Brain and Cognition 90 (2014) 100–108

Contents lists available at ScienceDirect

Brain and Cognition journal homepage: www.elsevier.com/locate/b&c

Reasoning from transitive premises: An EEG study Mathilde Bonnefond a,b,⇑, Thomas Castelain a, Anne Cheylus a, Jean-Baptiste Van der Henst a a b

Laboratoire sur le Langage, le Cerveau et la Cognition (L2C2), CNRS – Institut des Sciences Cognitives, Université de Lyon 1, 67 Boulevard Pinel, 69675 Bron Cedex, France Radboud University, Donders Institute for Brain, Cognition and Behaviour, Kapittelweg 29, 6525 Nijmegen, The Netherlands

a r t i c l e

i n f o

Article history: Accepted 13 June 2014

Keywords: Transitive reasoning Inference Expectation P300 P3b P600 N2

a b s t r a c t Neuroimaging studies have contributed to a major advance in understanding the neural and cognitive mechanisms underpinning deductive reasoning. However, the dynamics of cognitive events associated with inference making have been largely neglected. Using electroencephalography, the present study aims at describing the rapid sequence of processes involved in performing transitive inference (A B; B C therefore ‘‘A C’’; with AB meaning ‘‘A is to the left of B’’). The results indicate that when the second premise can be integrated into the first one (e.g. A B; B C) its processing elicits a P3b component. In contrast, when the second premise cannot be integrated into the first premise (e.g. A B; D C), a P600-like components is elicited. These ERP components are discussed with respect to cognitive expectations. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction The ability to combine different pieces of information often amounts to making deductive inferences. For instance, if I come to know that Niki Lauda is seating to the left of Jackie Stewart and Jackie Stewart is seating to the left of Mario Andretti, I could surely derive that Niki Lauda will be seating to the left of Mario Andretti. This conclusion would result from what is called a transitive inference (TI). Obviously, not only such kind of inference can be made within the spatial domain, as in the provided example, but also within the temporal domain (before–after), and in any situation that involves some form of comparison, be it social (richer–poorer) or non-social (hotter–colder). Its great pervasiveness makes it likely to be at the core of our inferential abilities (Ragni & Knauff, 2013).

⇑ Corresponding author at: Radboud University, Donders Institute for Brain, Cognition and Behaviour, Kapittelweg 29, 6525 Nijmegen, The Netherlands. E-mail addresses: [email protected] (M. Bonnefond), tcastelain@isc. cnrs.fr (T. Castelain), [email protected] (A. Cheylus), [email protected] (J.-B. Van der Henst). http://dx.doi.org/10.1016/j.bandc.2014.06.010 0278-2626/Ó 2014 Elsevier Inc. All rights reserved.

The integration of information leading to transitive inferences amounts to eliminating the middle term. In the example provided above, the two premises are integrated by ‘‘eliminating’’ Jackie Stewart in the conclusion. According to William James, this illustrates the Axiom of skipped intermediaries1 which ‘‘seems to be on the whole the broadest and deepest law of man’s thought’’ (James, 1890, p. 146). Infants, as well a wide range of animals, show signs of transitive inference skills (Mou, Province, & Luo, 2014; Vasconcelos, 2008). Transitive reasoning is a very broad and universal type of deduction, and in contrast with categorical and propositional reasoning, it does not necessarily rely on language. Since the work of Piaget (Piaget, 1921) and Burt (Burt, 1919), cognitive scientists have long explored the processes underlying TI. In humans, most theoreticians concurred with the idea that TI relies, at least partly, on analogical processes, which are typically involved in visuo-spatial manipulation (Evans, Newstead, & Byrne, 1993; Johnson-Laird, 1983). In other words, the premises of a transitive argument would be mapped onto an analogical visuo-spatial mental line from which the conclusion could be directly read off:

1

‘‘the law that skipping the intermediaries leaves the relation the same’’.

M. Bonnefond et al. / Brain and Cognition 90 (2014) 100–108

101

ð1Þ

The advent of PET and fMRI studies has made out a strong case for this view. During the last 15 years, a number of results have revealed that drawing transitive inference recruits a brain network which involves the manipulation of visuo-spatial information (Acuna, Eliassen, Donoghue, & Sanes, 2002; Fangmeier & Knauff, 2009; Fangmeier, Knauff, Ruff, & Sloutsky, 2006; Goel, 2008; Goel & Dolan, 2001; Goel, Gold, Kapur, & Houle, 1998; Goel, Makale, & Grafman, 2004; Heckers, Zalesak, Weiss, Ditman, & Titone, 2004; Knauff, Fangmeier, Ruff, & Johnson-Laird, 2003; Knauff & Johnson-Laird, 2002; Prado, Chadha, & Booth, 2011; Prado, Noveck, & Van Der Henst, 2010; Prado, Van Der Henst, & Noveck, 2010). In particular, transitive inference activates the bilateral posterior parietal cortex, which is known to be systematically associated to a wide range of spatial cognition tasks (Corbetta & Shulman, 2002), while propositional and categorical inferences activate more language-related networks (see Prado et al., 2011, for a meta-analytic review). Hence, these studies offered the possibility to provide a fairly precise identification of the specific cerebral network engaged by TI. The drawback of this approach is that the neural description of TI is only viewed through its localization in the brain. In other words, the how question is only addressed through the where question. However, it is likely that inference making, be it transitive or more language-related, involves a brain activity that cannot only be described by the identification of the site where this activity takes place. There are two main reasons for that. First, inference making is relatively complex and involves a set of computations which are associated with distinct neural events. In particular, in the case of transitive inference the two premises are combined, the middle term is eliminated, a new conclusion is drawn and stored in working memory. Yet, showing that the bilateral posterior parietal cortex is recruited by transitive inference although being highly informative, leaves open the question of how this network contributes to the completion of each of these substeps. In a nutshell, the neural dynamics associated with transitive inference remains unknown. Second, the description of this neural dynamics is also necessarily limited by the low temporal resolution of fMRI and PET techniques. The cascade of neural events associated with different types of computation unfolds in a very short period of time which far exceeds the temporal resolution of these techniques. Interestingly, several fMRI studies have begun to address the temporal dimension of reasoning by isolating the cerebral network activated at the time a conclusion is drawn (inference generation phase) from the cerebral network activated at the time a given conclusion is endorsed or rejected (evaluation phase; Fangmeier & Knauff, 2009; Fangmeier et al., 2006; Reverberi et al., 2007). However, these attempts were obviously limited to a macroscopic distinction (i.e. inference generation vs. conclusion evaluation), and in

