Processing Presuppositions and Implicatures: Similarities and Differences

Presuppositions and Scalar implicatures are traditionally considered to be distinct phenomena, but recent approaches analyze certain Presuppositions as Scalar Implicatures. All else being equal, this ‘Scalar Implicature approach to Presuppositions’ predicts uniform behavior for the two types of inferences. Initial experimental studies comparing them yielded conflicting results. While some found a difference in the Response Time patterns of Scalar Implicatures and Presuppositions, others found them to be uniform. We argue that the difference in outcomes is attributable to a difference in the type of response being measured: Response Times associated with acceptance and rejection responses seem to pattern in opposite ways. Next, we report on a series of experiments to support this, and to compare the behavior of Presuppositions and Scalar Implicature more comprehensively. Experiments Ia and Ib look at both acceptance and rejection responses for both inference types, and find uniform patterns once the acceptance vs. rejection variable is factored in. Experiment II adds a new dimension by testing for the influence of prosody on the two inference types, and in this regard clear difference between them emerge, posing a first substantive challenge to the Scalar Implicature approach to Presuppositions. A third set of experiments investigates yet another prediction: according to the Scalar Implicature approach to Presuppositions, the presuppositional inference is introduced as a simple entailment in affirmative contexts. This predicts that these presuppositional inferences behave parallel to other entailments. But in Experiment IIIa, a comparison of rejections of affirmative sentences based on either their presuppositional inference or their entailed content finds them to differ, with greater Response Times for the former. As an additional control, Experiments IIIb and IIIc test for parallel differences between two entailments associated with always, which yield uniform results. In sum, while Experiments Ia and Ib are in line with previous findings that Presuppositions and Scalar Implicatures under negation show uniform response time patterns, the differences found in Experiments II IIIa-c pose a substantial challenge to approaches assimilating Presuppositions and Scalar Implicatures, while being entirely in line with the traditional perspective of seeing the two phenomena as distinct.


INTRODUCTION
There are various well-developed proposals for accounting for presupposition projection in traditional 152 terms, but we will not review these here in any detail for reasons of space. What is crucial for us, as before, 153 is that all of these accounts treat presuppositions in a way that is very different from their treatment of SIs. 154 Finally, notice that traditional approaches quite generally assume presuppositions to be conventionally 155 encoded in the lexical entries of the relevant expressions. This means that sentences containing a 156 presupposition trigger necessarily introduce the corresponding presupposition. In order to reconcile 157 this with cases of apparent suspension of presuppositions, as in (21), a further mechanism is assumed, 158 e.g. one that 'accommodates' the presupposition locally, which results in the absence of any contextual 159 constraints at the sentence level (Heim 1983; see also von Fintel 2008). This gives rise to the meaning 160 paraphrased in (22), which is compatible with the continuation of (21), asserting that John never went to 161 the movies. The traditional approach to SIs, which sees them as distinct from Ps, goes back to Grice (1975)  In brief, the idea is that the hearer reasons that the speaker said (23-a), rather than something else, and 172 in particular the more informative sentence in (24). Assuming that (24) is relevant to the purposes of the 173 conversation, and that speakers are assumed to be committed to conveying the most informative relevant 174 information at their disposal, the hearer will infer that the speaker's reason for not saying (24) is that the 175 speaker believes (24) to be false. Therefore, the hearer derives the inference (23-b). 7

176
(24) John always went to the movies.  This brief review of the traditional perspective on Ps and SIs, while glossing over many intricacies, will 184 suffice for our purposes. We primarily wish to provide a sense of how Ps and SIs are traditionally analyzed 185 in clearly distinct ways. We now turn to more recent accounts of these inferences, in particular the SI 186 approach to Ps. 187 2.3 The scalar implicature approach to presuppositions 188 The scalar implicature approach to presuppositions generally attempts to assimilate (certain) 189 presuppositions to implicatures. In particular, some of the accounts within this general approach treat the 190 presupposition associated with verbs like 'stop' as scalar implicatures of a sort (Simons, 2001;Abusch, 191 2002, 2010; Chemla, 2010; Romoli, 2012Romoli, , 2015. In this section, we briefly sketch the simplest version of  The SI approach to Ps offers a rather different explanation. First, (27-b) is simply (and only) an entailment 201 of (28) on this account. This is in line with the observation that (27-b) is a non-cancelable ingredient of the 202 overall meaning of (28), as asserting (28) and negating (27-b) sounds contradictory.

