Paul Grice (1975) provided what is arguably the best known account of discourse connectives. In his seminal work, he described expressions such as but and so in the context of conventional implicatures. Unlike conversational implicatures, whose extra-sentential propositions are inferable from a speaker’s utterance in context, conventional implicatures are triggered directly by specific lexical items. This makes them non-calculable, because the hearer does not need to evaluate contextual information and world knowledge to “work out” the implicature. Note that the implicated information that we drew out with respect to the examples in (1b) and (1c) is directly due to the discourse connectives. That is, the words but and so license inferences that, in turn, provide the hearer with the means to derive the speaker’s informative intention.

While Grice viewed the extra-logical contribution of discourse connectives as pragmatic in nature, his approach did not lead to a consensus. Here, we cite three prominent accounts that essentially provide semantic alternatives to Grice’s approach. Bach (1999), for one, vehemently argued against Grice’s notion of conventional implicatures and proposed instead that the contribution of discourse connectives can be analyzed solely in terms of the entailments that they generate. Bach (1999) added that while the second entailment created by a discourse connective does not concern the at-issue content, it is still truth-conditional. For example, in (1c), so appears to establish that Camille’s meeting is the cause that is prompting his running late. That causal link would become false if the sentence is followed by “He is at a lab meeting indeed but that is not why he is running late”. Similarly, Potts (2005) has proposed that the double entailment of an expression such as but reflects a multidimensional meaning. According to this approach, the sense of contrast carried by but and the sense of causality carried by so are each semantic contributions to their respective words. A third influential approach comes from Segmented Discourse Representation Theory (SDRT) (Asher & Vieu, 2005), which analyzes discourse in terms of rhetorical relations, or “what a sentence does to another sentence” (Jasinskaja & Karagjosova, 2020, p. 3). Given that a discourse is assumed to be hierarchical, it is generally accepted that rhetorical relations can be broken down into two sorts – those that provide linguistic effects that can be described as (a) coordinating (staying on the same hierarchical level) or else as (b) subordinating (those that make links to a different level). This analysis leads to an exhaustive list of relations: Coordinating cases refer to rhetorical relations described as Parallel; Contrast, as in (1b); Narration; and Result, as in (1c). Subordinating cases describe rhetorical relations such as Elaboration and Explanation. A good example of an (explanatory) subordinating relation can be seen with the connective because, as in Mary is talented because she won first prize. While SDRT has not been concerned with the relative processing costs of discourse connectives, as we are here (as far as we know, no proponent of SDRT suggests, say, that a connective expressing a subordinating relation should be more time-consuming than one expressing a coordinating relation), it is conceivable that one can derive processing predictions based on its principles. We will address this further in the Section 4.

A more sympathetic reaction to Grice’s conventional implicature approach comes from Relevance Theory. Blakemore’s (1987) account begins by making a distinction between conceptual words, such as boy and runs, and words encoding an instruction regarding how to process a concept (procedural words), such as but and so. Blakemore considers discourse connectives as good examples of procedural words in that a discourse connective constrains the kind of cognitive effects that an utterance can draw (for discussion, see Blakemore, 2000; Wilson, 2016). The examples in (1b) and (1c) fit well into Blakemore’s scheme. Aside from conjoining, the discourse connectives but and so encode procedures that help addressees capture the speaker’s intended meaning.

Likewise, Relevance Theorists view and in procedural terms, as well. By comparing cases in which two elements are conjoined by and to those that have juxtaposed sentences without and, Blakemore and Carston (1999, 2005) argue that a sentence that introduces and insures a communicative effect. In other words, these authors claim that and prompts a minimal, weak procedure. Given that a but or a so implicitly expresses a form of conjunction too, we consider this proposal compatible with our initial one as well as with our goal, which is to investigate whether the additional information implicit in but and so prompt extra, isolable cognitive processing, compared to and.

Note that the elementary procedural contribution of and should be distinguished from the myriad ways that context often provides additional meaning to sentences that use this term. For example, sentences conjoined with and are often associated with temporal readings based on the order of the mentioned segments. Consider how Mary had a baby and got married can be taken to imply that the two events occurred in that order, so that and ought to be interpreted as and then. I. A. Noveck and Chevaux (2002) argued that such interpretations are due to conversational implicatures and, in support of that claim, they presented evidence showing that the developmental patterns for such temporal inferences resemble findings for scalar terms (I. Noveck, 2001). That is, seven-year-old children tend to accept as true (and 10-year-olds and adults tend to reject as false) a sentence conjoined by and that presents two (previously-described and ordered) events as inverted. This finding indicates that these so-called temporal inferences are optional and ultimately defeasible. This claim holds for a host of contextually determined meanings, including adversative and causal readings, that could appear to be part of and’s meaning.3

Discourse connectives have played a role in another linguistic tradition, one in which scholars aim to understand what makes a text (or units of discourse) cohesive, above and beyond grammatical structure. Halliday and Hasan (1976, p. 5) argued that cohesion can be achieved through a set of devices – reference, repetition, substitution, ellipsis, and conjunction – so that speakers can create textual contiguity.4 In this approach, conjunction is comprised of linkers which connect sentences to each other, and these come in a variety of forms that can be taxonomically described (Martin, 2002). That is, conjunctions can be introduced via addition, comparison, temporality, and causality. One can see how discourse connectives fit into this scheme. For example, in (2a–2c), which are borrowed with slight modification from Hussein (2009), cohesion is carried out through linking linguistic expressions such as and, yet, and now, which are referred to as additive, adversative and temporal.

