Abstract

It is a core cognitive ability of humans to represent and reason about relational information, such as “the train station is north of the hotel” or “Charles is richer than Jim.” However, the neural processes underlying the ability to draw conclusions about relations are still not sufficiently understood. Central open questions are as follows: (1) What are the neural correlates of relational reasoning? (2) Where can deductive and inductive reasoning be localized? (3) What is the impact of different informational types on cerebral activity? For that, we conducted a meta-analysis of 47 neuroimaging studies. We found activation of the frontoparietal network during both deductive and inductive reasoning, with additional activation in an extended network during inductive reasoning in the basal ganglia and the inferior parietal cortex. Analyses revealed a double dissociation concerning the lateral and medial Brodmann's area 6 during deductive and inductive reasoning, indicating differences in terms of processing verbal information in deductive and spatial information in inductive tasks. During semantic and symbolic tasks, the frontoparietal network was found active, whereas geometric tasks only elicited prefrontal activation, which can be explained by the reduced demand for the construction of a mental representation in geometric tasks. Our study provides new insights into the cognitive mechanisms underlying relational reasoning and clarifies previous controversies concerning involved brain areas.

INTRODUCTION

Consider the following relational information about locations: The shop is north-west of the cathedral. John is currently south-east of the cathedral. Given this information, it is easy for most healthy individuals to infer that from his actual position, John has to go north-west to find the shop. Such and other examples demonstrate that relations are ubiquitous in everyday communication, and this is not limited to spatial relations (cf. Goodwin & Johnson-Laird, 2005). Furthermore, it is not only possible to infer implicit relational knowledge from given information but also to create new knowledge. This process can take place in two forms: it can be either “deductive” or “inductive.” “Deductive reasoning,” as seen in the example above, is drawing a definitive conclusion from given information. It is characterized by an inference mechanism that allows to draw the conclusion with certainty (Knauff, 2006). By that, the conclusion does not contain more information than the premises convey but makes the implicit information explicit. In contrast, “inductive reasoning” is based on the consideration of different instances from which an underlying relation can be inferred, a relation that holds for all instances. Therefore, by finding the underlying relation, more information is generated than conveyed by the premises. For example, a person visiting 10 European towns observes that the central train station is in the center of the city. Hence, this person could infer, with some probability, the rule that the central stations in Europe are in the center of the city.

Although reasoning about relations has been researched for the past 70 years, only recently it has been investigated by methods such as PET and functional magnetic resonance imaging (fMRI). Although initial findings remained inconclusive and partly contradicting, Goel (2007) and Prado, Chadha, and Booth (2011) conducted meta-analyses about the neural correlates of deductive reasoning. Prado and colleagues (2011) showed that deductive relational reasoning involves the right middle frontal gyrus (MFG), the left medial frontal gyrus (MeFG), and the bilateral posterior parietal cortex (PPC). The central debate in the field has been whether inductive reasoning and deductive reasoning share similar cerebral and cognitive processes or whether they diverge when it comes to neural processes. In the late 1990s and early 2000s, several neuroimaging studies investigated this question, exhibiting evidence for the latter. Based on mental model theory (MMT), Osherson et al. (1998) hypothesized that deductive reasoning and inductive reasoning lead to activation in the right hemisphere due to mental model construction and manipulation. They tested this hypothesis by neuroimaging methods, revealing diverging brain region activations for deductive (left dorsolateral pFC [DLPFC], BA 8, BA 10, and right insular cortex) and inductive reasoning (right-sided posterior and bilateral frontal activation, visual cortex, right superior parietal lobule [SPL], and thalamus). Goel, Gold, Kapur, and Houle (1997) showed that deductive tasks draw on the left inferior frontal gyrus (IFG; BA 45, BA 47), whereas inductive tasks mainly engage the left MeFG, cingulate gyrus, and superior frontal gyrus (SFG; BA 8, BA 9, BA 24, BA 32). The main difference between reasoning types was the additional engagement of the left SFG (BA 8, BA 9) in inductive reasoning.

Parsons and Osherson (2001) discovered hemispherical differences between reasoning types, showing that deductive reasoning engages the right hemisphere and inductive reasoning engages the left hemisphere. For deductive reasoning, they found activation in language-dependent areas and the limbic system, whereas for induction reasoning, prefrontal areas and the BG were involved. Goel and Dolan (2004) supported the engagement of the left IFG (BA 44) for deductive reasoning and the left DLPFC (BA 8, BA 9) for inductive reasoning, indicating mainly prefrontal differences between reasoning types. Hence, the question how exactly deductive and inductive reasoning diverge remains unsolved and inconclusive. Concerning inductive reasoning, Jia and Liang (2015) conceptualized inductive reasoning as a four-stage model with respectively four brain regions engaged. They showed that the DLPFC is active in relation generation, that is, the identification of the implicitly given relation. For relational inferences or application, that is, when a deductive inference about the relational information is drawn, the striatum and thalamus, the bilateral precuneus, the SFG, the MFG, and the left DLPFC were active. In a former study, Jia et al. (2011) showed that the bilateral SPL and the left DLPFC are active during inductive reasoning. Moreover, particular involvement of the frontoparietal network in relation inference processes was shown.

Because reasoning problems can come in various contents, we additionally aimed at identifying to what extent differences in neural activation can be accounted for by content effects. These differentiations have been made by Hobeika, Diard-Detoeuf, Garcin, Levy, and Volle (2016). In categorizing the literature, they rather focused on the type of relation that has to be drawn, rather than on the presentation format of the premises. Considering the problems' presentation, we classified three distinct forms: semantic, symbolic, and geometric form problems. In problems that are conveyed by sensible sentences (i.e., semantic problems), activation was located in the left hemisphere linguistic system (Goel & Dolan, 2001), whereas reasoning about symbols elicits rather parietal activation, especially in the left inferior parietal lobule (IPL; BA 40), the bilateral SPL (BA 7), and the bilateral inferior occipital gyrus (BA 19; Goel & Dolan, 2001). The third group, geometric form problems, mainly includes problems like Raven's progressive matrices (Raven, 2000). Because the demand on working memory is considerably higher in these tasks due to up to eight premises, we decided to account for these tasks with a separate category. Hobeika et al. (2016) found that these problems elicit an enhanced involvement of the attention and frontoparietal network, potentially because multitasking is required.

Because the neurocognitive mechanisms of relational reasoning remain vague, we decided to conduct a meta-analysis of neuroimaging data to clarify these issues. This is necessary to foster research in the field of reasoning because the meta-analyses and neuroimaging studies about deductive and inductive reasoning do not covey a consistent pattern so far. Hence, more insights into the neural and cognitive mechanisms of relational reasoning and its variations concerning task setup and content are necessary.