order to capture the precise neural dynamics of the inference described above, it is needed to follow a more microscopic approach. Recently, several studies have addressed this issue by investigating the time-course of inference making when reasoners deal with linguistic conditional arguments (Bonnefond, Kaliuzhna, Van der Henst, & De Neys, 2014; Bonnefond & Van der Henst, 2009, 2013; Bonnefond et al., 2012, 2013; Luo, Yang, Du, & Zhang, 2011; Luo et al., 2013; Pijnacker, Geurts, van Lambalgen, Buitelaar, & Hagoort, 2011; Wang et al., 2008):

If P then Q P

If John is sleeping; then he is snoring John is sleeping

Therefore Q

Therefore John is snoring:

ð2Þ

By taking advantage of the high temporal resolution of electroencephalography (EEG) and magnetoencephalography (MEG), they reported that processing the minor premise (i.e. P) in the context of the major premise (If P then Q), elicited a cascade of distinct eventrelated potentials/fields (ERPs/ERFs). Some of these components could be seen as reflecting the satisfaction of expectations raised by a conditional statement (i.e. a parietal positive component, the P3b component) and others as the generation of an inference (i.e. a later parietal component, the Positive-slow wave component; Bonnefond & Van der Henst, 2009, 2013; Bonnefond et al., 2012). Furthermore, they also reported that when a conclusion did not logically follow from the premises its processing led to a complex of two ERP components potentially indicating the detection of a violation (i.e. a frontal negative component, the N2 component) and its repair (a late parietal positive component, P600). In the case of a TI task we speculate that participants will have expectations regarding the content of the second premise and the content of the conclusion to be evaluated. At the premise level, we presume that participants will seek to draw inferences from the two premises and will therefore expect the second premise to match the first one. That is, if A–B is the first premise, they will be more likely to expect a second premise like B–C than C–D. Indeed, B–C can be integrated to A–B and lead to another relation (i.e. A–B & B–C ? A–C) while this is not the case for C–D. Hence, C– D is supposed to disrupt the inferential process and violate the expectations regarding the second premise. Similarly, we presume that at the conclusion level, participants would expect the presented conclusion to be identical to the conclusion they would have inferred. That is, if the premises are A–B and B–C, they will expect A–C rather than C–A. If C–A is presented, it will violate the expectations regarding the conclusion. In the current study, we will thus explore the components associated with the satisfaction of expectations such as the P3b (Picton, 1992; Verleger, 1988), and those related to the violation of expectations in a formal

102

M. Bonnefond et al. / Brain and Cognition 90 (2014) 100–108

context such as the N2 (Folstein & Van Petten, 2008) and the P600 (Bonnefond & Van der Henst, 2013; Friedman, 1984).

requires a left-to-right integration of the premises as in (3) (see Van der Henst & Schaeken, 2005 for further details).

2. Experiment The procedure followed in the experiment was similar to that of Fangmeier et al. (2006). First, because it included a reasoning task as well as a memory task that served as a control, and second, because the premises and the conclusion were not linguistically presented but appeared as a pictorial display: ‘‘A B’’ instead of ‘‘A is to the left of B’’ and ‘‘B C’’ instead of ‘‘B is to the left of C’’. The iconic mode of presentation was chosen because each premise and the conclusion could be presented at once, and consequently the two items of each relation could be presented together. In contrast, due to the constraints of the EEG methodology, a linguistic presentation would have required a word-by-word presentation, and might have delayed the integration of the two letters. In the reasoning task, participants had to assess whether the conclusion (e.g. ‘‘A C’’) logically followed from the two premises. In the memory task, participants had to decide whether the third spatial relation was identical to one of the two prior spatial relations. In order to capture the most basic form of transitive inference, we sought to eliminate any extra processing cost and we thus chose the less effortful horizontal transitive inference, the one that

ð3Þ

2.1. Participants Fourteen healthy native French-speaking volunteers (8 females) with no history of neurological or psychiatric disorders participated in the study. Participants were aged between 20 and 26 (mean age: 24 years). All subjects were right-handed as measured by the Edinburg Handedness Inventory (Oldfield, 1971) and gave written informed consent according to the principles of the Declaration of Helsinki.

Fig. 1. Experimental design. Top: Reasoning task; bottom: Memory task. The numbers correspond to the number of trials in each condition. Only conditions of interest were named.

M. Bonnefond et al. / Brain and Cognition 90 (2014) 100–108

2.2. Design

103

second relation, and the memory invalid condition, which included the reverse of those relations (see Fig. 1, bottom).