While many adhere to this general view – that discourse markers are critical for understanding text (understood as a kind of linguistic unit) because they maintain cohesion – scholars often disagree about the structure or the source of these expressions (see Fraser, 1990; Schiffrin, 1987; Zwicky, 1985). As to be discussed in Section 1.2, one of the earliest attempts to create a psychologically plausible taxonomy of coherence relations (T. J. M. Sanders, Spooren, & Noordman, 1992) emerged from this general approach that connectives maintain cohesion.

For Fraser (1996, 1999), speakers employ discourse connectives to highlight how they intend two sentence parts to relate. It then becomes the interlocutor’s task to shape an interpretation of the utterance which is compatible with the discourse relation signaled by the speaker. Anscombre and Ducrot (1977, 1989), on the other hand, claim that by signaling specific discourse relations, discourse connectives constrain the argumentative direction that the discourse can possibly take. This, in turn, is believed to impact the hearer’s processing of the post-connective part of the utterance. In a third approach, Schiffrin (1987, 2005) assigns to discourse connectives the role of creating a coherent flow in between the different ideas expressed in the discourse. In her analysis, discourse is structured on several levels (planes) and connectives such as but and so intervene in the ideational plane of discourse.

While the above-referenced scholars generally agree that discourse connectives play a crucial role in utterances, they generally do not agree about the frameworks in which the connectives are described and the purposes they serve in comprehension. Nonetheless, most of the theoretical and classificational approaches to the study of discourse connectives could serve as inspiration for an experimental investigation. Below, we turn to prior experiments.

For the purposes of providing a summary, we break down exisiting experimental work on discourse connectives into two thematic categories. One is comprised of experiments from researchers of text and discourse who underline the importance of coherence for comprehension. The other is driven by experimenters who lack such theoretical commitments but who are generally interested in the way a discourse connective affects, say, the speed of integration of the second segment or other expressions downstream from a connective.

The current work aims to address both of the above questions. Here, we compare the processing profiles of discourse connectives expressed in English – and, but and so – as they are used in simple conjunctive sentences. We are interested in (a) the way a participant processes the connectives when they are initially encountered, as well as (b) how they affect the processing of the segment that follows each sort.

Our predictions are drawn from Relevance Theory, according to which utterances are signals that are presumed to help a listener determine the speaker’s intended meaning (Sperber & Wilson, 1986/1995). As far as an addressee is concerned, incoming input is characterized through two features. One is the cognitive effects that an input produces (e.g., in terms of new conclusions produced) and the other is how much effort it takes to process that input. The word relevance refers to the processing of incoming input via the interplay of effects produced in the addressee and the effort it takes to carry them out (e.g., highly relevant input provides maximal cognitive effects, while being minimally costly to process; relatively low relevant input provides minimal effects, while being costly to process). We assume that an extra-logical procedure, such as the ones in but and in so, prompts added effects in an addressee when compared to and; all things being equal, it is reasonable to assume that this relative gain in anticipated information is offset by a processing cost. Therefore, we predict that we will find – for a series of out-of-the-blue statements presented in ceteris paribus conditions – a processing cost difference between the discourse connectives but and so, on the one hand, and and, on the other, from the moment that they are encountered. We add that, while the procedures attached to but and to so may differ from one another (along with their respective processing costs), we do not make specific predictions in that regard. For the purposes of the current work, we are only concerned with whether we can demonstrate that but and so each have extra-logical features that generate further processing and are not assumed to be carried by the more neutral and.

Given that the effects arise from what we are assuming to be obligatory procedures, it follows that one ought to find differences in the post-connective region among the three connectives as well. For example, one would expect that a segment that follows but and that provides a contrast with the first segment should be easier to process (as measured by error rates and processing time) than one that does not. In the event that a test sentence does not provide a contrast when but is employed, this is likely to slow down processing. Likewise, while causality is part of the meaning of so, its procedural meaning might add gratuitous processing if nothing causal can account for the second segment. Prior to the experiments, it was unclear whether a connective that ended up being part of a weakly relevant expression (but used without a cashed-out contrast or so without an evident cause-effect relationship) would affect validity judgements. This, in itself, was of interest to us. To summarize, we endeavour to determine whether a discourse connective’s hypothesized procedure can be said to manifest itself through two dependent measures – validity judgements and latencies.

