The representation of modal meaning of French sentence adverbs in a qualitative and quantitative approach *

Our aim is to give a representation of the modal contribution of sentence adverbs in comparison to other forms conveying modal meaning, such as tenses and modal verbs. Our analysis will focus on modal sentence adverbs conveying epistemic meaning. These will be compared with the modal verbs pouvoir (can) and devoir (must) as well as with some uses of the future tense (called epistemic uses), with the purpose to present a model allowing to apprehend modal meanings transmitted by lexical and grammatical forms in order to differentiate their functioning. We will then substantiate our qualitative analysis by quantitative studies on the collocates that the modal sentence adverbs co-occur with in contemporary corpora constituted of 21 st century newspapers, as well as in two other corpora representing two different genres and time periods: Universalis Encyclopedia and the digital edition of the Encyclopedia of Diderot and d’Alembert.


Introduction
Our aim is to give a representation of the modal contribution of sentence adverbs in comparison to other forms conveying modal meaning, such as tenses and modal verbs. Our analysis will focus on modal sentence adverbs conveying epistemic meaning. This category includes the following items1: assurément (certainly), certainement (certainly), certes (admittedly), indubitablement (undoubtedly), peut-être (maybe), probablement (probably), sans doute (undoubtedly), sûrement (surely), vraisembablement (probably). These will be compared with the modal verbs pouvoir (can) and devoir (must) as well as with some uses of the future tense (called epistemic uses). Any form in this paradigm (adverb, verb, or tense) is likely to convey an epistemic evaluation by the speaker.
1. « L'heure de l'antidisciplinaire est peut-être venue » (Internet) 'Maybe the time has come for antidisciplinarity' In this use, the sentence adverb peut-être can be replaced by any modal form conveying an epistemic evaluation: 2. L'heure de l'antidisciplinaire doit être/peut être/sera venue 'The time must/may/will have come for antidisciplinarity' Other modal sentence adverbs could also be used: 3. L'heure de l'antidisciplinaire est probablement/certes/certainement/sans doute/… venue 'The time has probably/certainly/undoubtedly come for antidisciplinarity' Although all of the above-mentioned forms can convey a similar modal meaning, which can be considered as being epistemic in the sense that the speaker gives an evaluation about the plausibility of the state of affairs, they do not share the same usage. Thus, the purpose of this article is to present a model to apprehend modal meanings transmitted by lexical and grammatical forms in order to differentiate their functioning. First, we will distinguish modal sentence adverbs from other modal forms, such as the future tense and the modal verb (pouvoir), cf. sect 1.1 to 1.3. Then, we will go deeper into the analysis of modal sentence adverbs looking at the properties that distinguish the use of some of them, cf. sect 1.4 and 1.5.
In the second part, we will present quantitative analyses of the collocates that the modal sentence adverbs co-occur with in contemporary corpora constituted of 21 st century newspapers (sect. 2). We will interpret these results (sect. 2.2.) by comparing them with two other corpora representing two different genres and time periods: Universalis Encyclopedia (sect. 2.2.1.) and the digital edition of the Encyclopedia of Diderot and d'Alembert (sect. 2.2.2). Finally (sect. 3), we will discuss the correlations between qualitative and quantitative analyses of the adverbs in comparison with a similar quantitative analysis of the modal verb pouvoir since it shares, as we will see, one particular use with three among the modal sentence adverbs.
Only in (4) does peut-être convey an epistemic meaning. In (5), the gender of the speaker cannot be doubted, but peut-être can nevertheless be used. The two states of affairs in (5) show some incompatibility (to be a woman is seen as incompatible with the capacity of changing a tire) which is resolved by mais. In such a use the adverb does not by itself endorse a concessive value which is conventionally triggered by mais, but we will see that its functioning is compatible with such a value. According to our analysis, these differences of use exemplified by (4) and (5) depend on the mode in which the core meaning is activated (cf. parameter 2), but not on a difference regarding the core meaning in itself. 2 Such an assumption is also valid for a verbal modal form such as pouvoir or for a temporal modal form such as the future.
We assume that the verb pouvoir conveys an indication of "conceivability" in the following different uses: 6. Il peut avoir la grippe, il y a une épidémie actuellement 'He may have the flu, there's an epidemic going on at the moment' 7. Il peut avoir la grippe, mais je l'ai vu nager comme un poisson à la plage 'He may have the flu, but I saw him happily swimming at the seaside' In (6) pouvoir can be replaced by probablement since it conveys a clear epistemic meaning, whereas this is not the case in (7), where it can commute with the peut-être used in (5).
We also assume that the future tense conveys the same indication of "posteriority" in any of the following uses: 8. I Demain, il aura vingt ans 'Tomorrow he'll be twenty years old' 9. Il est trop tard pour lui téléphoner, à cette heure elle dormira 'It is too late to call her, she will be sleeping at this hour' 10. Federer sera une fois de plus le meilleur, il vient de remporter la victoire à New York 'Once again Federer has proven to be the best (lit. will be the best), he's just won the match in New York' In (9), the future conveys an epistemic stance of the speaker, but not in (10), since the speaker knows the result of the match, nor in (8), where it conveys a genuine temporal meaning.
As previously said, the above differences concerning the interpretation of the form do not depend on the core meaning, but on the mode in which it is activated. There are two modes of activation of the core meaning: a "standard" mode when the form applies to the propositional content of the utterance, or a "diverted" mode when it applies to the occurrence of the utterance, as explained in the next section.