In this review, we present a meta-analysis of neuroimaging about relational reasoning. Our objective is to elucidate the neural mechanisms of relational reasoning and its subtypes across different experimental setups and conditions. For that, 47 experiments with a total of 806 participants are considered and 813 foci are analyzed by the Activation Likelihood Estimation (ALE) method (Eickhoff, Bzdok, Laird, Kurth, & Fox, 2012; Turkeltaub et al., 2012; Eickhoff et al., 2009) to identify the neural sites that are most likely to be active during task completion. The aim is to answer three questions: First, which brain regions are relevant for relational reasoning? Second, what are the neural correlates of deductive and inductive relational reasoning? Third, what is the impact of content (symbolic, semantic and geometric form) on cerebral activation during reasoning? Finally, the results are interpreted in the light of prior neurocognitive and neuropsychological research of reasoning.

Hypotheses

Following the experimental background of reasoning research, we formulate several hypotheses concerning the neural activation accompanying the aforementioned differentiations.

Deductive Problems

In the process of drawing definitive conclusions from given information, we suppose activation mainly in the right-sided hemisphere (cf. Parsons & Osherson, 2001) and in the right MFG, the left MeFG (cf. Prado et al., 2011), the left rostrolateral pFC (RLPFC; cf. Ackerman & Courtney, 2012) and DLPFC, the right insular cortex (cf. Osherson et al., 1998), and bilateral PPC (cf. Prado et al., 2011).

Inductive Problems

In finding an underlying relation and generating new information, the literature reports general left-hemispherical activation (cf. Parsons & Osherson, 2001) as well as right-sided parietal (SPL) and bilateral frontal activation and occipital and thalamic activation (cf. Osherson et al., 1998). Moreover, activation is expected in the left MeFG, the left cingulate gyrus, and the left SFG (cf. Goel et al., 1997).

Semantic, Symbolic, and Geometric Form Problems

Considering the content-wise differentiation between semantic, symbolic, and geometric form tasks, we assume symbolic and semantic problems to elicit left-sided parietal and prefrontal activation, respectively. Moreover, we expect the semantic tasks to elicit less parietal activation than the symbolic tasks (cf. Goel & Dolan, 2001). In geometric form problems, we expect right-sided activation, particularly differentiable in the RLPFC (cf. Hobeika et al., 2016; Crone et al., 2009).

METHODS

We conducted a meta-analysis of neuroimaging studies mainly using fMRI, except for Goel et al. (1997), in which PET was used. We conducted an ALE for finding the neural underpinnings of relational reasoning to draw conclusions about the corresponding cognitive mechanisms. For that purpose, the ALE method is apt because several comparable meta-analyses were conducted with the GingerALE software, which have had similar aims of finding the neural correlates of cognitive processes (e.g., Farrell, Laird, & Egan, 2005). Our study builds on studies that take the cerebral as well as the cognitive level into account during study conception and analysis (Table 1).

Table 1. 

Overview of the Experiments Included in the Meta-analysis with Details on the Experimental Setup