2.2.1. Reasoning conditions In the reasoning conditions both the second premise and the conclusion were manipulated. At the second premise level, two conditions were designed (see Fig. 1, top). In the matching premise condition, the second premise could be combined with the first premise since the left item of the second premise matched the right item of the first premise. In the mismatching premise condition, the two premises had no items in common and therefore could not result in the inference of a novel (i.e. non-explicit) relationship. This condition was primarily used to describe the EEG response elicited by a premise that blocks the integration process. In this condition, the expected response to any conclusion subsequently presented would be ‘‘INDETERMINATE’’. At the conclusion level, logical validity was manipulated and resulted in two conditions (see Fig. 1, top): the logically valid condition included conclusions that were consistent with the transitivity principle, and the logically invalid condition included conclusions that were inconsistent with this principle (i.e. the reverse of valid conclusions). These two conditions were mainly used to investigate the evaluation process of valid and invalid conclusions and they always occurred after two matching premises.

2.2.2. Memory conditions In the memory task, participants were presented with a sequence of three relations that corresponded to the two premises and the conclusion of the reasoning task. However, they did not have to infer and evaluate a conclusion but rather had to decide whether the third relation was identical to the first or second relation. The second relation of the memory task was used as a control for both the matching and mismatching premise conditions and was labeled the memory condition (see Fig. 1, bottom). We did not include a second relation which matched the first one in order to avoid the participants integrating the two relations. The verbal report of a pre-test indicated a tendency to integrate both relations in order to lower memory load. In the memory condition, the first two relations presented were thus highly similar to the two premises of the mismatching condition. The two conditions only differed with respect to the instructions. In the memory condition, the participants’ task was to retain each of the independent relations in order to assess whether the last relation was identical to one of them. In contrast, in the mismatching premise condition, participants were expected to integrate the two premises so as to infer a conclusion. Because those premises do not share any item in common, the participants should evaluate any conclusion following them as ‘INDETERMINATE’. The last relation was used as a control for both the logically valid condition and the logically invalid condition. As for the reasoning task, the validity of the last relation was manipulated and resulted in two conditions: the memory valid condition, which included either the first or the

2.3. Material and procedure For each trial, the stimuli consisted of three horizontal relationships between two letters that did not yield any meaningful word. As a consequence, the pair ‘‘E–T’’ was never presented because it means ‘‘and’’ in French. Letters Y and W were also excluded because they are orally expressed by two syllables in French. In the reasoning task, participants received 100 trials in the Matching premise condition and 100 trials in the Mismatching premise condition. Fifty trials of the Matching premise condition resulted in a matching conclusion (Matching conclusion condition) and the other 50 trials resulted in a mismatching conclusion (Mismatching conclusion condition; see Fig. 1). In the mismatching premise condition, the presented conclusion was a pair of two letters that did not appear in the two previous premises. Such conclusions only served as fillers. Participants also received 100 trials in the memory task. For half of these trials the third relation was one of the two preceding relations (a quarter matched the first premise and the other quarter matched the second premises) and the other half differed from any of the premises (see Fig. 1). Stimuli were generated with Presentation 10.2 software (Neurobehavioral Systems, http://www.neurobs.com/) and were displayed on a computer screen. In the reasoning task, participants were informed that they will have to make three sorts of conclusion evaluation (‘‘CORRECT’’, ‘‘INCORRECT’’ and ‘‘INDETERMINATE’’) and were given an example of an argument corresponding to each type of evaluation: the conclusion was considered as correct when it was inferable from the premises (i.e. the Matching conclusion condition), incorrect when it contravenes the inferable conclusion (i.e. the Mismatching conclusion condition) and indeterminate when the two premises could not be combined (i.e. the Mismatching premise condition). In the memory task, participants were instructed that they will have to decide whether the third relation was identical to the first or the second relation (‘‘IDENTICAL’’ vs. ‘‘DIFFERENT’’). Each trial started with the presentation of a visual central mark (a cross) in the center of the screen for 800 ms. The two letters of each relation appeared simultaneously with a 2 cm distance between them. The three relations were presented for 900 ms on different screens. They were separated by the presentation of a cross in the center of the screen for 800 ms (see Fig. 2). Participants could answer only after they were invited to do so by the phrase ‘‘your response’’ which was displayed soon after the conclusion. The experiment was divided into four blocks, with two blocks including the reasoning task (100 trials in each block) and two blocks including the memory task (50 trials in each block). Trial order within each block was randomized and the block order was counterbalanced across participants. Participants were asked to refrain from making eye movements and vocal articulations (audible or inaudible) during the trial. They were instructed to

Fig. 2. The timing of stimulus presentation. The sign ‘‘’’ represents the fixation cross.