P2: The diverted mode of activation of the core meaning
The assumption according to which a core meaning can be activated in a diverted mode is based on the theoretical background of Ducrot (1984), as indicated in Ricci (2017: 19-20), according to which any utterance can be used by the speaker as an object she/he can comment on. Following this idea, our model assumes that each utterance implies a projection of its occurrence. It is on such a projection, i. e. the OCCURRENCE OF THE UTTERANCE (OCC [U]), that the speaker can make a comment, which can be expressed by means of some modal forms. The core meaning of the modal form applies thus to the projected occurrence of the utterance, that is OCC [U]. For instance, the core meaning that can be associated to peutêtre is POSSIBILITY (POSS). When peut-être is used as conveying an epistemic stance 4, its core meaning applies to the propositional content of the utterance: POSS (P). But when it is used as in (5) the core meaning applies to the projected occurrence of the utterance: POSS (OCC [U]). Thus it is not the propositional content (speaker being a woman) that is qualified by peut-être, which would make no sense, but it is the projection of the occurrence of the utterance, which the speaker comments on as being possible. She/he utters a content P but at the same time, he/she produces a rhetorical figure (which could be assessed as a "preterition") to communicate that the occurrence of such an utterance is not actual but only possible. Such a rhetorical "trick" allows him/her to distance herself/himself from the endorsement of the propositional content of the utterance that just occurred. The label "preterition" is used in French to designate formulae that allow the speaker to attract the attention of the hearer to certain contents, by pretending not to say them. The formulae used are: I do not need to say P, I am not competent to say P, I did not say P… This explains why such a use of peut-être is compatible with a polyphonic interpretation, as assumed in Nølke (1993). According to our model, the polyphony is not intrinsic to peut-être: it is a consequence of the diverted use of peut-être, whose core meaning applies to the OCC [U] instead of applying to the content of the utterance.
Such an analysis is also relevant for modal and non-modal uses of temporal forms. When the future is used as in (8), its core meaning, which is posteriority (POST), is applied to the verbal predicate. But when it is used as in (9) or (10), it is impossible to apply it to the verbal predicate since it refers to a simultaneous or a past event. However, the core meaning does not change. The future is used in a diverted mode. Instead of applying to the content, it applies to the projection of the occurrence of the utterance: POST (OCC [U]). The future indicates that the occurrence of U is postponed. This rhetorical "trick" allows the speaker to distance himself/herself from the endorsement of the content of their utterance, which can be motivated by different causes: in the case of example (9), the motivation for the distancing is the intention of the speaker to show his/her caution. This motivation gives rise to the nuance of conjecture that the future conveys in this example.