PublicationYearParticipantsContentInference
Goel et al. 1998  12 Semantic Deductive 
Goel & Dolan 2001  14 Semantic, Symbolic Deductive 
Christoff et al. 2001  10 Geometric form Inductive 
Prabhakaran, Rypma, & Gabrieli 2001  Semantic Deductive 
Knauff, Mulack, Kassubek, Salih, & Greenlee 2002  12 Symbolic Deductive 
Acuna, Eliassen, Donoghue, & Sanes 2002  15 Geometric form Deductive 
Knauff & Johnson-Laird 2002  12 Semantic Deductive 
Knauff, Fangmeier, Ruff, & Johnson-Laird 2003  12 Semantic Deductive 
Luo et al. 2003  10 Semantic Inductive 
Ruff et al. 2003  12 Symbolic Deductive 
Goel, Makale, & Grafman 2004  14 Semantic Deductive 
Fangmeier, Knauff, Ruff, & Sloutsky 2006  12 Symbolic Deductive 
Green, Fugelsang, Kraemer, Shamosh, & Dunbar 2006  14 Semantic Inductive 
Lee et al. 2006  36 Geometric form Inductive 
Kalbfleisch, Van Meter, & Zeffiro 2007  14 Geometric form Inductive 
Melrose, Poulin, & Stern 2007  19 Geometric form Inductive 
Wendelken et al. 2008  20 Semantic Inductive 
Wartenburger, Heekeren, Preusse, Kramer, & van der Meer 2009  15 Semantic Inductive 
Eslinger et al. 2009  16 Symbolic Inductive 
Fangmeier & Knauff 2009  12 Symbolic Deductive 
Goel, Stollstorff, Nakic, Knutson, & Grafman 2009  17 Semantic Deductive 
Prado, Noveck, & Van Der Henst 2010  15 Symbolic Deductive 
Geake & Hansen 2010  16 Symbolic Inductive 
Golde, von Cramon, & Schubotz 2010  16 Geometric form Inductive 
Wendelken & Bunge 2010  16 Symbolic Deductive 
Prado, Van Der Henst, & Noveck 2010  13 Symbolic Deductive 
Hinton, Dymond, von Hecker, & Evans 2010  24 Symbolic Deductive 
Cho et al. 2010  17 Symbolic Deductive 
Preusse et al. 2010  17 Symbolic Inductive 
Volle, Gilbert, Benoit, & Burgess 2010  16 Symbolic Inductive 
Hampshire, Thompson, Duncan, & Owen Experiment 1 2011  16 Geometric form Inductive 
Hampshire, Thompson, Duncan, & Owen Experiment 2 2011  21 Geometric form Inductive 
Preusse, van der Meer, Deshpande, Krueger, & Wartenburger 2011  40 Symbolic Inductive 
Jia et al. 2011  20 Symbolic Inductive 
Brzezicka, Kamiński, Kamiński, & Blinowska 2011  17 Symbolic Deductive 
Wendelken, Chung, & Bunge 2012  22 Semantic, Symbolic Inductive 
Green, Kraemer, Fugelsang, Gray, & Dunbar 2010  23 Semantic Inductive 
Prado, Mutreja, & Booth 2013  30 Semantic Deductive 
Shokri-Kojori, Motes, Rypma, & Krawczyk 2012  20 Geometric form Deductive 
Watson & Chatterjee 2012  23 Symbolic Inductive 
Kalbfleisch et al. 2013  34 Geometric form Inductive 
Bazargani, Hillebrandt, Christoff, & Dumontheil 2014  37 Symbolic Deductive 
Liang, Jia, Taatgen, Zhong, & Li 2014  23 Symbolic Inductive 
Parkin, Hellyer, Leech, & Hampshire 2015  20 Geometric form Inductive 
Jia, Liang, Shi, Wang, & Li 2015  15 Symbolic Inductive 
Jia & Liang 2015  13 Symbolic Inductive 
Liang, Jia, Taatgen, Borst, & Li 2016  15 Symbolic Inductive 
PublicationYearParticipantsContentInference
Goel et al. 1998  12 Semantic Deductive 
Goel & Dolan 2001  14 Semantic, Symbolic Deductive 
Christoff et al. 2001  10 Geometric form Inductive 
Prabhakaran, Rypma, & Gabrieli 2001  Semantic Deductive 
Knauff, Mulack, Kassubek, Salih, & Greenlee 2002  12 Symbolic Deductive 
Acuna, Eliassen, Donoghue, & Sanes 2002  15 Geometric form Deductive 
Knauff & Johnson-Laird 2002  12 Semantic Deductive 
Knauff, Fangmeier, Ruff, & Johnson-Laird 2003  12 Semantic Deductive 
Luo et al. 2003  10 Semantic Inductive 
Ruff et al. 2003  12 Symbolic Deductive 
Goel, Makale, & Grafman 2004  14 Semantic Deductive 
Fangmeier, Knauff, Ruff, & Sloutsky 2006  12 Symbolic Deductive 
Green, Fugelsang, Kraemer, Shamosh, & Dunbar 2006  14 Semantic Inductive 
Lee et al. 2006  36 Geometric form Inductive 
Kalbfleisch, Van Meter, & Zeffiro 2007  14 Geometric form Inductive 
Melrose, Poulin, & Stern 2007  19 Geometric form Inductive 
Wendelken et al. 2008  20 Semantic Inductive 
Wartenburger, Heekeren, Preusse, Kramer, & van der Meer 2009  15 Semantic Inductive 
Eslinger et al. 2009  16 Symbolic Inductive 
Fangmeier & Knauff 2009  12 Symbolic Deductive 
Goel, Stollstorff, Nakic, Knutson, & Grafman 2009  17 Semantic Deductive 
Prado, Noveck, & Van Der Henst 2010  15 Symbolic Deductive 
Geake & Hansen 2010  16 Symbolic Inductive 
Golde, von Cramon, & Schubotz 2010  16 Geometric form Inductive 
Wendelken & Bunge 2010  16 Symbolic Deductive 
Prado, Van Der Henst, & Noveck 2010  13 Symbolic Deductive 
Hinton, Dymond, von Hecker, & Evans 2010  24 Symbolic Deductive 
Cho et al. 2010  17 Symbolic Deductive 
Preusse et al. 2010  17 Symbolic Inductive 
Volle, Gilbert, Benoit, & Burgess 2010  16 Symbolic Inductive 
Hampshire, Thompson, Duncan, & Owen Experiment 1 2011  16 Geometric form Inductive 
Hampshire, Thompson, Duncan, & Owen Experiment 2 2011  21 Geometric form Inductive 
Preusse, van der Meer, Deshpande, Krueger, & Wartenburger 2011  40 Symbolic Inductive 
Jia et al. 2011  20 Symbolic Inductive 
Brzezicka, Kamiński, Kamiński, & Blinowska 2011  17 Symbolic Deductive 
Wendelken, Chung, & Bunge 2012  22 Semantic, Symbolic Inductive 
Green, Kraemer, Fugelsang, Gray, & Dunbar 2010  23 Semantic Inductive 
Prado, Mutreja, & Booth 2013  30 Semantic Deductive 
Shokri-Kojori, Motes, Rypma, & Krawczyk 2012  20 Geometric form Deductive 
Watson & Chatterjee 2012  23 Symbolic Inductive 
Kalbfleisch et al. 2013  34 Geometric form Inductive 
Bazargani, Hillebrandt, Christoff, & Dumontheil 2014  37 Symbolic Deductive 
Liang, Jia, Taatgen, Zhong, & Li 2014  23 Symbolic Inductive 
Parkin, Hellyer, Leech, & Hampshire 2015  20 Geometric form Inductive 
Jia, Liang, Shi, Wang, & Li 2015  15 Symbolic Inductive 
Jia & Liang 2015  13 Symbolic Inductive 
Liang, Jia, Taatgen, Borst, & Li 2016  15 Symbolic Inductive 

Study Acquisition and Selection

For data acquisition, we aggregated papers from previous meta-analyses and reviews (Hobeika et al., 2016; Maier, Ragni, Wenczel, & Franzmeier, 2014; Prado et al., 2011; Knauff, 2006) and retrieved the respective papers about relational reasoning. To complement the data sets, we conducted online researches via PubMed, ScienceDirect, and Google Scholar with the following search terms: “(fMRI OR PET OR Neuroimaging OR TMS) AND (relational reasoning) AND (visual reasoning OR spatial reasoning OR visuospatial reasoning)” in the time frame from 2004 (since the list from Knauff reports studies up to 2004) to 2017. Our criteria for selecting suitable papers entail that they need to be peer-reviewed PET or fMRI studies on healthy individuals. We have labeled a task as testing for relational reasoning when (1) the reasoner was asked to detect a relation between the premises' items and draw a conclusion or when (2) he or she was asked to detect a relation between items and extrapolate the “new” item fitting the sequence. Because of a review of the meta-analysis conducted by Prado et al. (2011), “reasoning versus baseline” conditions (such as fixation cross or maintenance tasks; see e.g., Wendelken, Nakhabenko, Donohue, Carter, & Bunge, 2008; Ruff, Knauff, Fangmeier, & Spreer, 2003, respectively) as well as “high- versus low-level reasoning” conditions were included because they both represent an aspect of reasoning. Experimental data were only included when the data were reported in Montreal Neurological Institute (MNI) or Talairach space and yielded from whole-brain analyses. To ensure independence of the data sets, only one contrast per study was included, mainly the one testing for reasoning versus baseline.