Our experimental approach differs from those that currently populate the literature. We simply seek to determine whether one finds indications of processing costs and benefits as participants process the three terms – and, but and so – from the moment each is presented. To test our hypotheses, we designed two self-paced reading experiments in which participants read simple statements broken down into two parts, which we refer to as segments, like the one in (6). Note that the vertical pipe indicates where the first segment ends and where participants advance the text. Once the sentence is completed, the participants’ task is to decide if the sentence accurately describes the letters in a target word (here and elsewhere we will always use the word BET for expository purposes). There are two experiments, because in Experiment 1 we present the word (which is the source of a truth value judgement) before the two segments are read, and in Experiment 2, we present the word after the two segments are read. The latter Experiment has the advantage of separating the reading time of the second segment from the truth-evaluation.

As we indicated, we will compare the processing costs of but and so trials to those of the trials containing and, which serves as a baseline, in order to determine whether, and at what moment, one finds costs (and, in some cases, benefits) from an extra-logical procedure. One will notice that we designed our experimental material so that participants rely on as little context and world knowledge as possible, while still having content that remains meaningful enough (by virtue of the target word, the sentence has a denotation and can, thus, be true or false). Ultimately, we are in a position to isolate the processing role of each discourse connective by ensuring that each one would be the only possible source of variability in a test-sentence (in principle, no other discourse relations could emerge from the semantics of the sentence alone).

This approach is unlike most experimental work in the field and is, to the best of our knowledge, novel. As reviewed above, experimental work concerning discourse connectives systematically includes rich thematic content (e.g., about exams, racetracks, or shopping adventures), which inevitably encourages the processing not only of discourse connectives but of a very wide variety of other contextual inferences that could vary as a function of background information. These thematic texts arguably mask the effects generated by the discourse connectives themselves.

We will now present our experiments. To anticipate, the results of both experiments support our main hypothesis that but and so trigger procedures that are cognitively costly, from the moment that they are read, relative to the processing of the truth-functional and. They will also show that these terms prompt specific processes that become apparent downstream.

This experiment was designed to test our hypothesis that the presentation of each of the discourse connectives but and so would be associated with a procedure that distinguishes them from and, which we assume lacks an extra-logical procedure. This would be expressed through slowdowns at the moment of their mention and, eventually, through specific effects in processing downstream in a paradigm whose sentences varied with respect to the polarity of the second sentence and sentence validity. While accuracy rates remained very high (all conditions yielded rates of correct responses that were at least 93 per cent), one can see that our findings were largely consistent with our pre-registered predictions. We review the highlights of Experiment 1 below and in order of their appearance.

Answer Accuracy results revealed no effects of connective type, neither as a main effect nor as an interaction. In other words, it appears from our results that, whether or not one accepts the proposal that there is an extra-logical procedure linked to but and to so, validity judgments indicate that participants are thoroughly unaffected by the choice of connective. At this point, one might be left with the impression that but and so are simply equivalent to and. The only main effect is due to the lower accuracy that occurs in the wake of a negative second segment, which is unsurprising. A look at the reaction times, however, tentatively reveals that readers are, indeed, incorporating specific procedures after encountering but and so. We turn to these now.

The RT1 data provide unique insight into the processing of the extra-logical import of but and so by comparing these to the mean RT1 of trials with the connective and. As predicted, RT1’s associated with and were consistently faster, relative to those recorded in but and so trials. This is direct evidence that participants incrementally integrate the extra-logical import of but and so from the moment that they are encountered. It is difficult to adduce these findings to other extraneous features, such as the word-length of the connective. These data are consistent with the indirect evidence that was culled from previous studies discussed in the Section 1 (e.g., Köhne-Fuetterer et al., 2021).

The last variable recorded in this experiment was RT2 (the reading time of the second segment plus validity decision time). Our analyses reveal two interesting findings. One is that the RT2 data indicate that but and so are linked to longer reaction times than and. This indicates that but and so processing, first detected as a source of slowdowns in RT1, continues downstream. However, this does not capture the subtlety of each of the extra-logical procedures (in but and so). A second, and more important, finding is the interesting interaction that points to participants’ efforts to integrate the procedure linked to but. As captured in Figure 9 and further illustrated in Figure 10, one finds a relatively long latency, i.e., an apparent slowdown, when the second segment following but is affirmative. This indicates that participants are noticing a clash between but’s procedure setting up a contrast and the subsequent lack of finding one. However, the but-by-Negative-sentence interaction indicates that participants react with alacrity when the second segment is expressed with a negation, thus providing the anticipated contrast. To make this concrete, consider the case of sentences in which a but was followed by an affirmative second segment (as in There is a B but there is a T, with respect to the word BET). According to our account, the procedure intrinsic to but ought to prompt participants to seek out a contrast. When there is no obvious one, as in the above type of sentence, it prompts a relatively slow response (see Figure 10); when there is a contrast in a negative second segment (as in There is a B but there is not a G, with respect to the word BET), it leads to reaction times that are as fluid as those for and in the negative-second-segment condition. Note, too, that Figure 9 shows that a false second segment also appears to satisfy the contrast-seeking procedure linked to but, as viewed by the speed-up that the false (and the false/negative second segment) cases provide.