203
(29) #John stopped going to the movies but in fact he never went. 204 Assuming that (27-b) is an entailment of (28) is neither novel nor surprising: many accounts of Ps in the 205 traditional approach share the view that the presuppositional inference is entailed in affirmative contexts. 206 What is novel in the SI approach to Ps is to argue that (27-b) is only an entailment of (28). Second, the 207 fact that (27-b) is standardly inferred from negated sentences like (27-a) as well is derived as a scalar 208 implicature in a fashion parallel to the reasoning above for standard SIs. In particular, the idea is that the 209 speaker said (27-a) rather than the relevant and more informative sentence (30). Therefore, the hearer infers 210 that the speaker believes the latter to be false, which is equivalent to (27-b).

211
(30) John didn't use to go to the movies.
If this approach is correct, then the inferences associated with soft triggers such as stop are simply entailments when occurring in affirmative contexts, but (indirect) SIs when occurring under negation, leading to the two key predictions in (6-a) and (6-b) above. On this view, verbs like stop are completely parallel to strong scalar items like always, which give rise to parallel inferences in positive contexts and in 216 the scope of negation.

THE PROCESSING OF SCALAR IMPLICATURES AND PRESUPPOSITIONS
In this section, we briefly review previous work on the processing of SIs and Ps, focusing in particular on 218 RT experiments. 8 reading of the sentence, (31-a) should thus be judged 'false.' 9 As discussed above, however, the sentence 227 also has a no-inference (or 'literal') 'some and possibly all' reading, which is compatible with common 228 knowledge, and thus should lead to a 'true' judgment.

229
(31) a. Some elephants are mammals. The logic of the design in Bott and Noveck (2004)    individual and a 5-day calendar strip, with each day being filled with an iconic representation of an activity 321 that the individual had engaged in on that day (see Figures 1 & 2). In addition to these two 'visible pictures' 322 there was a 'Covered picture'. Participants were told that one of the three pictures was a match for the 323 presented sentence. One of the visible pictures was a 'Target picture', which was either consistent or  that while the +LIT/+INF picture could be accepted on either a no-inference or an inference interpretation, 343 the difference in RTs suggests that at least a sizable portion of Target choices was based on the latter; this 344 assumption justifies the use of 'inference' and 'no-inference' in the schematic illustration below, and will 345 also be utilized in the data analysis of the experiments in the next section.) 346 12 Romoli and Schwarz (2015) label the conditions INFERENCE-TRUE and INFERENCE-FALSE respectively; we choose the more transparent labels here to clearly signal that the images shown in the former can in principle be accepted on either a literal or an inference interpretation. 13 Note that, in principle, selection of the +LIT/+INF Target picture could also be motivated by a no-inference/literal interpretation. However, if all these selections were based on such an interpretation, then we would expect participants' behavior in these two conditions to be equivalent. Therefore, the fact that Romoli and Schwarz (2015) found substantial variance in the RT results, suggests that, at least a sizable portion of Target picture selections in the relevant condition are motivated by inference interpretations.    This raises the question of what is behind these seemingly conflicting findings. One possibility relates to 356 differences in the types of responses that were compared between these studies. As mentioned, previous

THE EXPERIMENTS
In this section, we report on three series of experiments testing the two predictions of the SI approach to Ps

369
The first experiment adopted the approach taken in Romoli and Schwarz (2015) and applied it to on the other. It also offers a more comprehensive perspective on the role of response type in RT patterns.

