grid. Overall, visual inspection of the plots suggests that, although the model still predicts a high number of exhaustive and non-exhaustive responders for clefts and definite pseudoclefts, there is high uncertainty in the model estimates for many participants—and more so for the Akan participants in comparison to the German participants. Looking first at the exclusive condition in both languages, one can see that all participants are predicted to have mean proportions of ‘true’ responses—along with most credible intervals—within the first tertile (exhaustive responders), although for Akan participants slightly more variability is found. The canonical condition, by contrast, showed higher variability in both languages, although the majority of participants (German: 50/64 participants; Akan: 43/58 participants) have mean proportions of ‘true’ responses within the third tertile (non-exhaustive responders).19

Turning now to the main conditions of interest: For German clefts (Figure 6), participants are largely projected to be either exhaustive or non-exhaustive responders—with the predicted means for the majority of participants in the first and third tertile, largely at the extremes, and roughly 2/3 having credible intervals clearly on one side of the scale (cf. the post hoc analysis in De Veaugh-Geiss et al. 2018: §3.3, albeit employing different methods). Clefts in Akan generally exhibit a similar shape (Figure 7). That said, there are proportionally fewer non-exhaustive responders, and moreover, there is more gradience in Akan from exhaustive to non-exhaustive responders—with most participants having very broad credible intervals indicating uncertainty in the directionality of the predicted response. Nevertheless, for both languages there is a considerable subset of participants for whom clefts are predicted to be judged non-exhaustively; moreover, a similar distribution of individual responses is found for definite pseudoclefts. In fact, for the cleft and definite pseudocleft conditions there is a very strong positive correlation found in the model (r = 0.90, CrI: [0.80, 0.97]): that is, when exhaustive or non-exhaustive responses are predicted for clefts, the same is predicted for pseudoclefts. To sum up: Model 1 predicts a broad range of individual responses, including many non-exhaustive responders, and a strong positive correlation in judgments for clefts and pseudoclefts.