104

M. Bonnefond et al. / Brain and Cognition 90 (2014) 100–108

respond as quickly and as accurately as possible. The task began with 10 training trials for each task. 2.4. Electroencephalogram (EEG) recording Subjects were seated in a dimly lit, electrically shielded, soundattenuating chamber. EEG was recorded with an Electric Geodesics Inc.™ (EGI) System 200 EEG with 64 channels. Amplified analogue voltages (0.1–200 Hz bandpass) were sampled at 500 Hz. Electrode impedance was kept below 40 KX, as recommended by EGI for this type of high input impedance amplifiers. During the recording, the reference electrode was placed at Cz, and signals were off-line re-referenced to the average mastoids. The signals were offline low-pass filtered (20 Hz) with a zero-phase fifth order Butterworth filter. ERP analyses were conducted using ELAN-Pack software developed at INSERM U821 (Lyon, France). Artifact-free trials were averaged over a 900 ms interval around the onset of the minor premise and the conclusion, including a 100 ms pre-stimulus interval. A baseline correction for all conditions was calculated from the 100 ms preceding the first premise to overcome top-down effects which inhere in others conditions. Trials contaminated by eye blinks or eye movements (threshold: ±100 lV) were not included in the analyses. Analyses were also restricted to trials on which subjects made the correct response. 2.5. Data analysis Each analysis was run with the same electrode positions. Twelve representative electrodes of the 10–20 system were chosen to define different scalp regions (frontal: F3, Fz and F4; central: C3, Cz and C4; centroparietal: CP3, CPz and CP4 and parietal: P3, Pz

and P4). We ran multiple ANOVAs using repeated measures including Conditions (defined for each analysis) and two levels of Electrode Site: laterality (Left, Midline and Right) and anterior– posterior location (Frontal, Central, Centroparietal, Parietal) as within-subject factors. A Greenhouse-Geisser adjustment was used to correct for violations of sphericity. Relevant post hoc comparisons were computed with Tukey HSD tests. 3. Results 3.1. Behavioral results Task performance was high ( 0.09). A second three-way ANOVA was conducted on the matching level (matching vs. mismatching), laterality and anterior–posterior location. It revealed a main effect of the anterior–posterior location (F(3, 39) = 9.04 p < .01, e = 039, g2 = 0.41) and of the matching level (F(1, 13) = 16.31 p < .01, g2 = 0.56). It also showed a significant interaction between laterality and anterior–posterior location (F(6, 78) = 3.86 p < .05, e = 0.60, g2 = 0.23). 3.2.1.2. Non-integration: P600-like component. As shown by Fig. 3, there was no clear peak for the N2 component and we thus did not analyze this component. We however observed a late positive component peaking at 516 ms with larger amplitude at

105

centro-parietal sites. In a violation context, such topography and latency typically characterize the P600 component (Friederici, 2004). To examine whether this component had a larger amplitude in the mismatching premise condition than in the memory condition and the matching condition respectively, we performed two ANOVAs. A first three-way ANOVA was conducted on the type of task, laterality and anterior–posterior location. This analysis revealed a main effect of antero-posterior location (F(3, 39) = 15.91 p < .001, e = 0.44, g2 = 0.55) and type of task (F(1, 13) = 9.84 p < .01, g2 = 0.43). It also indicated a significant interaction between laterality and anterior–posterior location (F(6, 78) = 8.57 p < .001, e = 0.45, g2 = 0.40) and between anterior–posterior location and the type of task (F(3, 39) = 6.55 p < .01, e = 0.54, g2 = 0.34). Tukey HSD post hoc tests indicated that the P600 was larger in the mismatching premise condition than in the memory relation condition in central, centro-parietal and parietal electrodes (p < .001). The P600-like component was also larger in the mismatching premise condition than in the matching premise condition. The three-way ANOVA conducted on the matching level, laterality and anterior–posterior location revealed a main effect of anterior– posterior location (F(3, 39) = 16.81 p < .001, e = 0.44, g2 = 0.56) and of the matching level (F(1, 13) = 7.15 p < .05, g2 = 0.35). It also showed a significant interaction between laterality and anterior– posterior location (F(6, 78) = 12 p < .001, e = 0.46, g2 = 0.48), and between anterior–posterior location and the matching level

Fig. 4. Stimulus locked grand-average waveforms evoked by the appearance of the verb in the memory valid conclusion condition (black line), the memory invalid conclusion condition (dashed black line), the logically valid conclusion condition (blue line) and the logically invalid conclusion condition (dashed blue line) across the 12 sites of interest. Left electrodes are shown in the left column, midline electrodes in the middle column, and right electrodes in the right column. The components of interest are shown by an arrow; these components are indicated only on electrodes showing statistical effect. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