The so trials produce a different kind of RT2 profile. These appear to prompt general slowdowns that are otherwise parallel to those found with and. Taken together with RT1, we consider the findings linked to so as indicative of participants applying a procedure that prompts a search for a causal explanation. Given that causal explanations for letter combinations are non-obvious, the use of so arguably prompts gratuitous processing. Note that the lack of an obvious cause-consequence relationship between mentioned letters does not slow participants down as much as but does in, affirmative second-segment condition. When it comes to a negative second segment, there is a pay-off for but in this paradigm. What is impressive is that participants cannot ignore the procedure imposed by so, even if it is gratuitous.

Overall, the results from this first experiment confirm our predictions and can be taken as evidence that discourse connectives, even in such a stark and repeatable paradigm, encode procedural meaning (RT2 results indicated that expectations are created following but and so), and that this extra-logical import comes at a processing cost, relative to a truth-functional conjunction (as can be seen as soon as RT1). Nevertheless, caution dictates that we consider two alternative accounts for the difference in RT1 observed between but and so, on the one hand, and and, on the other hand. One of these will lead to our next Experiment.

The first alternative explanation is that the RT1 results can be accounted for by an effect of frequency. According to the Corpus of Contemporary American English, for instance, and appeared 44247 times per one million words, against 8077 and 4232 times for, respectively, but and so (Davies, 2008). One could argue that participants are able to process and fastest simply, because it is more frequent than the two other connectives. However, a more careful analysis of these frequencies makes this account doubtful. When it comes to effects of frequency, the word recognition literature usually classifies words in three categories (low, medium and high frequency) in order to predict the reading and processing speeds of a given word. A word is usually considered highly frequent when it exceeds the threshold of 100 occurrences per million words (Brysbaert et al., 2018). All three connectives used in this study are, thus, highly frequent function words that very largely exceed this threshold. We thus consider it unlikely that frequency would play a role in reading time among such highly frequent words. Besides, the slowdowns are also associated with effects downstream. If but and so were just plain slower, one would not have other specific effects related to them in, for example, RT2. This leads to a second possible explanation.

It could be argued that what we consider to be gratuitous processing (what follows when a procedure does not get applied) amounts to infelicity, even upon the first encounter of the discourse connective (RT1). One could argue, for example, that but often (though not always) appears in sentences that do not provide a contrast; thus, it is possible that this conditioned participants to expect infelicity, even when it appears in the first segment. Such effects would, presumably, arise as part of a learning effect in which participants become increasingly sensitive to the infelicity of but. It follows from this argument that the difference in RT1 between and and but trials would increase as a function of trial order. We addressed this concern in a post-hoc analysis. We fitted a multilevel model, on the RT1 data, that included the variable of trial order and the interaction between Connective and trial order. We found no effects of either trial order or of the interaction between trial order and Connective. This argues against the notion that, even at the RT1 juncture, participants were becoming increasingly sensitive to the gratuitous processing of but in the experiment. This lack of trial effects applies to so as well, which we turn to now.

It could be similarly argued that the gratuitous processing that follows so amounts to infelicity because it is odd for an utterance to express causality when a participant eventually determines that there is no obvious reason for invoking it at all. To make this concrete, consider the two sentences described above, but conjoined with a so: There is a B so there is a T and There is a B so there is no G, with respect to the word BET. For both of these cases, we are assuming that so at RT1 prompts a procedure that anticipates a causal connection to consider; by the time participants read the second segment, they would be justified to wonder what cause is being cashed out.

There are two reasons why we are doubtful of accounts pointing to infelicity. One concerns the near-ceiling rates of Accuracy and their consistency across connectives. If one would want to claim that participants are so distracted by, say, two affirmative segments conjoined by but, one would have to predict higher error rates specific to those cases. Likewise, if the mere presence of the discourse connective so is disturbing, then arguably, one would find much longer RT’s overall and they would be longer for the so case than in the but case, which prompts gratuitous processing nearly half the time. Or, one might argue – from the high rates of Accuracy – that the extra-logical meanings are simply ignored, but the reaction time data indicate otherwise. The other reason we are doubtful of such an infelicity account with respect to our data is that participants have little reason to doubt the relevance of the discourse connective, at least when it first appears (at the end of the first segment). Arguably, the second segment could reveal the reason for the causal connection or for a contrastive one. Note, too, that if one adopts the infelicity argument, it is tantamount to accepting our procedural meaning account, because the infelicities are presumably due to the obligatory procedures attributed to but and so that do not get exploited.