Study Categorization

After selecting 47 studies, we categorized them along two parameters: content and inference (see Tables 1 and 2). In the content differentiation, we categorized data that include sentences in real language (semantic), signs or symbols (symbolic), or shapes (geometric form) as objects to which the relation is applied. Apart from that, we differentiated by the type of inference, which could either be deductive or inductive. We classified inferences as deductive, when the information that has to be drawn as a conclusion was implicitly included in the premises and as inductive when this was not the case, that is, when the conclusion contains a degree of uncertainty. To exemplify these differentiations, we chose three representative sample tasks. The problem “Officers are heavier than generals. Generals are heavier than privates. Privates are lighter than officers.” (Goel, Gold, Kapur, & Houle, 1998) is categorized as deductive, because the conclusion can be drawn with certainty and as semantic, because the content is composed of sensible sentences conveying meaning. Another example is the abovementioned Raven's progressive matrices (Raven, 2000) as used by Christoff et al. (2001). These are categorized as induction, because the relation cannot be determined with certainty. Moreover, the task content is composed of geometric forms. Another example is the task by Geake and Hansen (2010), in which the participants are confronted with the two premises “abc → abd” and “hhwwqq → hhwwdd” and had to decide whether a plausible analogy can be drawn between those two. Because it is only a plausible analogy, the task is considered as inductive and symbolic because it involves letters that do not convey semantic content. We acknowledge that the tasks differ along further axes and that these differences reflect variations in neural activation but chose not to take these into consideration. This is because ALE meta-analyses exhibit more robust results with more studies included (Eickhoff et al., 2016).

Table 2. 

Details of the Study Categorizations with Regard to the Quantitative Parameters of the Groups

CategorizationNumber of StudiesNumber of ParticipantsActivation Foci
All 47 806 813 
Inference 
 Deductive 21 340 377 
 Inductive 26 503 436 
Content 
 Semantic 14 222 271 
 Symbolic 23 414 370 
 Geometric form 13 253 249 
CategorizationNumber of StudiesNumber of ParticipantsActivation Foci
All 47 806 813 
Inference 
 Deductive 21 340 377 
 Inductive 26 503 436 
Content 
 Semantic 14 222 271 
 Symbolic 23 414 370 
 Geometric form 13 253 249 

Activation Likelihood Estimation

ALE is an established method for conducting meta-analyses of neuroimaging data (Eickhoff et al., 2009, 2012; Turkeltaub et al., 2012). It has been successfully applied by, among others, Hobeika et al. (2016) for the same purpose as ours, the investigation of the neural correlates of reasoning. The software (GingerALE 2.3.6, 2016) features a statistical program to determine how likely a brain region is to be activated during a specific task. For that, the stereotactic coordinates representing the activation as the change in BOLD response between two testing conditions are the starting point for the ALE analysis. ALE facilitates cross-study meta-analyses for finding brain areas involved in cognitive tasks. For this, either a single data set is analyzed with a chosen thresholding method or data sets can be compared in conjunction and contrast analyses to investigate shared and distinct areas, which are likely to be active during a specific subtask.

GingerALE generates modeled activation (MA) maps from the data of each experiment. These are virtual brain maps on which the data points are represented. Because the reported data are extensionless, the program reconstructs the scanning data by assigning each data point the center of a Gaussian distribution, which is blurred by the FWHM. The FWHM is determined by the subject size of the respective data set (Eickhoff et al., 2009). From the MA maps, the ALE output is rendered, which is a combination of the MA map of all studies. The confidence of the likelihood of finding each value is calculated for each voxel by neglecting the spatial information from the data set and analyzing how probable it is for a value to be part of an MA map. The MA map and the p value image, in addition to a chosen threshold, are then combined to create the thresholded ALE map reporting peak activations (Eickhoff et al., 2009, 2012). As a thresholding method, the cluster-level family-wise error method was chosen because it is conservative and recommended for our aim (Eickhoff et al., 2016). By this method, a random data set tantamount to the set at hand (regarding subject size, number of foci, and number of studies) is generated, and both are compared. In conjunction and contrast analyses, the ALE maps of two conditions are examined in activation likelihood for their overlap and distinctness, respectively (Eickhoff et al., 2011).

ALE Parameters

In accordance with Eickhoff et al. (2016), we have chosen to run a cluster-level analysis with a p value of .01 and 1000 threshold permutations. We chose an uncorrected p value of .001, as well as the nonparametric statistic method by Turkeltaub et al. (2012). Concerning the conjunction and contrast analyses, we have applied the aforementioned parameters for analyzing the single groups and used an uncorrected p value of .01 and 10,000 permutations for comparing the respective groups. Foci originally represented in MNI space were converted to Talairach space by using the Convert foci feature of the software GingerALE 2.3.6.

RESULTS

In the following, we present the results of the ALE meta-analysis (Figure 1). After laying out the main results (detailed results of the analyses can be found in Appendix Table A1), the results are set into context of prior research. Table 3 encompasses the results from the single-study analyses, in which the results of the analyses on the mentioned sets are presented, and Table 4 depicts the analyses of the conjunction and contrast analyses.

Figure 1. 

From left to right, top to bottom: (A) Relational reasoning. (B) Deductive. (C–E) Inductive. (F) Semantic. (G) Symbolic. (H) Geometrical form.

Figure 1. 

From left to right, top to bottom: (A) Relational reasoning. (B) Deductive. (C–E) Inductive. (F) Semantic. (G) Symbolic. (H) Geometrical form.

Table 3. 

Simplified Representation of the Significant Activation Clusters of the Single-study Analyses

 Frontal LobeParietal LobeOccipital LobeSublobar
BA 6BA 8BA 9BA 10BA 32BA 44BA 46BA 7BA 39BA 40BA 19CaClL
All ◑ ◗ ◐     ◖ ◖ ◑   ◑   ◗     
Deductive ◑ ◗ ◖   ◑     ◖ ◗ ◐         
Inductive ◖   ◐         ◑   ◖ ◗ ◑   ◖ 
Semantic     ◖         ◖             
Symbolic ◖ ◗ ◐     ◖   ◐   ◐     ◗   
Geometric form ◖     ◖                     
 Frontal LobeParietal LobeOccipital LobeSublobar
BA 6BA 8BA 9BA 10BA 32BA 44BA 46BA 7BA 39BA 40BA 19CaClL
All ◑ ◗ ◐     ◖ ◖ ◑   ◑   ◗     
Deductive ◑ ◗ ◖   ◑     ◖ ◗ ◐         
Inductive ◖   ◐         ◑   ◖ ◗ ◑   ◖ 
Semantic     ◖         ◖             
Symbolic ◖ ◗ ◐     ◖   ◐   ◐     ◗   
Geometric form ◖     ◖                     

Circles indicate whether a significant cluster was found in the respective cerebral hemisphere. Semicircles indicate the laterality of activation in the respective Brodmann's area. If both semicircles are indicated, the filled one indicates the hemisphere in which the larger areas was active. Ca = caudate (body and/or tail); Cl = claustrum; L = lenticular nucleus/globus pallidus.

Table 4. 