374
Note that, for this experiment (and Experiment Ib), the relevant uniformity prediction is that the relative processing patterns of each trigger will be similar. That is, the prediction is not that the RTs will be exactly  assumption that no-inference interpretations are in principle available but generally somewhat dispreferred.

396
That is, as the Covered picture could be completely 'False', if there is a possible reading that makes the 397 Target picture 'True' the participant has a good reason to go with that reading, even if it is a dispreferred 398 reading. At the same time, as noted above, having the Covered Picture as a response option ensures that 399 subjects need not feel forced to give a response that they may feel uncomfortable about.

400
The basic logic of the design was parallel to that of Romoli and Schwarz (2015), in that the overt Target 401 picture either was consistent with a given interpretation or not. More concretely, sentences (i) and (ii) in Figure 3 were displayed with one of the pictures in Figure 3 and a Covered picture. 16  as above that at least a sizable portion of responses here is based on an inference interpretation).

416
The same general logic applies to the ISI sentences (ii), though with different mappings onto the pictures.

417
The picture in Figure   16 Note that the condition labels presented in Figure 3 relate to the truth-value of the two critical elements of the sentence; namely, the literal content and the inferential content. For example, in the case of the condition '+Lit/-Inf' for the DSI sentence, the picture is consistent with the literal content that John went to the movies at least once, but is inconsistent with the inference that John didn't always go to the movies. Moreover, in the case of the '-Lit/+Inf' conditions, the target picture should not be able to be selected, due to it not satisfying the literal content of the relevant sentence, despite the fact that it is consistent with the inference (corresponding to the literal meaning of the paraphrase).

Acceptance-acceptance comparison
Rejection-rejection comparison John didn't always go to the movies John sometimes went (ISI)       Ps should be uniform. Note that, as in Experiment Ia, the uniformity prediction that we are testing is the 535 expectation that the relative processing patterns of Ps will be the same as SIs, not that the RTs will be 536 exactly the same across these inferences. under negation lends itself to a direct comparison with SIs (and specifically ISIs). We therefore focus the 544 discussion in the present section on that case. The case of 'stop' in affirmative sentences will be discussed 545 separately in Section 4.4. An illustration of the negative conditions is provided in Fig. 6. The sentence in 546 Figure 6 was displayed with one of the pictures in Figure 6 and a Covered picture.

547
The picture in Figure 6a, paired with the negative 'stop' sentence, constitutes the Target-selection control, 548 as both the putative presupposition (that John went to the movies before Wednesday) and the asserted part 549 (that he went to the movies from Wednesday on) are true. The picture in Figure 6c provides the Covered

550
Picture-selection control, as the asserted part is false (since he did stop going to the movies), although the 551 presupposition is true. Figure 6b constitutes the critical case, as the putative presupposition is false, while 552 the assertion is true. If a participant accesses an inference interpretation, the Covered Picture should be a.
-LIT/+INF John didn't stop going to the movies on Wednesday John used to go to the movies before Wednesday  items were presented in the +LIT/+INF condition, again drawn from a total of 24, with counter-balancing 563 between it and an affirmative variant. In addition, there were 21 fillers from another sub-experiment.