All that said, we want to further rule out claims that say that our findings are due to paradigm-related issues, such as purported infelicities. This leads to Experiment 2, which was designed to present the sentences while the truth values were still undetermined, by essentially presenting the word after the test statement. If we replicate our main findings while the truth values are not declared (via the prior presentation of the word), it would strengthen our claim that participants are working out the meaning of the sentence (based on the procedures attached to but and so), even while being unaware as to whether the statement can ultimately be considered felicitous or true.

The main goal of Experiment 2 is to attempt to replicate the results of Experiment 1 in a more refined design in which the truth values of the sentences cannot be determined while reading. In other words, the test word in Experiment 1 is placed after the conjunctive sentence. A participant who is producing measures for each segment cannot know whether There is a T but there is a B is true or false (or know, in principle, whether it is felicitous or infelicitous) if the word BET in the paradigm comes at the end of the trial. Participants are merely processing simple sentences in the anticipation of finding out what the word will be. The upshot is that the choice of conjunction can readily be accepted as the communicator’s internal choice. We do not anticipate that this modification will affect the outcomes reported in Experiment 1. As will become clear, this effort also leads to two other fortuitous design changes that lead to cleaner dependent measures.

Experiment 2 was designed to further test our hypotheses concerning the presence of extra-logical procedures linked to but and to so that distinguish them from and, which we assume lacks an extra-logical procedure. The design of the current experiment allowed participants to read the test sentences without the burden of storing the three-letter words (the basis for making validity judgements) while making their evaluations. In other words, the main innovation of this design is putting the three-letter words at the end. One of the advantages of our design change is that it also allowed us to collect reading times of the second-segment (what is called RT2a here) independently of the validity judgement latency measure (what is called RT2b here), while keeping everything else the same.

The results of Experiment 2 largely replicated those of Experiment 1. As in Experiment 1, the RT1 data showed that, as predicted, first segments ending with but and so were processed more slowly, relative to those ending with and. In fact, this difference in RT1 was proportionally larger than it was in Experiment 1. Moreover, one could see that the speeds of processing RT1’s were generally faster in Experiment 2 (one can compare Figures 6 and 16). Both of these observations can be explained by the fact that participants carried a slight cognitive load in Experiment 1 – in the form of maintaining a word in memory – but not in Experiment 2. Experiment 2’s modification allowed the RT1 to collect a less encumbered measure. It also led to a clearer reaction-time difference between and, on the one hand, and but and so, on the other.

The reading time of the second segment, RT2a, also revealed that affirmative segments preceded by but and so are generally linked to longer reaction times than those preceded by and. This is remarkable, in that participants in the Experiment have yet to see the three-letter word when the RT2a is recorded. The main effect of Connective can thereby be attributed to participants placing the procedures of contrast and causality in play via but and so, respectively.

It is the interactions in this context that point to a discourse connective’s procedure. Both RT2a and RT2b revealed a positive interaction between Connective (but) and Sentence type (negative) indicating that the presence of but, prior to the contrasting negation, not only facilitates its processing (RT2a), but also facilitates the task of recalling and verifying the sentence (RT2b), relative to when the negation is introduced by and. RT2a’s are particularly fast when but is followed by a Negative second segment. In other words, the presence of but, prior to the contrasting negation (as in but… there is no T), facilitates its processing. As we indicated after Experiment 1, this is consistent with our account, because we propose that a procedure intrinsic to but prompts participants to seek out a contrast, which is provided by the negation. This precise interaction continues to resonate in the RT2b measures (which are the latencies linked to validity judgements).

One new interaction revealed itself in Experiment 2 which was not seen earlier: Participants were particularly fast at making False judgements in the wake of sentences containing so. One possible explanation for this effect is that, when reading the two segments of the trial sentences, the notion of causality carried by so encourages participants to look for a causal link. In doing so, participants are arguably considering possible words that comprise the two letters mentioned in the sentence. This extra effort (before seeing the three-letter word) pays off downstream when they quickly recognize words that do not match the letters in the trial sentence.

The Answer Accuracy results in Experiment 2 provided very high rates of correct responding, as in Experiment 1. The analyses pertaining to Answer Accuracy provided two effects in Experiment 2 that diverged slightly from those in Experiment 1. First, the connective but was linked with reduced accuracy, relative to and-trials. The plots of the mean accuracy results (see Figure 14) showed that this main effect was largely due to a drop in accuracy in positive test sentences (the baseline in our statistical model), but not in negative ones. Second, so-trials were linked with lower Answer accuracy in sentences with Negative second segments. These two effects were not predicted, but they could indicate that design changes of Experiment 2 allowed the extra-logical procedures to play a bigger role in participants’ processing, to a point that it affected validity judgments. For but-trials, the absence of contrast in positive sentences may have complicated their evaluation. For so-trials, as can be seen in the RT2b results, participants arguably adopted a predicted behavior that could have helped the evaluation of the sentence but that would have been difficult to adopt in negative sentences. We point out that, despite these new effects, rates of correct responses in Experiment 2 remain as high overall as those reported in Experiment 1.