P3: Rhetorical nuances of the diverted mode of activation of the core meaning
Every diverted use of a specific form implies a motivation which determines the specific value of the form. Such a value can be considered as semi-conventional. It is conventional in the sense that it is attached to a specific form, but it is semibecause not all uses of the form convey such a nuance (unlike the first parameter, which determines the core meaning). The resulting value depends on the contextualization of the form. This parameter is necessary not only to differentiate or bring together forms pertaining to the same language, but also to capture the differences and similarities between equivalent forms in different languages. For instance, we have seen that in (9) and (10), the future conveys very different nuances. In both cases the future is used in a diverted mode, since it cannot be interpreted as applying to the predicate (the time reference being past for both events), but the motivation involving this "trick" is different. In (9), the indication POST (OCC [U]) -which implies that the endorsement of the content P is postponed -is motivated by the speaker showing his/her caution. This confers a conjectural value to the future. In 10, the same indication is motivated by the speaker showing advanced knowledge of events. Although she/he knows at the moment of the enunciation that Federer has won, she/he indicates that the endorsement of its content is postponed, making it understood as a prediction in hindsight. This confers a value of retrospective prediction to the future. Such a value is not shared by the Italian or German future as shown in Ricci (2017) as well as in Hütsch (2016). In both languages, the future in (10) is understood as conveying a conjectural value. In contrast, in Italian, the future can convey a value which is not transmitted by the future in French, but by the modal sentence adverb peut-être as illustrated in (5) or by the modal verb pouvoir as shown in (7): 11. Sarò anche una donna, ma posso cambiare una gomma 'I may be a woman (lit. Perhaps I will be a woman), but I can change a tire' In the latter example, the nuance conveyed by the future in Italian is equivalent to the one conveyed by pouvoir or peut-être in French. This is due to the fact that according to the third parameter (P3) the motivation of the speaker is the same: he/she shows that P is not relevant. Such a motivation explains the diverted use of the form, allowing him/her not to endorse the content.
To summarize, the core meaning of each of these three forms suspends the endorsement of the content: the future by indicating that it is postponed, the modal sentence adverb peut-être by indicating that it is potential, and the modal verb pouvoir by indicating that it is conceivable (hence not done). The resulting value conveyed by each of these three forms is the same: P is in the background of the current discourse.

Pouvoir: CONC (OCC [U])
When pouvoir conveys an epistemic value as in (6), its value is the result of a standard use of the form, whose core meaning applies to the propositional content: the form indicates that the predicate "have the flu" is conceivable. 3 To sum up, an epistemic meaning can be the result of a standard use (as in the case of peutêtre or pouvoir indicating that an event is possible/conceivable) or of a diverted use (as in the case of the future indicating that the content of the utterance is not endorsed, since OCC [U] is postponed). This difference in the mode in which an epistemic interpretation occurs allows to predict that the utterance does not have the same properties. A conjecture made with the future cannot be cancelled (as noted in Ricci 2017: 46), whereas it can be cancelled when it is made with peut-être or pouvoir: 12. Marie peut être enceinte, mais je n'en suis pas sûr 'Marie may be pregnant, but I'm not sure' 13. Marie est peut-être enceinte, mais je n'en suis pas sûr 'Marie may be pregnant (lit. Maybe Marie is pregnant), but I'm not sure' 14. Marie sera enceinte, ??mais je n'en suis pas sûr 'Marie may be pregnant (lit. Marie will be pregnant), but I'm not sure' The reason is that, with the future, the occurrence of utterance is presented as postponed. So, its endorsement is understood as something that will happen. Such an indication is not compatible with a subsequent content that cancels the former. With pouvoir or peut-être, the event is presented as a possibility or as something conceivable, which can be weakened in a subsequent utterance.