Simplified Representation of the Significant Activation Cluster of the Contrast and Conjunction Analyses

 Frontal LobeParietal LobeOccipital LobeSublobar
BA 6BA 9BA 10BA 7BA 39BA 40BA 19Ca
Deductive ∪ Inductive ◐ ◐   ◖   ◖     
Deductive \ Inductive ◗               
Inductive \ Deductive ◖           ◗ ◑ 
Semantic ∪ Symbolic   ◖   ◖         
Symbolic \ Semantic ◑       ◖   ◗   
Semantic \ Geometric form   ◖             
Geometric form \ Semantic ◖   ◖           
Symbolic ∪ Geometric form ◖ ◖   ◖         
 Frontal LobeParietal LobeOccipital LobeSublobar
BA 6BA 9BA 10BA 7BA 39BA 40BA 19Ca
Deductive ∪ Inductive ◐ ◐   ◖   ◖     
Deductive \ Inductive ◗               
Inductive \ Deductive ◖           ◗ ◑ 
Semantic ∪ Symbolic   ◖   ◖         
Symbolic \ Semantic ◑       ◖   ◗   
Semantic \ Geometric form   ◖             
Geometric form \ Semantic ◖   ◖           
Symbolic ∪ Geometric form ◖ ◖   ◖         

Circles indicate whether a significant cluster was found in the respective cerebral hemisphere “∪” indicates the conjunction analysis of the two sets. “\” indicates the subtraction analysis of the right form the left set. Semicircles indicate the laterality of activation in the respective Brodmann's area. If both semicircles are indicated, the filled one indicates the hemisphere in which the larger areas was active. Ca = caudate (body and/or tail).

Relational Reasoning Processes

During relational reasoning, activation is mainly clustered in the bilateral prefrontal and parietal cortex. Activation was identified in the left IFG (BA 9), the bilateral MFG (BA 9, BA 46, BA 8), the right SFG (BA 6), and the precentral gyrus (PreCG; BA 9). Concerning the parietal cortex, the bilateral SPL (BA 7), the IPL (BA 40), and the precuneus (BA 7) were located. Moreover, activation in the right BG was found.

Deductive and Inductive Reasoning Processes

Concerning deductive reasoning, we determined activation in the left MeFG (BA 32) and the bilateral MFG (BA 9, BA 8), as well as in the left SPL and the precuneus (BA 7), the bilateral IPL and the supramarginal gyrus (BA 40), and the right angular gyrus (BA 39). In contrast to inductive reasoning, the main area specific to deductive reasoning is the right MFG (BA 6). During inductive reasoning, the left IFG (BA 9), the PreCG and the SFG (BA 6), and the bilateral MFG (BA 9) were active. Moreover, the bilateral SPL (BA 7), the right precuneus (BA 7), the left IPL (BA 40), and the right superior occipital gyrus (BA 19) were engaged. Also, the bilateral BG were active during inductive reasoning. In contrast to deductive reasoning, it mainly involves the left MFG (BA 6), the right precuneus and the superior occipital gyrus (BA 19), and the bilateral BG. The areas that both deductive and inductive reasoning commonly elicit are the bilateral MFG (BA 9), the SFG (BA 6), the left IPL (BA 40), and the SPL (BA 7).

Semantic, Symbolic, and Geometric Form Processes

Semantic tasks elicit activation in the left MFG, the IFG (BA 9), and the precuneus (BA 7). In contrast to symbolic processes, semantic tasks pose a demand on the left MFG (BA 9). Symbolic tasks elicit activation in the left IFG (BA 9, BA 44), the PreCG and the SFG (BA 6), and the bilateral MFG (BA 9), as well as in the bilateral IPL (BA 40) and the SPL (BA 7). Furthermore, the left cuneus (BA 7) and the right BG are engaged. In contrast to semantic tasks, symbolic tasks demand activation in the right SFG and the left MeFG (BA 6), the left angular gyrus (BA 39), and the right precuneus (BA 19). Contrasting geometric form processes, the symbolic tasks elicit left-sided activation in the MFG (BA 9) and the precuneus (BA 7). Geometric form tasks evoke the activation of the left MFG and the IFG (BA 6, BA 10), areas found to be specific to geometric form tasks in contrasts to semantic tasks. The processes semantic and symbolic tasks commonly elicit are in the left MFG, the IFG (BA 9), and the SPL (BA 7). Areas symbolic and geometric form tasks share are in the left MFG (BA 6).

DISCUSSION

Previous meta-analyses have often focused on general brain activation patterns during deductive relational reasoning. The goal of our study was to investigate the impact of specific dimensions of relational reasoning. Hence, we focused on differences between deductive and inductive reasoning tasks and the presentation format of the stimuli (semantic, symbolic, and geometric form). Toward this goal, we have first developed a formally rigorous and improved classification of deductive and inductive reasoning and conducted the so far largest meta-analysis about relational reasoning including 47 studies based on the classification schema. We will now structure the discussion according to three main research questions in which we situate the findings within the literature from neuroimaging, lesion studies and cognitive modeling to complement and support our findings.

Which Brain Regions Are Relevant for Relational Reasoning?

For overall relational reasoning, the frontoparietal network is the most consistently activated brain network. We identified enhanced activation within the bilateral pFC, including the bilateral DLPFC (BA 9, BA 46), the SMA (BA 6), the bilateral superior (BA 7), and the inferior PPC (BA 40). Additional activation was located in the right-sided BG (cf. Table 4). In the following, we relate our results to findings from the literature and discuss implications for cognitive theories like the MMT. In previous studies, relational reasoning was found to involve the DLPFC, the MeFG (BA 6), the PPC, and the left RLPFC (Crone et al., 2009). Although our results overlap with these findings, we did not find any enhanced activation in the RLPFC (BA 10), similarly to the findings in the meta-study conducted by Prado et al. (2011). The bilateral DLPFC is central to working memory and executive functions (Waltz et al., 1999), and its activation can be related to the mental processing of relational reasoning for maintaining a mental model. The SMA (BA 6) plays a role in complex planning tasks (Hanakawa et al., 2002), and the SPL (BA 7) plays a role in the construction and manipulation of mental models (e.g., in a TMS study for spatial relational reasoning; Ragni, Franzmeier, Maier, & Knauff, 2016). Because the activation cluster in the BG is mainly due to inductive studies, we will discuss the BG involvement in the following section.

From a processing perspective in cognitive architectures (e.g., ACT-R; see Borst & Anderson, 2015; Anderson, 2007), BA 45/BA 46 is typically associated with declarative memory and BA 7 with an imaginal module conserving the internal representation. This attribution has been proven to be relevant in a previous cognitive model (Ragni, Fangmeier, & Brüssow, 2010). These findings are supported by lesion studies, for example, studies examining the effect of focal right-hemispheric lesions to the on transitive inference tasks (Caramazza, Gordon, Zurif, & DeLuca, 1976). In a patient study, Goel et al. (2007) showed that lesions in the pFC cause considerable difficulties with transitive reasoning tasks, suggesting the pFC's important role in reasoning. Generally, our findings agree with predictions of a mental model account of reasoning: Especially, the activation in areas relevant for the construction (PPC) and maintenance (bilateral pFC, particularly DLPFC) for mental models support our findings from previous studies (with TMS; Ragni et al., 2016; and the direct model-based design in Fangmeier et al., 2006).