To summarize, Experiment 2 replicated and reinforced the results of Experiment 1. The two experiments, indeed, provide evidence that discourse connectives trigger discourse expectations that can facilitate processing downstream but that also result in a specific additional processing cost on the connective.11

The connective and has served mostly as a control in our experiments, because our working hypothesis has been that it does not come with “extralogical information”; meanwhile, the conjunction intrinsic to and is shared with the other two discourse connectives investigated here. Empirical support for our argument can be seen from the fact that and is generally associated with (a) the highest rates of accuracy and (b) the fastest reaction times with respect to both segments. In light of exchanges with reviewers and audience members, we consider two other ways to view the data generated by and.

One alternative account, described in Section 1, is to view and as generating an (albeit weak) procedure that is considered part and parcel of but and so, as well. More specifically, and can be viewed as having a procedure that indicates that the two conjuncts are to be processed as a single unit. This makes all three of our studied connectives procedural, but with and still appearing to be the least effortful. Under this view, the three connectives studied here can be put on a continuum, with and clearly on the easy end, and but and so being more cognitively demanding. We will consider the first continuum-like view when we later address suggestions that come from SDRT.

A second alternative account that is compatible with our data on and is to assume its procedure is not entailed by but’s or so’s (i.e., it is independent of the other two). Under this guise, the three discourse connectives do not necessarily share features of conjunction or a fundamental procedural step; each of the three have independent procedures, and and’s happens to be easier to process. We consider this second alternative unlikely, but it is a logical possibility nonetheless.

We now take a closer look at the individual contribution of the connective so. So far, we have been referring to the extra-logical import of so as “causal”, without making a strong theoretical commitment with respect to our word choice. Our motivation has been to underline how so provides a causal link between the two segments and to show how this contribution is “extra-logical.” The exact nature of the discourse relation has not been relevant to our aims. Here, we spell out in greater detail how we view the causality carried by the connective so in our task.

The literature underlines that so can convey two types of causal relations. The first is the cause-consequence relation that is exemplified in (1c), where the first conjunct (Camille having a lab meeting) is presented as the cause of the second conjunct (his being late) that consequently follows. This connective is known as objective or as causal, as is described in T. J. M. Sanders et al. (1992); see their Table 1). The other reading of so is to describe a speaker’s reasoning as is exemplified in (1c’). Here, the first conjunct (about Camille’s lab meeting) describes the speaker’s justification for the second one (Camille must be dealing with an emergency).

Used in this way, this connective is known as subjective or diagnostic and is referred to as Claim-argument in T. J. M. Sanders et al.’s (1992) taxonomy (again, see their Table 1). For further discussion, see (Canestrelli et al., 2013).

Of the two, one is eliminable in the context of our paradigm. Given that the propositional contents of the two segments in our task are not naturally related (it is difficult to argue that world-knowledge in our task prompts cause-consequence inferences that lead to valid conclusions about a second letter), it follows that so is not expressing objective causality here. On the other hand, it is plausible to consider that participants interpret the speaker’s use of so in a statement such as There is a B so there is a T to mean that the speaker has a reason for making a link about the co-presence of B and T (even if it might be beyond the participant’s ken to understand what link the speaker has in mind). It follows that the causal so in the context of our task can be best described as subjective.

Generally, our data show that the connective so does not create confusion for participants, even if it is arguably the case that the speaker’s reason for using it is not apparent. Rates of correct responses with sentences conjoined by so are consistently high. Assuming that a procedure linked to so is prompted (and understood as a diagnostic or subjective causal), its items provide latencies that generally resemble those found for and, while being generally slower with respect to both segments (see Figures 10 and 18). We take this to indicate that participants are working out the meaning of so from the moment it is encountered and onward (through the presentation of the second segment).

There exist conditions under which so actually facilitates reaction times (compared to the baseline created by and), which occur when participants in Experiment 2 make decisions (post-so) about the presented word. That is, when so was employed and participants had received negative second segments, the test-words that follow prompt decision times that are faster than those that come after and (see Figure 20). Relatedly, when so is the connective and the presented word calls for a false judgment, decision times were faster than those associated with and (see Figure 21). This decision-making speed-up linked to so corroborates our argument that it prompts a procedure that is ultimately cashed out when given the opportunity. Given that we did not specifically set out to make such specific claims related to so (i.e., our experiments were not designed to test such effects), we remain cautious about our account of downstream processing linked to so. Nevertheless, these findings are consistent with our claim that so ultimately provides benefits through a procedure, even if it is relatively costly to process initially.