106

M. Bonnefond et al. / Brain and Cognition 90 (2014) 100–108

(F(3, 39) = 3.47 p < .05, e = 0.59, g2 = 0.21). Tukey HSD post hoc tests indicated that the P600 was larger in the mismatching premise condition in midline and right central, centro-parietal and parietal electrodes (p < .001). 3.2.2. Valid and invalid conclusions 3.2.2.1. Valid conclusions: P3b-like component. As shown by Fig. 4, the P3b-like component seemed larger in the logically valid condition as compared to the logic-invalid, the memory valid and the memory invalid condition. A four-way ANOVA conducted on the type of task (Reasoning vs. Memory), validity (Valid vs. Invalid), laterality and anterior–posterior location revealed a main effect of anterior–posterior location (F(3, 39) = 7.41 p < .05, e = 0.37, g2 = 0.36), of laterality (F(2, 26) = 10.66 p < .001, e = 0.37, g2 = 0.45), type of task (F(1, 13) = 25.19 p < .001, g2 = 0.66) and of validity (F(1, 13) = 29.38 p < .001, g2 = 0.69). It also showed a significant interaction between laterality and anterior–posterior (F(6, 78) = 5.29 p < .01, e = 0.53, g2 = 0.29), between anterior–posterior location and the type of task (F(3, 39) = 5.21 p < .05, e = 0.50, g2 = 0.29), between laterality, anterior–posterior location and validity (F(6, 78) = 3.11 p < .05, e = 0.49, g2 = 0.19), between anterior–posterior location, the type of task and validity (F(3, 39) = 5.07 p < .05, e = 0.40, g2 = 0.28). Tukey HSD post hoc tests indicated that the P3b was larger in the logically valid condition than in the other three conditions in the central, centro-parietal and parietal electrodes (p < .001 for all electrodes) and larger in the memory valid condition than in the logic-invalid and memory invalid conditions over the central electrodes (p < .05). 3.2.2.2. Invalid conclusions: P600-like component. As shown by Fig. 4, there was no clear peak for the N2 component and we thus did not analyze it. However, Fig. 4 shows that a P600-like component was larger in the logically invalid condition than in the logically valid, the memory invalid and the memory valid conditions. We performed a four-way ANOVA on the type of task (Reasoning vs. Memory), validity (Valid vs. Invalid), laterality and anterior– posterior location. This analysis revealed a main effect of anteroposterior location (F(3, 39) = 21.39 p < .001, e = 0.39, g2 = 0.62), of laterality (F(2, 26) = 5.61 p < .05, e = 0.86, g2 = 0.30) and of the validity (F(1, 13) = 45.38 p < .001, g2 = 0.78). It also showed a significant interaction between laterality and anterior–posterior location (F(6, 78) = 11.74 p < .001, e = 0.59, g2 = 0.47), between anterior–posterior location and the type of task (F(3, 39) = 5.20 p < .05, e = 0.48, g2 = 0.29) and between anterior–posterior location and validity (F(3, 39) = 6.48 p < .05, e = 0.53, g2 = 0.33). Finally, it revealed a significant interaction between anterior–posterior location, laterality, the type of task and the validity (F(6, 78) = 2.69 p < .05, e = 0.69, g2 = 0.17). Tukey HSD post hoc tests indicated that the P600 was larger in the logically invalid condition and in the memory invalid condition than in the logically valid and memory valid conditions in central, centro-parietal areas and parietal areas (p < .001) and larger in the logically invalid condition than in the memory invalid condition the left and midline central electrodes (p < .01). 4. Discussion The present study aimed at characterizing the ERP components elicited in non-verbal transitive reasoning. Overall, the results were consistent with previous research on verbal reasoning based on conditional statements and thus contribute to both broaden and enrich the temporal description of the neural events underlying deduction (Bonnefond & Van der Henst, 2009, 2013; Bonnefond et al., 2012, 2013, 2014; Luo et al., 2011, 2013; Pijnacker et al., 2011). As for conditional arguments, a P3b-like component was

observed when the second premise could be integrated to the first one and when the presented conclusion was identical to the inferred conclusion. The P3b is one of the most well-known ERP components and has been extensively investigated through the odd-ball paradigm. During an odd-ball task participants have to detect a rare and target stimulus within the context of frequent non-target stimuli (Johnson & Donchin, 1978). The target stimulus typically elicits a P3b component and a key factor that influences the P3b amplitude is stimulus probability: the lesser the probability the greater the P3b amplitude. The most influential cognitive account of the P3b is the context updating theory according to which the P3b reflects the revision of the current representation model in light of an incoming stimulus that differs from previously encoded stimuli (Donchin, 1981; Donchin & Coles, 1998). In this framework, the P3b has been interpreted as a signature of surprise and unexpectancy (Duncan-Johnson & Donchin, 1977). However, this interpretation was criticized based on the argument that a rare stimulus should not necessarily be seen as unexpected (Verleger, 1988, pp. 349–350). The very fact that a stimulus is the target one makes it highly awaited, and the less likely the target stimulus the more likely it will be awaited (Verleger, 1988). At the premise level, a relation (i.e. B–C) that matches an earlier relation (i.e. A–B), perfectly meets the requirement of the task and can be seen as a target to be detected in order to carry on with the task. Hence, the P3b-like component may be seen as an indication that the stimulus is relevant. In each of three conditions – memory, mismatching premise and matching premise – the second piece of information involved an update of the current context of processing, but only the matching premise condition does result in the possibility of integrating information. Hence, in the current study, the P3b indexes more than a context updating operation and can be associated with integration. Interestingly, this component was also observed at the conclusion level especially in the logically valid condition. A valid conclusion is high in relevance since it is exactly the target that should be detected in the context of a reasoning task. This fits well with the idea that the P3b is associated with the processing of relevant stimuli. It is worth noting that the P3b amplitude was higher in the logically valid condition than in the memory valid condition. This may be accounted for by the greater amount of information stored in the memory task than in the reasoning task. In the former two relations are stored and expected whereas only one relation is stored in the reasoning task. In other words expectations are more specific in the reasoning task than in the memory task. However, the greater P3b amplitude might also simply result from the experimental design. In the reasoning task, the valid conclusions represent 25% of the entire set of stimuli (see Fig. 1) while in the memory task, the valid memory condition represents 50% of the overall stimuli (see Fig. 1). Studies based on the oddball paradigm have largely reported that the rarer the target stimuli, the larger the P3b they evoke (see Picton, 1992 for a review). Hence, the lower likelihood of a valid conclusion in the reasoning task, as compared to the valid memory condition, might account for the larger P3b component it elicits. However, it is also important to note that in the reasoning task, once a matching premise is presented, the likelihoods of the subsequent conclusions are identical (i.e. 50% for matching and mismatching conclusions). In this experiment, we also investigated the components elicited by the mismatching premise and the logically invalid conclusion. The mismatching premise and the invalid conclusion conditions are partially similar as in both cases the reasoning process, which should lead to the endorsement of a sound conclusion, is disrupted and the expectations participants may have about incoming information are violated. In the case of a mismatching premise, the information cannot be integrated and the transitive inference cannot be drawn. In the case of an invalid conclusion,