564
Instructions and practice trials were as described for Experiment Ia.

572
The RT results are summarized in Fig. 7. We find a pattern that is generally parallel to that for implicatures, 573 and which corresopnds to a cross-over interaction between type of reading (inference vs no-inference) and 574 type of response (acceptance vs rejection) when coded as corresponding to inference and no-inference  To investigate this result statistically, we analysed the data as a 2 × 2 interaction design, using the same 579 statistical analyses as detailed for Experiment Ia. The detailed results are summarized in SIs and Ps (i.e. (6-b)). Next we turn to investigating the effect of one more variable, that of prosody, on 595 these inferences, as a further test of their uniformity. The sentences were slight variations of those above, with a more uniform wording for the always and  The design was between-groups, so each participant was only exposed to one mode of presentation 635 (WRITTEN, NO-STRESS, STRESS). The NO-STRESS data was collected as part of an eye-tracking 636 18 Note that this experiment is different from the previous two in that we are no longer looking for uniformity in processing patterns. Instead we are investigating whether there is uniformity in the response of these inferences to prosodic stress, measured through rates of derivation. While the measure is different, the SI approach to Ps' prediction is similar to that made for Experiments Ia and b; namely, that there will be uniform effects of prosodic stress on the pattern of derivation rates. That is, we do not take this approach to be requiring that the effect needs to be to the same extent for both these inferences, just that it needs to be in the same direction.  SIs and Ps might 'just' be a sign of this scalar diversity, rather than evidence of different derivational 687 mechanisms. However, the fact that the prosodic stress appears to have, not just different, but opposite 688 effects on the derivation rates of these inferences is more in-line with a qualitative distinction between 689 them (à la different derivational mechanisms), than a quantitative difference (à la scalar diversity). b. John did go to the movies before.

701
Both these inferences are derived from the same sentence and, according to the SI approach to Ps, they are 702 equivalent in status (i.e. they are both simply entailed). As a result, we take it that the SI approach to Ps 703 would predict a greater degree of uniformity in the behavior of these inferences, compared to others we 704 have investigated thus far. In particular, we take it that the SI approach to Ps predicts that rejecting a picture  The materials of this experiment were part of the same overall experiment reported as Experiment Ib on 714 stop in negative sentences above. Affirmative sentences with a presupposition trigger such as stop differ 715 from those with DSIs in that they cannot be judged true in a context where the inference of interest (that 716 the relevant activity had been going on before) is false. This renders such sentences unsuitable for a direct 717 comparison with affirmative SI sentences (i.e., DSIs), but they provide a possible angle for assessing the 718 status of the inference. Note first that rejection responses in such contexts are captured on both traditional 719 accounts and the SI approach to Ps, though in different ways: the former sees it as a case of presupposition 720 failure, whereas the latter sees it as a simple rejection based on unmet entailments. The contexts we used 721 are depicted in Fig. 10. In the -LIT/+INF condition, the overt picture does not match the sentence based on 722 its simply entailed content, since the movie-going continued past Wednesday, but the inference that John 723 was going to the movies before Wednesday is met. In contrast, in the +LIT/-INF condition, the inference 724 -be it both a presupposition and an entailment, or merely an entailment -is not met, while the simply 725 entailed content, that there was no 'movie-going' after Wednesday, does hold.

727
The data stem from the same 34 participants as in Experiment Ib, and the sentence-picture combinations 728 that they saw were variants of the negative versions reported there. In particular, subjects saw 6 sentences in the -LIT/+INF condition and 6 in the +LIT/-INF condition, drawn from a total of 24 sentences, Bill et al.

738
The observed difference in RTs points to a difference between the two ingredients of meaning at play. This 739 pattern is not predicted by the SI approach to Ps, which would expect uniformity between these conditions,    A potential concern about this first follow-up is that it involved empty calendar slots. In particular, one 779 might worry that the NEVER PICTURE version, which conceptually corresponded to the more difficult 780 stop-condition with an unmet presupposition, might lend itself to a relatively easy task-strategy of rejection 781 based on the completely empty calendar strip, thus hiding potential delay effects. A second follow-up 782 addressed this issue by filling the relevant calendar slots with another image type instead (see right side 783 of Fig 12). While there was a small numerical difference between the ALWAYS PICTURE (5505ms) and

GENERAL DISCUSSION
We set out to investigate the SI approach to Ps by trying to answer the main question outlined in (48).

795
The predictions of the SI approach to Ps in regards to this question are repeated in (49-a) and (49-b).

796
Experiment Ia, Ib and II set out to test prediction in (49-b). Experiments IIIa-c tested the prediction in 797 (49-a).