Synthesis
Three parameters are attached to any modal form; the application of these three parameters produces an outcome giving the semantic value that the form eventually conveys. When, according to P2, the form has a standard use, the value depends on its contextualization. There are no particular rhetorical motivations, the use of the form not being diverted. But when the form has a diverted use, this use is motivated by a rhetorical purpose, called "motivation". This motivation is attached to a specific form. It gives rise to a nuance that is considered as semi-conventional.
Below we give a synthesis of the indications related to any of the three parameters for the three forms examined. Their core meaning applies to the content of the utterance. Some of them have a diverted use that allows them to occur with events which are not compatible with an epistemic reading. In that case, their core meaning applies to the occurrence of the utterance giving rise to one particular rhetorical value (indicating that P is in the background of the current discourse). The speaker usually utters another utterance which is interpreted as the foreground of his/her discourse, generally introduced by mais (but). Therefore the entire sequence corresponds to a concessive structure.  (2017) In addition to peut-être, certes and sans doute are found in such contexts, with some peculiarities for sans doute: in the context given by (20), the axiological evaluation given by mûre introduces ambiguity allowing for a possible access to an epistemic interpretation (i. e. the speaker can judge herself as mûre), even if the latter interpretation is not the most accessible (since the evaluation is made by the speaker on herself). The same example in the third person gives rise to an epistemic interpretation (compatible with any adverb of the paradigm):
Firstly, they cannot be particularized in relation to the degree of certainty they express, since they convey different grades of certitude: sans doute and certes represent strong certainty and peut-être weak certainty: 24. Tu m'as convaincue: tu as sans doute/certes 4 raison 'I'm convinced: you are certainly right' 25. ??Tu m'as convaincue: tu as peut-être raison 'I'm convinced: you may be right' Secondly, they cannot be particularized in relation to their dialogical uses, which can be a condition to be compatible with concessive contexts, as assessed in Rossari 2016, since all the modal sentence adverbs can be used to answer a yes/no question, as observed in many studies: Borillo (1976: 87), Molinier (1990: 32-33), Guimier (1996: 110), Rossari et al. (2004: 15 Therefore, isolating these adverbs on the basis of a common property that may not be shared by the other adverbs of the paradigm proves to be particularly tricky. Our quantitative analysis will give us some clues to particularize them.

The indications given by the quantitative approach
The purpose of the quantitative analysis is to see if there are some indications that allow us to understand why only some of these modal sentence adverbs have this non-epistemic use. We take into account the three adverbs that have the capacity to occur in non-epistemic contexts (peut-être, sans doute, and certes) and one of those that do not have this capacity (probablement). We have selected it for its high frequency (it is the most frequent adverb in the press corpus consulted, 5 after peut-être, sans doute, and certes, with the frequencies following this order in both corpora (cf. Rossari and Salsmann 2017).
We have focused on how these adverbs are used rhetorically. We would like to know if the utterance following the one where the adverb occurs is used to support (with connectives such as car, parce que) or to add reservations to the former (with mais) and, more precisely, when the adverb is used in a sequence with mais, to look at its position: before mais, it underlines the background role of the utterance and, after mais, its foreground role. Therefore, we have identified the connective collocates taking the adverb as pivot (search term) based on the loglikelihood value (LL) in a span of 10 and 20 tokens in the context to the right of the pivot. We present the results extracted from the press corpora Le Monde 2008 (20 410 766 tokens) available on the platform BTLC (http://persan.rom.uni-koeln.de/btlsc) (cf. Diwersy (2013)). Using the query for co-occurrence analysis, we have obtained the lists of specific collocates for each pivot. The specificity of these associations between items is calculated by a statistic measure of significance. This measure compares the observed and estimated frequencies of co-occurrence. Applying a threshold value of 10.83, all co-occurrences are considered to be specific if their log-likelihood values are above it, indicating less than a 0.01-percent chance that the co-occurrences are random.
Taking into account these two spans allows us to extract connectives which have a high probability to be linked to the utterance where the adverb occurs. We present below the lexicograms of each adverb for both spans extracted by the platform BTLC from the corpus Le Monde 2008.