M. Bonnefond et al. / Brain and Cognition 90 (2014) 100–108

the information is rejected as it does not match with what has been inferred. Interestingly, both conditions led to a similar pattern, and elicited a late positive component displaying a scalp topography and a latency that evoke the well-known P600 component. This component was initially observed in the field of language processing as a marker of syntactic violations and syntactic complexity (Hagoort, Brown, & Groothusen, 1993; Hagoort, Brown, & Osterhout, 1999; Osterhout & Holcomb, 1992). Later studies suggest that this component extends beyond the linguistic domain since it can be elicited whenever stimuli violate harmonic structures of music (Besson & Faita, 1995; Patel, Gibson, Ratner, Besson, & Holcomb, 1998), arithmetic progressions (Nunez-Pena & Honrubia-Serrano, 2004), abstract sequences (Lelekov, Dominey, & Garcia-Larrea, 2000; Lelekov-Boissard & Dominey, 2002) or arithmetic computations (e.g. 5  8 = 34, see Niedeggen, Rosler, & Jost, 1999). Rather than being specific to language, the P600 seems to reveal a violation in any rule-governed sequence and reflects the difficulty in integrating information into preexisting structure (Patel et al., 1998). In the present task it arises when the inferential sequence is violated at the premise or conclusion level and probably reflects the difficulty in integrating mismatching information into an argument structure (see also Bonnefond & Van der Henst, 2013; Luo et al., 2013). Although this interpretation is plausible, the late positive component might also be viewed as a delayed P300 rather than a P600. The P300 has been observed in a wide variety of tasks and has been sometimes be found to be associated with categorization processes (Johnson & Donchin, 1980). In the current experiment, it might be that the P3b indexes the categorization of incoming information into the matching or mismatching category. The longer latency of the P300 for mismatching information could be explained by a longer time to categorize such stimuli. In order to assess whether the late positive component is qualitatively distinct from the P3b, source localization would be useful. However, such an analysis would need more trials than in the present experiment and would require the MRI of each participant. Alternatively, MEG study could also be performed as it offers a better spatial resolution than EEG (Bonnefond et al., 2013). Hence, this issue will have to be investigated in future research. In contrast to previous work on conditional inference (Bonnefond & Van der Henst, 2009, 2013; Bonnefond et al., 2012, 2013) the mismatching premise and the invalid conclusion did not elicit a larger N2 component. At the premise level, this might result from the fact that even in the matching premise condition the second relation does not perfectly match the first one (i.e. it introduces a new item). Hence, both the matching and the mismatching premises involve some element of mismatching which may lead to a similar N2 profile. On the contrary, at the conclusion level, the absence of N2 modulation might be related to the presence of the matching items, although in the reverse order (e.g. T A; A C; C A). The N2 component would thus reflect a purely perceptual mismatching (Folstein & Van Petten, 2008). fMRI and PET investigations of deductive reasoning have reported a large body of results showing that the brain response highly differ across studies (Goel, 2007). While some researchers deplored the lack of constancy of those studies (Monti, Osherson, Martinez, & Parsons, 2007), others argued that reasoning is not a unitary mechanism and that different types of arguments engage distinct brain networks (Prado, Noveck, et al., 2010; Prado et al., 2011, Reverberi et al., 2010). In particular, in their meta-analysis Prado et al. (2011) highlighted three subsystems of reasoning, one for categorical arguments (supported by the left inferior frontal gyrus and the left basal ganglia), one for propositional arguments (supported by the left precentral gyrus) and one for transitive arguments (supported by the bilateral posterior parietal cortex and the right middle frontal gyrus). In contrast to this fragmented picture, EEG studies suggest that some form of unity can