798
(48) Main question: Do behavioral patterns in experimental data, e.g., in terms of (RTs) and response First, we will focus on Experiments Ia and Ib, as these produced results that were consistent with the 805 prediction in (49-b). Following this, we will consider the other experiments, which produced results that 806 were not in line with the predictions in (49-a) and (49-b), and discuss the challenge they pose for the SI 807 approach to Ps.

809
To briefly recap the situation in the literature, the classic finding since Bott and Noveck (2004) is that 810 rejecting a sentence when its SI is false takes more time than accepting it. The same paradigm was then 811 applied to Ps by Chemla and Bott (2013) and they found the opposite result: rejecting a negated sentence 812 whose presupposition is not globally met takes less time than accepting it. On the basis of this result, 813 21 Note that the overall longer RTs here are due to a slight variation in task, where a context sentence was included and the events in the calendar were revealed in two steps. Since the main measures of interest are a comparison between the two always-conditions and the interaction, this main effect of the task does not affect the interpretation of the results for our purposes.
to the question in (48) is positive: the processing of Ps and SIs is different, which in turn is a challenge for 815 unified accounts like the SI approach to Ps. On the other hand, Romoli and Schwarz (2015) found that 816 accepting negated sentences with a true presupposition is faster than accepting it when its P is not satisfied 817 in the context, and they found parallel results for SIs, with faster acceptance of inference interpretations 818 than no-inference interpretations. On the basis of this result, these authors concluded that there is no clear 819 overall evidence for either SIs or Ps being associated with a delay or for the two inferences being different.

820
On the face of it, the results from these two studies appear in conflict and they seem to give us opposite to Ps. Moreover, we found no evidence for either Ps or SIs being associated with a delay in RTs, a point 843 that we will return to in a moment. stimuli, but increased for Ps. These results run against the SI approach to Ps' prediction of uniformity of 850 behavior across these inferences.

851
22 Note that, while as far as RTs are concerned our results are comparable for ISIs and DSIs, the rate of implicature interpretations is significantly higher for DSIs. It's possible that this is simply due to complexities introduced by negation, but a more detailed explanation will have to be fleshed out in future work. 23 Note that these results touch on an issue that has been investigated in detail elsewhere; namely, the effect of accepting/rejecting positive/negative sentences. In general, the work in this area seems to be consistent with our results, in that, judging sentences as true has been found to take longer than judging them as false (Wason, 1959 pattern where responses based on an inference interpretation were slower. On their own, these might be 901 seen as compatible with an account based on processing delays for inference interpretation. But given the 902 cross-over interaction in our results, an alternative explanation of the effects is called for.

903
In the following, we sketch how the RT patterns in our data can be captured in terms of a conflict between incompatible with the inference interpretation ( Fig. 3a for DSIs, Fig. 3c for ISIs, and Fig. 6b for Ps).

913
Similarly, Covered Picture selections are also slow in the very same circumstances. One possibility then, is 914 that there are opposing pressures favoring the respective interpretations, and that delays arise precisely 915 when there is a conflict between these factors. More specifically, we assume that comprehenders follow a 916 general principle of charity, i.e., they generally try to construe utterances in such a way that they are true 917 of the circumstances at hand. In our case, charity can plausibly be seen as corresponding to selecting the no-inference interpretations are often thought to only be marginally available.

923
In sum, we assume the following two principles at work: conditions. 26 It is interesting to relate this account to an idea presented by Katsos and Bishop (2011), who explain acquisition data in terms of pragmatic tolerance: from our perspective, one could see this in terms 933 of the charity principle being stronger in children than the preference for inference interpretations. results. However, when we turned to Experiment II, we found that, counter to the predictions of the SI 950 approach to Ps, there was a difference in the way these inferences were affected by prosody. In Experiment 951 IIIa, we tested another prediction of SI approaches to Ps, namely that the relevant inferences of sentences as well as our current results, it would appear that the SI approach to Ps is faced with a genuine challenge.

CONFLICT OF INTEREST STATEMENT
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.