Interpretation of the quantitative data
The results for these first data are clear. The connective mais is the first right collocate as a connective for peut-être, certes, and sans doute in both spans. In contrast, mais does not appear among the results for probablement. Its first right collocate as a connective is car in span 20. The similar behavior of these three adverbs in comparison with probablement confirms the qualitative analysis, which shows that these three adverbs share the property of being used in non-epistemic contexts usually inserted in concessive sequences (sequences where the utterance with the adverb is followed by another utterance introduced by mais).
Since mais indicates that the utterance introduced should be interpreted as foreground (cf. Rossari 2016), the common use of these adverbs before mais can be considered as facilitating the understanding of the previous utterance as background, which corresponds to the motivation of their diverted use.
To deepen the interpretation of these data, we can focus on the strength of the attraction between the adverb and mais depending on whether the conjunction is positioned to the left or right of the adverb. We make the assumption that the greater the force of attraction with mais on the right, the more the adverb is able to occur in non-epistemic contexts, facilitating access to a background interpretation of the sequence. We take into account a span of 10 items for both left and right position of the adverb, which better ensures the semantic link between the adverb and the connective. We present the results for Le Monde and refer to Rossari and Salsmann (2017) for the additional press corpus (Le Figaro and Sud-Ouest show similar results).
The difference for peut-être, sans doute, and certes between right or left collocates of mais is clear cut. In addition, we can note that, in the case of certes, there is a dis-attraction between the latter and left mais, which can be interpreted as the effect of the conventionalization of the concessive value with certes (cf. Rossari et al. 2016). Even if for sans doute and peut-être the left mais can still be considered as specific (the value is over 10.83), the difference between the two positions of mais is significant (141 vs 44 for sans doute and 369 vs. 96 for peut-être).
For the other adverbs, the score is either in favor of left mais (sûrement, certainement) or the difference between left and right mais is non-significant.
These quantitative studies show results converging with the qualitative analysis. Adverbs that share the property of being able to be used in non-epistemic contexts also share the property of having the connective mais as a right collocate. The strength of the attraction (greater for certes and peut-être than for sans doute) is congruent with the fact that the non-epistemic context in which sans doute can occur should be more ambiguous than that for peut-être and certes, as can be seen in example (20) or in the following example: 27. Je suis sans doute trop gâté, c'est un fait. 'I may be too spoiled, it is a fact' The ambiguity is due to the addition of "it is a fact" that makes the epistemic judgment expressed by sans doute disappear.

Encyclopedia Universalis corpus
However, such clear results are not observable in any corpus. If we take into account an encyclopedic corpus, the outlines are not entirely convergent with the qualitative analysis. We present the results extracted from Encyclopedia Universalis 2005 (49 859 864 tokens) available on BTLC concerning the attraction with right or left mais.
The use of peut-être is different. Its attraction with mais is inverted in comparison with the corpus Le Monde. It is stronger with left mais than with right mais. With regard to sans doute and certes the results are similar in both corpora. So the attraction between one adverb and a particular connective seems to depend on the genre. However, it is not totally unpredictable that the attraction of peut-être with right mais is better represented in press discourse than in encyclopedic discourse. The former represents a more colloquial style than the latter and concessive uses of peut-être (which are represented by the sequence with right mais) fit better with such a style.

Encyclopedia of Diderot and d'Alembert corpus
Taking another diachronic period into account (the 18 th century) with the Encyclopedia of Diderot and d'Alembert (DDA) 6 shows a different picture of the relation between the adverb and mais.
The results are different from those observed in the corpus Le Monde 2008. The only clear attraction between a modal adverb and mais as right collocate is with sans doute. The other adverbs showing strong attraction in Le Monde 2008 (certes and peut-être) do not show any particular attraction with right mais: for peut-être both right and left mais show attraction and for certes there is even a dis-attraction for right mais whereas we saw the contrary in the press corpus.
Therefore, the only attraction observed in the three corpora is the one between sans doute and right mais, but the strength of this attraction is weaker in the 21 st corpora. There is no indication of attraction between peut-être and right mais and, for certes, the attraction with right mais seems to point at a sudden change (i. e. non-gradual) since the log-likelihood scores show dis-attraction in the 18 th corpus and the highest score in the 21 st corpus.
The attraction of one adverb with mais as right collocate is not only a question of discourse genre but also a question of historical period. The fact remains that the results obtained in the press corpora allow us to consider the connective mais as shaping the value of the adverb making it compatible with "new" contexts such as the non-epistemic ones.

The degree of attraction of pouvoir with mais
To challenge the model and assess its predictability concerning the properties of the modal sentence adverbs having non-epistemic uses, we conducted the same quantitative queries for the modal verb pouvoir since it shares with these adverbs the possibility to be used in nonepistemic contexts, cf. (7) or (16).
We measure the degree of attraction of pouvoir with mais as right or left collocate, in a first test without specifying a particular tense, and, in the second test, by conjugating pouvoir in the present tense only, since this tense seems much more natural in non-epistemic contexts: 28. ??Il pouvait/a pu avoir la grippe, mais je l'ai vu nager comme un poisson 'He may have had the flu, but I saw him happily swimming' This allows a close comparison with the data obtained for the paradigm of epistemic adverbs. Our test concerns pouvoir and devoir, since the latter, like probablement for instance, cannot be used in non-epistemic contexts: 29. ??Il pouvait/a pu avoir la grippe, mais je l'ai vu nager comme un poisson 'He may have had the flu, but I saw him happily swimming' 30. ??Il a probablement la grippe, mais je l'ai vu nager comme un poisson à la plage 'He probably has the flu, but I saw him happily swimming' One could expect that the results for pouvoir and devoir in the present tense show similar differences to those that appear for probablement vs. certes, peut-être, or sans doute. We limited our research to the corpus in which the difference between the adverbs is the clearest, i. e. the corpus Le Monde 2008.