These findings resonate with data on causal connectives from the text and discourse literature. There, one finds evidence showing that causal connectives, which are hypothesized to increase “inference generation,” provide benefits to participants’ comprehension when compared to a variety of control conditions that do not contain causal connectives. For example, Millis et al. (1995) showed that the causal connective because provides comprehension advantages to participants when compared to (a) cases where there is no connective, as well as to (b) cases where the causal is replaced by, and compared to, and. To make this clear, consider the two “statements” in Sherry quickly mopped up the soup on the wooden floor (Statement 1) because a waiter accidentally tripped on the step by the kitchen (Statement 2). When because is included, it provides added value to comprehension in several ways. For the sake of brevity, we will mention just two of those ways. First, performance on lexical decision tasks indicates that statements pertinently conjoined by because facilitate the speed of making lexical decisions when compared to the control condition, which does not contain any connective.12 Second, participants answer comprehension questions more quickly (and slightly more accurately) when the sentences are conjoined with a causal connective. Interestingly, the authors found similar advantages for because when it was compared to and, much as we do. The authors concluded that the connective because elicits causal inferences, whereas and does not.

Much as with so, we did not have a preconceived view on the connective but before we began our investigation, other than to posit that this connective prompts a procedure and that its extra-logical import can, at a minimum, be described as contrastive. That said, we were well aware that its procedure could also be described in more inferential terms – as a way to express denial of expectations – where but signals that the first conjunct raises expectations that are denied by the second conjunct. These two accounts do not exhaust the range of possible accounts of but, but they are generally considered the two most prominent (for a brief historical summary of each, see Winterstein, 2012).13 If the two are viewed as rival hypotheses, the denial of expectations description does not readily apply to our paradigm, because it is not obvious how the mention of one letter can raise expectations about a second (the choice of letters was generally randomized). This leads to the conclusion that the procedure linked to but, is indeed, best described as providing a contrastive meaning.

The data bear this out. Across both experiments, one finds that obvious contrasts – those made by adding negation in the second segment, as in There is a B but there is not a… – prompt reading times or decision times for the second segment that are comparable overall to those conjoined by and (see Figures 10 and 18). Furthermore, estimated parameters from our Bayesian analyses show that speed-ups arise when but is followed by a negative element (see Figures 9, 17, 19). A role for contrasts is not limited to affirmative/negative contrasts. In Experiment 1, one finds that (reading times and) responses are accelerated when the second segment renders the statement false (see Figure 9). For example, when participants receive the word BET and the sentence There is a B but there is a V, the combined reading and decision times (from the second segment onward) speed up, based on expectations derived from true statements that use and and affirmative statements. Here, the contrast is arguably cashed out by having a true segment followed by a false one. One also finds a weaker version of this effect in Figure 19, when the word comes after the two segments are read. The search for this (or any) contrast is, in our view, generated by the presence of but.

Another relevant data point is the way participants handle cases that do not provide an obvious contrast. For example, consider when participants read the entirely affirmative sentence There is a B but there is a T when it is preceded by the word BET in Experiment 1 (or followed by that word in Experiment 2). In this case, there is no obvious contrast to be drawn, and the prolonged latencies (see Figures 10 and 18) reveal an effort on the part of participants to seek a contrast nonetheless. As with so, the discourse connective but in these cases compels participants to understand why the speaker chose that connective. From our point of view, the gratuitous processing (when the instantiation of but does not lead to an obvious contrast) is a feature (and not a bug) of our paradigm. The slowdowns point to the inexorable application of but’s procedural meaning without affecting its conjunctive contribution.

We would be remiss at this point if we did not address how SDRT, arguably the best known semantic account of discourse relations in the linguistic literature, would account for this article’s data, and we begin with our characterization of and. In our view, advocates of SDRT would be agreeable with the first of the alternative accounts we presented above (in which and is considered to have a procedural meaning, albeit weaker than but’s and so’s). To explain how, we take a step back to describe SDRT in slightly more detail.

SDRT describes discourse relational structures (SDR’s) as containing discourse topics, representing the content in clauses, that can be viewed hierarchically. For example, as Asher and Vieu (2005) describe in an example, a speaker can describe his lovely evening by elaborating on it (e.g., the speaker can add that he had a great meal). The clause about the meal is an Elaboration that is subordinate to the lovely evening. The had a great meal segment can then be an antecedent to another subordination (e.g., the speaker could elaborate on what he ate). However, the having of a great meal clause could also be the antecedent to a Narrative relation, a coordination, wherein the speaker can go on to say that she won a dance competition. According to advocates of SDRT, this distinction between subordinating and coordinating is so consequential that, once a speaker is understood as coordinating, e.g., via and, it precludes the anticipation of a subordination. This would be and’s contribution to discourse, which arguably goes beyond its logical contribution (for an in-depth discussion, see Txurruka, 2003).

Can the SDRT approach account for our findings? To some degree, it does. As one reviewer pointed out, but and so are more specific than and, because and allows for all types of coordination, while but and so only allow for a subset of them. That an added restriction leads to extra processing is sensible and would make such an outcome compatible with our main prediction. While it is our view that our data speak positively to the SDRT account, this kind of prediction would be novel for SDR Theory-making, in that it is relies on real time processing concerning the connective itself.