107

be found across domains of reasoning as the present findings converge with previous studies on conditional reasoning. This is quite remarkable given the heterogeneity of the two types of arguments considered: conditional reasoning involves a logical connective and other linguistic entities, whereas in the present study, transitive reasoning is largely independent of language and requires visuo-spatial representation. Thus, the convergence of EEG studies indicate that whatever the argument type, the first premise raises specific expectations regarding the second premise and the combination of the two premises raise specific expectations regarding the conclusion. The reasons for the apparent discrepancy between EEG and fMRI results could be threefold: (1) fMRI signal has been correlated with oscillatory activities, which have not been studied here, rather than evoked potentials (e.g. Scheeringa, Petersson, Kleinschmidt, Jensen, & Bastiaansen, 2012; Scheeringa et al., 2008, 2009) and (2) the results obtained in fMRI depend highly on the control condition while in EEG, the differences between the baseline and the stimulus period are already informative. In an effort, to more closely link both literatures, future research would have to examine and localize in the brain both evoked potentials and oscillatory activities using EEG, MEG or EEG-fMRI combined. Taken together, studies on transitive and conditional inferences show that both the P3b and the P600 components are robust markers of cognitive operations involved in reasoning arguments. In the present study, we focused on a very simple form of transitive inference since the premises were not linguistically expressed and the task only required left-to-right arguments. In future research, it would be worthwhile to explore how inference complexity, or other factors, modulates the components reported here. Acknowledgments We thank Ira Noveck for helpful discussions. This work was supported by a Fyssen Foundation grant awarded to the first author and by the French ANR ‘‘Neuroreasoning’’ awarded to the last author. References Acuna, B. D., Eliassen, J. C., Donoghue, J. P., & Sanes, J. N. (2002). Frontal and parietal lobe activation during transitive inference in humans. Cerebral Cortex, 12(12), 1312–1321. Besson, M., & Faita, F. (1995). Event-related potential (Erp) study of musical expectancy – Comparison of musicians with nonmusicians. Journal of Experimental Psychology-Human Perception and Performance, 21(6), 1278–1296. Bonnefond, M., Kaliuzhna, M., Van der Henst, J. B., & De Neys, W. (2014). Disabling conditional inferences: An EEG study. Neuropsychologia, 56, 255–262. Bonnefond, M., Noveck, I., Baillet, S., Cheylus, A., Delpuech, C., Bertrand, O., et al. (2013). What MEG can reveal about inference making: The case of if ... then sentences. Human Brain Mapping, 34(3), 684–697. Bonnefond, M., & Van der Henst, J. B. (2009). What’s behind an inference? An EEG study with conditional arguments. Neuropsychologia, 47(14), 3125–3133. Bonnefond, M., & Van der Henst, J. B. (2013). Deduction electrified: ERPs elicited by the processing of words in conditional arguments. Brain and Language, 124(3), 244–256. Bonnefond, M., Van der Henst, J., Gougain, M., Robic, S., Olsen, M., Weiss, O., et al. (2012). How pragmatic interpretations arise from conditionals: Profiling the affirmation of the consequent argument with reaction time and EEG measures. Journal of Memory and Language, 67(4), 468–485. Burt, C. (1919). The development of reasoning in school children. Journal of Experimental Pedagogy, 5(2), 68–77. Corbetta, M., & Shulman, G. L. (2002). Control of goal-directed and stimulus-driven attention in the brain. Nature Reviews. Neuroscience, 3(3), 201–215. Donchin, E. (1981). Surprise!. . . surprise? Psychophysiology, 18(5), 493–513. Donchin, E., & Coles, M. G. (1998). Context updating and the P300. Behavioral and Brain Sciences, 21(01), 152–154. Duncan-Johnson, C. C., & Donchin, E. (1977). On quantifying surprise: The variation of event-related potentials with subjective probability. Psychophysiology, 14(5), 456–467. Evans, J. S. B., Newstead, S. E., & Byrne, R. M. (1993). Human reasoning: The psychology of deduction. Hove, UK: Psychology Press, Taylor & Francis Group. Fangmeier, T., & Knauff, M. (2009). Neural correlates of acoustic reasoning. Brain Research, 1249, 181–190.

108

M. Bonnefond et al. / Brain and Cognition 90 (2014) 100–108

Fangmeier, T., Knauff, M., Ruff, C. C., & Sloutsky, V. (2006). FMRI evidence for a three-stage model of deductive reasoning. Journal of Cognitive Neuroscience, 18(3), 320–334. Folstein, J. R., & Van Petten, C. (2008). Influence of cognitive control and mismatch on the N2 component of the ERP: A review. Psychophysiology, 45(1), 152–170. Friederici, A. D. (2004). Event-related brain potential studies in language. Current Neurology and Neuroscience Reports, 4(6), 466–470. Friedman, D. (1984). P300 and slow wave: The effects of reaction time quartile. Biological Psychology, 18(1), 49–71. Goel, V. (2007). Anatomy of deductive reasoning. Trends in Cognitive Sciences, 11(10), 435–441. Goel, V., & Dolan, R. J. (2001). Functional neuroanatomy of three-term relational reasoning. Neuropsychologia, 39(9), 901–909. Goel, V., Gold, B., Kapur, S., & Houle, S. (1998). Neuroanatomical correlates of human reasoning. Journal of Cognitive Neuroscience, 10(3), 293–302. Goel, V., Makale, M., & Grafman, J. (2004). The hippocampal system mediates logical reasoning about familiar spatial environments. Journal of Cognitive Neuroscience, 16(4), 654–664. Goel, V. (2008). Fractionating the system of deductive reasoning. In E. Poppel, B. Gulyas, & E. Kraft (Eds.), The neural correlates of thinking. New York: Springer Science. Hagoort, P., Brown, C., & Groothusen, J. (1993). The Syntactic Positive Shift (SPS) as an ERP measure of syntactic processing. Language and Cognitive Processes, 8(4), 439–483. Hagoort, P., Brown, C. M., & Osterhout, L. (1999). The neurocognition of syntactic processing. In C. M. Brown & P. Hagoort (Eds.), The neurocognition of language (pp. 273–317). Oxford: Oxford University Press. Heckers, S., Zalesak, M., Weiss, A. P., Ditman, T., & Titone, D. (2004). Hippocampal activation during transitive inference in humans. Hippocampus, 14(2), 153–162. James, W. (1890). The principles of psychology. New York: Henry Holt. Johnson, R., & Donchin, E. (1978). How P300 amplitude varies with utility of eliciting stimuli. Electroencephalography and Clinical Neurophysiology, 44(4), 424–437. Johnson, R., Jr., & Donchin, E. (1980). P300 and stimulus categorization: Two plus one is not so different from one plus one. Psychophysiology, 17(2), 167–178. Johnson-Laird, P. N. (1983). Mental models. Cambridge: University Press Cambridge. Knauff, M., Fangmeier, T., Ruff, C. C., & Johnson-Laird, P. N. (2003). Reasoning, models, and images: Behavioral measures and cortical activity. Journal of Cognitive Neuroscience, 15(4), 559–573. Knauff, M., & Johnson-Laird, P. N. (2002). Visual imagery can impede reasoning. Memory & Cognition, 30(3), 363–371. Lelekov, T., Dominey, P. F., & Garcia-Larrea, L. (2000). Dissociable ERP profiles for processing rules vs instances in a cognitive sequencing task. NeuroReport, 11(5), 1129–1132. Lelekov-Boissard, T., & Dominey, P. F. (2002). Human brain potentials reveal similar processing of non-linguistic abstract structure and linguistic syntactic structure. Neurophysiologie Clinique/Clinical Neurophysiology, 32(1), 72–84. Luo, J., Liu, X., Stupple, E. J., Zhang, E., Xiao, X., Jia, L., et al. (2013). Cognitive control in belief-laden reasoning during conclusion processing: An ERP study. International Journal of Psychology: Journal International de Psychologie, 48(3), 224–231. Luo, J., Yang, Q., Du, X., & Zhang, Q. (2011). Neural correlates of belief-laden reasoning during premise processing: An event-related potential study. Neuropsychobiology, 63(2), 112–118. Monti, M. M., Osherson, D. N., Martinez, M. J., & Parsons, L. M. (2007). Functional neuroanatomy of deductive inference: A language-independent distributed network. Neuroimage, 37(3), 1005–1016.