What Are the Neural Correlates of Deductive and Inductive Relational Reasoning?

Our findings for deductive reasoning partially confirm previous findings from neuroimaging studies and meta-analyses (cf. Waechter, Goel, Raymont, Kruger, & Grafman, 2013; Ackerman & Courtney, 2012; Osherson et al., 1998). We located wide-spread activation in the bilateral PPC (BA 7, BA 40, BA 39) sharing multiple connections to the visual cortex (Culham & Kanwisher, 2001) is known to be involved in working memory (Jansma, Ramsey, Coppola, & Kahn, 2000; LaBar, Gitelman, Parrish, & Mesulam, 1999; Jonides et al., 1993) and mental imagery (Trojano et al., 2000). This supports the mental model view on the cognitive processes underlying relational reasoning (Knauff, 2009, 2013). In addition, several neuroimaging studies have identified significant activation of the precuneus during nonimageable tasks and suggest its role in successful episodic memory retrieval irrespective of the process of mental imagery, for example, a paired word associate memory with abstract nouns and musical episodic memory (for a review, see Cavanna & Trimble, 2006). The activation of the left RLPFC cannot be supported by our meta-analysis. Waechter et al. (2013) provide a potential explanation by showing that patients with focal lesions to the parietal cortex were impaired in the task relative to the patients with focal lesions to RLPFC and the control group, whereas there was no difference in task performance between the RLPFC and the control groups. Because the groups performed similarly on a working memory task, working memory cannot fully account for the result, suggesting a specific role of the parietal cortex in transitive inference but not necessarily the RLPFC. Activation in the bilateral DLPFC (BA 8, BA 9) was identified, indicating the demand on working memory required by the tasks. Further neuropsychological evidence shows that patients with damage to the pFC exhibit deficits in reasoning tasks, specifically in tasks requiring the integration of multiple relations (for two relations), whereas patients perform normally for tasks requiring only one or zero relations or for episodic and semantic memory tasks (Waltz et al., 1999). Although there was partially overlapping activation in the DLPFC during the two component processes as the common processes of working memory involved, there was higher brain activity in the DLPFC that is more specific to the identification component. This indicates the premier role of the DLPFC in the integration of multiple relations and the identification of the underlying relation. This is further supported by a lesion study by Goel et al. (2007), in which patients with lesions in the pFC experienced considerable difficulties with transitive reasoning tasks.

In inductive reasoning, we encountered activation patterns similar to the literature (cf. Parsons & Osherson, 2001; Osherson et al., 1998; Goel et al., 1997), mainly concentrating on the left-sided frontoparietal network, which seems to be specific to inductive reasoning as compared with nonreasoning tasks (Liang et al., 2016). Moreover, it is assumed to be involved in executive control, an ability severely limited in adolescents with traumatic brain injury (Krawczyk et al., 2010). In addition, Koscik and Tranel (2012) described that damage to the ventromedial pFC resulted in a deficit in the ability to use transitive inference. This deficit was not driven by deficient learning of relationships between items, extrapolation to novel pairings in general, or differences in reinforcement or punishment during a training phase. In this network, specifically the bilateral DLPFC (BA 9) was active. A number of previous neuroimaging studies support the importance of the DLPFC in inductive reasoning, for example, in information integration (Goel & Dolan, 2004; Goel et al., 1997), relation integration (Christoff et al., 2001), cognitive monitor (Prabhakaran, Smith, Desmond, Glover, & Gabrieli, 1997), retrieval of rule knowledge (Geake & Hansen, 2005), rule identification (Zhong et al., 2011), and access to world knowledge (Goel & Dolan, 2004). Reverberi, Toraldo, D'Agostini, and Skrap (2005) presented inductive and recognition tests to patients and discovered that the left lateral prefrontal lesion subgroup failed to generate hypotheses (relation induction), even on the relation recognition test. The DLPFC was described to be a potential marker for mild cognitive impairment, measured by inductive reasoning tasks, in aging (Yang, Liang, Lu, Li, & Zhong, 2009). Furthermore, we located activation in the left medial and the lateral SMA (BA 6) and the bilateral PPC (BA 7, BA 40, BA 39), previously associated with relation application (Jia et al., 2011). The PPC, near the intraparietal sulcus, has been reported to be activated in figural inductive reasoning adapted from Raven's progressive matrices (Christoff et al., 2001; Prabhakaran et al., 1997). In addition, we found activation in the bilateral BG. Patients with degenerating striatum such as in Huntington's disease show deficits in relation application including arithmetic operation (Teichmann et al., 2005). Moreover, the striatal–thalamic network plays an important role in figural inductive reasoning (Liang et al., 2010). Thus, the striatal–thalamic network is an important component of the neural system mediating neural activity of the application process in inductive reasoning.

Both inductive and deductive reasoning rely on activation in the frontoparietal network. The shared areas between both are located in the bilateral DLPFC (BA 9) and the SMA (BA 6), as well as in the left PPC (BA 7, BA 40). Regions specific to the respective problems were located in the right SMA for deductive tasks and the left SMA, the right parieto-occipital junction (BA 19), and the bilateral BG for inductive problems. We showed rather medial and lateral SMA activation in deductive and inductive tasks, respectively, suggesting a task specificity concerning the SMA. This can be explained by the functional double dissociation found in SMA in which the medial part is crucial to updating verbal information and the lateral part to spatial information (Tanaka, Honda, & Sadato, 2005). We could, however, not confirm the claimed dissociation concerning lateralized pFC activation as proposed by Parsons and Osherson (2001). Taken together with the additional activation of the parieto-occipital junction, inductive reasoning seems to be more dependent on the earlier steps of reasoning proposed by MMT model construction and maintenance.

What Is the Impact of Content on Brain Activation during Reasoning?

Regarding semantic representation, we can confirm the involvement of the left DLPFC (BA 9; cf. Parsons & Osherson, 2001; particularly in contrast to geometric form tasks) and the precuneus (BA 7). These findings are further supported by Liang, Goel, Jia, and Li (2014), in which they located a left frontotemporal and superior medial frontal system for the identification of logical inconsistencies in semantic tasks. In a lesion study, Schmidt et al. (2012) differentiated between associative and categorical analogies and showed that the former relies on a left-lateral language network whereas the latter one recruits areas from both hemispheres. Hence, strong left lateralization in semantic tasks can be due to its linguistic form, which is mainly processed in the left hemisphere. Our findings further support the mental model account of relational reasoning, because even semantic, context-laden tasks draw upon these two areas needed for mental model construction and manipulation. Semantic tasks share activation with symbolic tasks regarding activation in all of these areas as well, refuting the hypothesis by Hobeika et al. (2016) that the left RLPFC is a domain-general region engaged in the processing of both content types.