That said, given its reliance on the role played by conceptual content, it would be difficult for SDRT to account for our findings in other respects. That is, Rhetorical Relations (whether they be coordinating or subordinating) rely on the semantic, truth-conditional content of each clause. It is through the truth-conditional content that one determines that having a great meal and winning a dance competition are part of a coordinating phrase, just as it is through content that one knows that having a great meal and eating salmon have a subordinating relationship. The narrator’s choice of connective necessarily coalesces with the content. In contrast, our participants are processing our sentences and making inferences based almost entirely on the discourse connective itself. It could be said that, in Experiment 1, participants have the means to at least determine whether the letters are true or false as they read the sentence (since the word comes first, they rely on the truth-conditional content to some degree). However, in Experiment 2, participants process the critical sentences without knowing whether the content of the sentence is true (because the word comes after the clue). So, in Experiment 2, there is no reliance on content to determine the relationship across the two segments. Processing depends entirely on the presence of the connectives and, but and so. Remarkably, whether or not the truth-conditional content is known as the test sentence is presented, participants’ processing outcomes across the two Experiments are very similar.

Now that we have concluded that but and so provide extra-logical information, when compared to and, how shall one characterize this extra information? Should it be viewed as part of a complex semantic representation, or does this procedure qualify as pragmatic? This question is relevant to the extent that different theoretical accounts are likely to make very different claims about our findings, so let us briefly spell out what we consider these accounts to be.

One possible answer is that but and so provide an extra layer of semantic meaning, one that is added to the at-issue meaning of the utterance, as has been argued by authors such as Bach (1999), Potts (2005) and Karttunen and Peters (1979). While such accounts aim to address, or to formalize, the meaning conveyed by discourse connectives such as but and so, they are generally not directly concerned with the psychological realisation of that meaning. As such, it is unclear what these approaches would predict in terms of processing. The most plausible prediction seems to be that semantic meaning is automatic and that the additional layer of semantic meaning contained in these discourse connectives should not cause them to be processed more slowly than logical connectives. Moreover, we do not see how a semantic approach to discourse connectives would account for the very specific processing profiles that each appears to produce (as seen with negations following but and for false statements containing so). Semantic accounts do not distinguish between the conceptual content in the clauses and the procedures generated by the connectives (Bezuidenhout, 2004). With this view, it is difficult to see how one can account for any of the reported differences – both with respect to accuracy and to processing – as reported in the current work.

This leads to a second possible answer concerning the nature of the extra-logical contribution, which puts it on the pragmatic side and which hews more closely to our hypothesis. Our explanation is that, while all three terms are by definition conjunctive, the procedural meaning inherent in but and so intervenes at the pragmatic level, while and remains primary and semantic. This distinction is motivated by two features that have come up in the above discussion. One is that extra-logical procedural information in but and so puts the two in a position to entail and. The other is that the nature of procedural information is such that there are ways to direct a listener to make – and for an addressee to understand – implicit connections among clauses that would not be available without such procedures. For example, let us revisit (1b) and consider a reading that is inferred in (1b’), due the inclusion of the connective but:

The inferred information in brackets arises through the speaker’s introduction of but, at which point the addressee aims to account for a contrast of some sort. In other words, the presence of but implicitly prompts the addressee to make adjustments that lead to modifications of the conceptual information. Ultimately, this modification integrates a contrast.

The inferred information in (1b’) is, moreover, cancelable. In fact, but in this context could easily generate other interpretations. For instance, one could imagine that the speaker is a Masters student explaining to a fellow student that “Camille is in fact at the lab meeting, which is running longer than expected”. Here, the contrast that gets manifested is between the predicted and actual length of the meeting. These multiple interpretations arise because the conceptual content, in combination with but, generates them. The same holds for so.

Here, we turn to and comment on our methodological approach, which reduced contextual information as much as possible. This could be valuable for future research, because this approach puts one in a position to introduce some complexity found in natural discourse in a controlled step-by-step way. For instance, it is known that the question under discussion (QUD) helps both the speaker and the hearer to, respectively, tailor their utterance and work out the intended meaning (Degen & Tanenhaus, 2019). In experimental studies, QUD manipulations have helped refine the understanding of well known pragmatic processes (Degen & Goodman, 2014; Potts, 2012; Sedivy et al., 1999). As far as discourse connectives are concerned, QUD manipulations could help us understand what, exactly, is causing a delay in the processing of but or so relative to and. In other words, this paradigm would allow for future work to consider other theoretical frameworks to determine the extent to which a discourse connective, such as but, generates relatively effortful processing in cases where the QUD triggers an expectation of contrast.

To summarize, this study provides evidence showing that discourse connectives (such as but and so) convey information that make them costlier to process than the truth functional logical conjunction (and). We argue that this additional cost can be viewed through a pragmatic lens. According to Relevance Theory, for example, our results make sense, because discourse connectives prompt the involuntary initiation of a pragmatic procedure. Theoretically, this extra cognitive effort should also come with a benefit, which we assume is the facilitation of processing downstream.