Mou, Y., Province, J. M., & Luo, Y. (2014). Can infants make transitive inferences? Cognitive Psychology, 68, 98–112. Niedeggen, M., Rosler, F., & Jost, K. (1999). Processing of incongruous mental calculation problems: Evidence for an arithmetic N400 effect. Psychophysiology, 36(3), 307–324. Nunez-Pena, M. I., & Honrubia-Serrano, M. L. (2004). P600 related to rule violation in an arithmetic task. Brain Research. Cognitive Brain Research, 18(2), 130–141. Oldfield, R. C. (1971). The assessment and analysis of handedness: The Edinburgh inventory. Neuropsychologia, 9(1), 97–113. Osterhout, L., & Holcomb, P. J. (1992). Event-related brain potentials elicited by syntactic anomaly. Journal of Memory and Language, 31(6), 785–806. Patel, A. D., Gibson, E., Ratner, J., Besson, M., & Holcomb, P. J. (1998). Processing syntactic relations in language and music: An event-related potential study. Journal of Cognitive Neuroscience, 10(6), 717–733. Piaget, J. (1921). Une forme verbale de la comparaison chez l’enfant. Archives de Psychologie, 18, 141–172. Picton, T. W. (1992). The P300 wave of the human event-related potential. Journal of Clinical Neurophysiology, 9(4), 456–479. Pijnacker, J., Geurts, B., van Lambalgen, M., Buitelaar, J., & Hagoort, P. (2011). Reasoning with exceptions: An event-related brain potentials study. Journal of Cognitive Neuroscience, 23(2), 471–480. Prado, J., Chadha, A., & Booth, J. R. (2011). The brain network for deductive reasoning: A quantitative meta-analysis of 28 neuroimaging studies. Journal of Cognitive Neuroscience, 23(11), 3483–3497. Prado, J., Noveck, I. A., & Van Der Henst, J. B. (2010). Overlapping and distinct neural representations of numbers and verbal transitive series. Cerebral Cortex, 20(3), 720–729. Prado, J., Van Der Henst, J. B., & Noveck, I. A. (2010). Recomposing a fragmented literature: How conditional and relational arguments engage different neural systems for deductive reasoning. Neuroimage, 51(3), 1213–1221. Ragni, M., & Knauff, M. (2013). A theory and a computational model of spatial reasoning with preferred mental models. Psychological Review, 120(3), 561–588. Reverberi, C., Cherubini, P., Frackowiak, R. S., Caltagirone, C., Paulesu, E., & Macaluso, E. (2010). Conditional and syllogistic deductive tasks dissociate functionally during premise integration. Human Brain Mapping, 31(9), 1430–1445. Reverberi, C., Cherubini, P., Rapisarda, A., Rigamonti, E., Caltagirone, C., Frackowiak, R. S., et al. (2007). Neural basis of generation of conclusions in elementary deduction. Neuroimage, 38(4), 752–762. Scheeringa, R., Bastiaansen, M. C., Petersson, K. M., Oostenveld, R., Norris, D. G., & Hagoort, P. (2008). Frontal theta EEG activity correlates negatively with the default mode network in resting state. International Journal of Psychophysiology, 67(3), 242–251. Scheeringa, R., Petersson, K. M., Kleinschmidt, A., Jensen, O., & Bastiaansen, M. C. (2012). EEG alpha power modulation of FMRI resting-state connectivity. Brain Connectivity, 2(5), 254–264. Scheeringa, R., Petersson, K. M., Oostenveld, R., Norris, D. G., Hagoort, P., & Bastiaansen, M. C. (2009). Trial-by-trial coupling between EEG and BOLD identifies networks related to alpha and theta EEG power increases during working memory maintenance. Neuroimage, 44(3), 1224–1238. Van der Henst, J. B., & Schaeken, W. (2005). The wording of conclusions in relational reasoning. Cognition, 97(1), 1–22. Vasconcelos, M. (2008). Transitive inference in non-human animals: An empirical and theoretical analysis. Behavioural Processes, 78(3), 313–334. Verleger, R. (1988). Event-related potentials and memory – A critique of the context updating hypothesis and an alternative interpretation of P3. Behavioral and Brain Sciences, 11(3), 343–356. Wang, Y., Liu, Y., Gao, Y., Chen, J., Zhang, W., & Lin, C. (2008). False belief reasoning in the brain: An ERP study. Science China Life Sciences, 51(1), 72–79.