Symbolic tasks involve a wide-spread left-hemispheric prefrontal activation (BA 9, BA 44, BA 6), bilateral PPC (BA 40, BA 7), and right-sided BG activation (right claustrum). Activation in the right BG, sharing multiple connection with the DLPFC (Alexander, DeLong, & Strick, 1986), correlates with reasoning task complexity and is associated with relation application (Jia et al., 2011). This suggests that, in contrast to semantic and geometric tasks, relation application is an essential part in symbolic content processing. Semantic and symbolic task processing share activation in the left DLPFC (BA 9) and the SPL (BA 7), further supporting a mental model account to conceptualize relational reasoning across different content modalities. Symbolic content tasks contrasted with semantic content tasks elicit activation in the bilateral SMA and the parieto-occipital junction (BA 39, BA 19), as shown by Goel and Dolan (2001). This supports the potentially enhanced demands posed by symbolic tasks because they cannot be solved using context but by the actual process of relation application, as suggested by the BG activation and the additional demand on executive function (BA 6) and mental representation (BA 39, BA 19). This can be interpreted as either an additional demand posed on the reasoner in symbolic tasks or as evidence for a dual-process account of reasoning. In the latter interpretation, the frontoparietal network, supporting MMT, builds the basis for relational reasoning and if required, the pFC–BG system is recruited. In contrast to geometric form tasks, symbolic tasks engage activation particularly in the left DLPFC (BA 9) and the PPC (BA 7), exhibiting the additional demand posed by symbolic tasks, but both share activation in the left MFG (BA 6), suggesting that they rely on general executive function. Surprisingly, we did not find activation in the left RLPFC as predicted to be particularly involved in analogical symbolic reasoning by lesion studies by Urbanski et al. (2016) and Zhong et al. (2011).

Geometric form tasks engage activation in the left DLPFC and the RLPFC (BA 6 and BA 10, respectively), supporting the interpretation proposed by Hobeika et al. (2016) that the left RLPFC is crucial to these contents. We could not find particular parietal activation in these tasks, as predicted by Hobeika et al. (2016) and Baldo, Bunge, Wilson, and Dronkers (2010). Hence, the content distinction helped to gain insights about the potential cognitive mechanisms underlying relational reasoning. The frontoparietal network is fundamental to semantic and symbolic tasks, supporting a model-based approach. Geometric tasks only elicit activation in the pFC, which might be explained by the lack of additional demand for mental model construction because the relations are already delivered in a visual format.

We now turn to the unresolved issues our results raise: First, the role of the left RLPFC (BA 10) in relational reasoning remains open to discussion: In contrast to Urbanski et al. (2016) and Zhong et al. (2011), we cannot support its role in symbolic tasks. This might be due to the, which tasks we categorized as symbolic contain a large variety of problems posing diverse demands on the reasoner. This implies that the RLPFC might have a more specialized role in relational reasoning as interpreted by the aforementioned studies. For identifying the exact function of the RLPFC, a more fine-grained analysis of the cognitive mechanisms required for solving symbolic tasks would be beneficial. Second, the contribution of the RLPFC for inductive tasks remains open, as the presented study material is rather diverse with respect to the relational complexity involved. This could be resolved by investigating inductive tasks more in depth with respect to the number of inferences to be drawn and the relational complexity of the rules. Third, we could replicate the claimed dissociation concerning lateralized pFC activation as proposed by Parsons and Osherson (2001). Because they tested conditional reasoning tasks, this might indicate that deductive and inductive reasoning do not engage task-independent regions as assumed in this study but that the type of inference needs to be considered.

We briefly discuss some limitations concerning the limited sample size. According to Eickhoff et al. (2016), 15 studies are the recommended lower boundary for conducting ALE meta-analyses. Because of a limited amount of applicable studies, we partly included marginally less than the recommended amount per group. This applies to the groups “semantic” (14 studies) and “geometric form” (13 studies). Therefore, we can only draw cautious conclusions when interpreting these results. Nonetheless, we decided to include them because they reveal tendencies in the data, which we consider valuable information when discerning neural activations.

Conclusion

The aim of this study was to disentangle the conceptual and neural foundations of relational reasoning. For that, we included 47 studies in a meta-analysis and separated the data along two axes: inference type (deductive and inductive processing) and problem content (semantic, symbolic, and geometrical form). Analyses revealed that the left DLPFC and the right SPL are central to all relational reasoning processes, supporting a mental model account of reasoning. We identified a task specificity concerning the medial and lateral BA 6 for deductive and inductive tasks, respectively. They share activation in the left DLPFC, as well as the bilateral PPC. During deductive problems, activation was located in the bilateral frontoparietal network, whereas for inductive problems, we found activation in the further left-sided pFC, the parieto-occipital junction, and the BG, suggesting additional cognitive demand. Concerning the content distinction, we can support involvement of the frontoparietal system in semantic and symbolic but not in geometric tasks, which only elicit prefrontal activation. This can be explained by the visual presentation of geometric form premises for which the model construction aspect can be abridged. In contrast to semantic tasks, symbolic tasks additionally evoke BG and BA 6 activation, which can be explained by additional cognitive resources concerning relation inference and application needed for symbolic relational reasoning.

Future studies need to focus on a temporally precise account of relational reasoning to potentially distinguish phases analogous to the three stages of deductive reasoning in former neuroimaging studies (Fangmeier et al., 2006). In addition, the type of premise presentation, which can typically be auditory or visual (Fangmeier & Knauff, 2009), could also be a starting point for more differentiated accounts of relational reasoning. Furthermore, the same procedure could be applied to syllogistic and conditional reasoning to eventually detect well-grounded differences and similarities between these main reasoning types. Lastly, symbolic tasks seem to be suitable tasks to elicit relation application and identification processes; hence, these problems can be valuable testing material for specifically targeting these cognitive processes.

APPENDIX: ADDITIONAL ANALYSIS MATERIALS

Table A1. 