Pouvoir/devoir present tense
Our expectations are partially met. On the one hand, the behavior of the modal pouvoir is very different from that of peut-être, certes, and sans doute, since the latter are much more attracted by the left mais than by the right mais. Pouvoir on the contrary shows much more attraction for the right mais. But, on the other hand, there are three aspects that met our expectations.
(i) Even if it is lower than with right mais, the attraction with left mais is still positive (well above 10.83) for pouvoir.
(ii) For devoir the association devoir…mais is instead negative.
(iii) The present tense shows a slightly higher attraction for pouvoir with the right mais than when it is used in any tense (LL 119 vs. 114).
The fact remains that the high attraction of pouvoir with left mais weakens the relevance of the association of "modal item… mais" as an indication of the non-epistemic use. Extensive research is required in order to be able to differentiate the values of pouvoir in relation to the right or left mais while at the same time looking at the proportion of pouvoir used in a diverted mode.

Synthesis
We have first presented a model that aims to describe how a modal value of a particular form is transmitted. We have seen that such a model allows to differentiate epistemic meaning transmitted by modal sentence adverbs or pouvoir and epistemic meaning transmitted by the future tense. The former is conveyed by the standard functioning of the form (parameter 2) whereas the latter is conveyed by a diverted functioning of the form, whose core meaning applies to the projection of the occurrence of the utterance (OCC [U]). Furthermore, the modal sentence adverbs can also have a diverted functioning. In that case, they can occur in non-epistemic contexts (like the future tense in Italian or pouvoir). Those contexts are usually interpreted as concessive, since they can easily be followed by a sequence introduced with mais. Only some of the modal sentence adverbs (certes, peut-être, and sans doute) can have this functioning. The purpose of the quantitative section has been to find regularities that particularize the functioning of these three adverbs. We have highlighted their attraction with right mais in the press corpus. But we cannot generalize our results for these three adverbs to corpora representing other discourse genres or another diachronic span. We have observed that in the encyclopedic corpus of the 21 st peut-être is more attracted by left mais than right mais, and that in the Encyclopedia of Diderot and D'Alembert only sans doute is attracted by right mais. Certes is neither attracted by left nor by right mais and peut-être is more attracted by left mais than by right mais. Finally, we have compared these results with those concerning pouvoir and devoir in the press corpus. This comparison reveals that, like probablement, devoir is not attracted by right mais, but with regard to pouvoir and peut-être the comparison shows differences, since pouvoir is more attracted by left mais than by right mais. However, the LL value of pouvoir with right mais is well above 10.83 which still indicates an attraction to right mais.

Broader perspectives
The quantitative research has put forward some data that merits further research. It reveals some similarities between the behavior of peut-être in Universalis and DDA and pouvoir in the press corpus. In these corpora, both forms show more attraction with left mais than with right mais, bringing out a similarity between peut-être and pouvoir. This could be an indication that the persistence principle of grammaticalization is still at stake for peut-être. The verb pouvoir would maintain some of its traits in peut-être, making the adverb behave similarly to pouvoir in less colloquial corpora (such as Universalis) or in a previous diachronic span (such as DDA). The results for pouvoir in both corpora shed light on this assumption: In both corpora, pouvoir shows a clear attraction to the right mais which is also at stake for peut-être in the same corpora. So, there are elements to consider that the balance between right and left mais, which we can observe for peut-être according to the three corpora selected, is the consequence of the persistence principle still upheld for peut-être. If this assumption holds, it is less surprising that in press corpora, which represent a less conservative mode of expression, the balance is inverted for peut-être (with attraction for the sequence Adv…mais instead of mais…Adv).
For further research, we could assume that the modal pouvoir has the potential to be used to indicate that the utterance in which it occurs is in the background (like the three modal sentence adverbs illustrated above) and thus attracted by left mais, but such a potential is linked to a grammaticalization process which is initiated for peut-être and not for pouvoir.