ALE Results of the Single-study and Conjunction Analyses

Data SetCluster Size (mm3)Peak Coordinates (MNI)Hem.LobeAssignmentBA
xyz
All 10184 28 −59 49 R, L SPL, IPL, PCUN 7, 40 
7040 −33 −54 50 IPL, SPL 40, 7 
6352 −48 18 30 IFG, MFG 9, 46 
3720 18 47 SFG 
3168 50 27 28 MFG, IFG, PreCG 9, 8 
2904 −28 57 MFG 
1728 32 54 MFG 
1488 31 26 −4 Claustrum – 
Deductive 3888 −32 −56 51 SPL, IPL, PCUN, SMG 7, 40 
1776 20 45 R, L MFG, SFG 6, 32 
1688 42 −49 48 IPL, ANG 40, 39 
1528 −48 25 32 MFG 
1088 52 25 32 MFG 
Inductive 4872 −47 16 30 IFG, MFG, PreCG 9, 6 
3776 28 −68 46 P, O SPL, PCUN, SOG 7, 19 
2592 −34 −52 48 IPL, SPL 40, 7 
2248 −27 59 MFG 
1600 13 CAU – 
1272 −12 PAL, CAU – 
1088 52 33 26 MFG 
1040 −1 17 49 SFG 
Semantic 2504 −47 22 30 MFG, IFG 
896 −19 −65 57 PCUN 
Symbolic 5848 −33 −56 46 P/O IPL, SPL, CUN 40, 7 
4776 32 −61 47 SPL, IPL 7, 40 
4472 −48 16 30 IFG, MFG, PreCG 9, 6, 44 
3240 −0 18 48 SFG 
1376 53 29 30 MFG 9, 8 
1320 −27 58 MFG 
1056 30 24 −4 Claustrum – 
Geometrical form 1456 −27 59 MFG 
1088 −40 50 −5 IFG, MFG 10 
Deductive ∪ Inductive 1152 −48 24 31 MFG 
696 −43 −44 47 IPL 40 
568 19 48 L, R SFG 
400 −27 −59 49 SPL 
224 50 31 27 MFG 
Deductive \ Inductive 224 36 49 MFG 
Inductive \ Deductive 608 14 13 CAU – 
424 −29 62 MFG 
384 37 −74 39 P/O PCUN, SOG 19 
128 −9 CAU – 
16 −4 34 44 SFGmed 
Semantic ∪ Symbolic 1672 −48 22 30 MFG, IFG 
112 −23 −63 53 SPL 
Symbolic \ Semantic 1176 −0 14 51 R, L SFG, SFGmed 
272 −29 −61 43 ANG 39 
112 32 −71 46 PCUN 19 
Semantic \ Geometric form −48 19 26 MFG 
Geometric form \ Semantic 872 −28 60 MFG 
−34 51 −5 MFG 10 
Symbolic ∪ Geometric form 928 −26 58 MFG 
152 −52 19 26 MFG 
104 −29 −66 44 PCUN 
Data SetCluster Size (mm3)Peak Coordinates (MNI)Hem.LobeAssignmentBA
xyz
All 10184 28 −59 49 R, L SPL, IPL, PCUN 7, 40 
7040 −33 −54 50 IPL, SPL 40, 7 
6352 −48 18 30 IFG, MFG 9, 46 
3720 18 47 SFG 
3168 50 27 28 MFG, IFG, PreCG 9, 8 
2904 −28 57 MFG 
1728 32 54 MFG 
1488 31 26 −4 Claustrum – 
Deductive 3888 −32 −56 51 SPL, IPL, PCUN, SMG 7, 40 
1776 20 45 R, L MFG, SFG 6, 32 
1688 42 −49 48 IPL, ANG 40, 39 
1528 −48 25 32 MFG 
1088 52 25 32 MFG 
Inductive 4872 −47 16 30 IFG, MFG, PreCG 9, 6 
3776 28 −68 46 P, O SPL, PCUN, SOG 7, 19 
2592 −34 −52 48 IPL, SPL 40, 7 
2248 −27 59 MFG 
1600 13 CAU – 
1272 −12 PAL, CAU – 
1088 52 33 26 MFG 
1040 −1 17 49 SFG 
Semantic 2504 −47 22 30 MFG, IFG 
896 −19 −65 57 PCUN 
Symbolic 5848 −33 −56 46 P/O IPL, SPL, CUN 40, 7 
4776 32 −61 47 SPL, IPL 7, 40 
4472 −48 16 30 IFG, MFG, PreCG 9, 6, 44 
3240 −0 18 48 SFG 
1376 53 29 30 MFG 9, 8 
1320 −27 58 MFG 
1056 30 24 −4 Claustrum – 
Geometrical form 1456 −27 59 MFG 
1088 −40 50 −5 IFG, MFG 10 
Deductive ∪ Inductive 1152 −48 24 31 MFG 
696 −43 −44 47 IPL 40 
568 19 48 L, R SFG 
400 −27 −59 49 SPL 
224 50 31 27 MFG 
Deductive \ Inductive 224 36 49 MFG 
Inductive \ Deductive 608 14 13 CAU – 
424 −29 62 MFG 
384 37 −74 39 P/O PCUN, SOG 19 
128 −9 CAU – 
16 −4 34 44 SFGmed 
Semantic ∪ Symbolic 1672 −48 22 30 MFG, IFG 
112 −23 −63 53 SPL 
Symbolic \ Semantic 1176 −0 14 51 R, L SFG, SFGmed 
272 −29 −61 43 ANG 39 
112 32 −71 46 PCUN 19 
Semantic \ Geometric form −48 19 26 MFG 
Geometric form \ Semantic 872 −28 60 MFG 
−34 51 −5 MFG 10 
Symbolic ∪ Geometric form 928 −26 58 MFG 
152 −52 19 26 MFG 
104 −29 −66 44 PCUN 

The significant clusters as well as differentiated anatomical localizations are reported. “∪” indicates the conjunction analysis of the two sets; “\” indicates the subtraction analysis of the right form the left set. Hem. = Hemisphere; BA = Brodmann's area; PCUN = precuneus; CAU = caudate; SMG = supramarginal gyrus; ANG = angular gyrus; SOG = superior occipital gyrus; PAL = lenticular nucleus/pallidum; CUN = cuneus; SFGmed = SFG, medial; F = frontal; P = parietal; O = occipital; S = sublobar.

Acknowledgments

This work was supported by the BrainLinks-BrainTools Cluster of Excellence, German Research Foundation (DFG, grant EXC 1086) and the Barbara Wengeler Foundation to J. W. and the DFG grants RA 1934/3-1, RA 1934/2-1, and RA 1934/4-1 to M. R.

Reprint requests should be sent to Julia Wertheim, Cognitive Computation Lab, Albert-Ludwigs-Universität Freiburg, Georges-Köhler-Allee 79, 79110 Freiburg, Germany, or via e-mail: wertheim@tf.uni-freiburg.de.

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