Jérôme Prado
email: jprado@isc.cnrs.fr

The relationship between deductive reasoning and the syntax of language in Broca's area: A review of the neuroimaging literature

A remarkable feature of the human brain is its ability to make deductions, that is, to infer valid conclusions from known information. In part because these deductions play an important role in spoken and written communication, it has been postulated that there is a close relationship between language and deductive reasoning in humans. Notably, some have proposed that deductive reasoning relies on a system of inferential rules that can be compared to the grammar of a natural language. Here I review the neuroimaging literature on deductive reasoning to evaluate whether there is some overlap between the neuro-cognitive operations that enable deduction and those that underlie the syntactic processing of language. Although some studies suggest that relatively simple deductions may involve Broca's area, no study to date has demonstrated that the mechanisms supporting the syntactic processing of language contribute to deductive reasoning. Implications for future directions in the literature are outlined.

Abstract (French)

Une caractéristique remarquable du cerveau humain est sa capacité à faire des déductions, c'est-à-dire à déduire des conclusions valides à partir d'informations connues. En partie parce que ces déductions jouent un rôle important dans la communication orale et écrite, il a été postulé qu'il pourrait exister une relation étroite entre le langage et le raisonnement déductif chez l'être humain. Certains ont notamment proposé que le raisonnement déductif reposerait sur un système de règles inférentielles qui pourraient être comparées à la grammaire d'un langage naturel. Dans cet article, je passe en revue la littérature en neuroimagerie sur le raisonnement déductif afin d'évaluer si les opérations neuro-cognitives qui sous-tendent le raisonnement déductif sont similaires à celles qui sous-tendent le traitement syntaxique du langage. Bien que certaines études suggèrent que des déductions relativement simples pourraient reposer sur l'aire de Broca, aucune étude à ce jour n'a démontré que les mécanismes soutenant le traitement syntaxique du langage contribuent au raisonnement déductif. Les implications de cette revue sur les recherches futures sont mentionnées.

(1) "Jerry was trying to decide what to wear to meet his fiancée's parents.

(2) 'I'd like to wear either my striped or my checkered shirt,' he thought.

(3) 'If I wear my striped shirt, I'll have to wear my blue pants since they match the shirt,' he thought, 'but I'm not sure where my blue pants are.' (4) He looked in his closet for his checkered shirt and saw that it was wrinkled, so he decided he could not wear that.

(5) 'So I'd better find my blue pants,' he thought" [START_REF] Lea | Predicting propositional-like inferences in text-comprehension[END_REF] Readers do not have much difficulty understanding short stories such as the one above.

Critical to this capacity are certain logical inferences that are carried out routinely. For example, sentence (4) eliminates one of the options from sentence (2), thus allowing the reader to infer that Jerry will have to wear his striped shirt (which is information that is never explicitly stated in the text). Additionally, the reader needs to integrate this inferred information with sentence

(3) to understand why Jerry has to find his blue pants. These inferences are necessary for understanding the conclusion of the story. Such inferences are deductive: a conclusion that follows from them has to be true if the premises are true. For example, this is the case for each of the arguments exemplified in Table 1, which rely on propositional connectives (e.g., modus ponens, modus tollens, disjunction elimination), linear relations, and inclusion of sets. Deductive reasoning is at the core of many of our cultural and scientific practices, including mathematics [START_REF] Michal | Deductive reasoning: in the eye of the beholder[END_REF][START_REF] Nunes | The contribution of logical reasoning to the learning of mathematics in primary school[END_REF], law [START_REF] Ellsworth | Legal Reasoning[END_REF] and medicine [START_REF] Wulff | Rational Diagnosis and Treatment[END_REF].

Deductive inferences play an important role in argumentation [START_REF] Mercier | Why do humans reason? Arguments for an argumentative theory[END_REF] and, as the story above illustrates, are made rather automatically when processing written discourse [START_REF] Lea | On-line evidence for elaborative logical inference in text[END_REF]. In fact, spontaneous deductive inferences are central, not only to written communication but to discourse generally. They are particularly critical to spoken discourse because speakers have to be understood on the fly (and thus inferences have to be made as sentences are spoken). For instance, a propositional inference such as modus ponens (see Table 1) is so automatic that it may be carried out without reasoners even being aware of it [START_REF] Reverberi | Cortical bases of elementary deductive reasoning: inference, memory, and metadeduction[END_REF]. Thus, many of the deductive inferences that people make are likely to be drawn automatically in understanding discourse, whether written or spoken. This suggests that one of the most important functions of deductive reasoning is to facilitate verbal interaction [START_REF] Braine | The"natural logic" approach to reasoning[END_REF].

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The hypothesis of deductive reasoning as a rule-based process

Based on the observations above, several researchers have postulated a close relationship between language and deductive reasoning in humans. For example, Polk and Newell have claimed that "the central processes in deductive reasoning are linguistic" because they involve a verbal encoding of the premises into some kind of internal representation [START_REF] Polk | Deduction as verbal reasoning[END_REF]. But it is possible that processes akin to those involved in natural language are engaged well after this initial verbal encoding of the premises. Indeed, two important theories of human deductive reasoning --PSYCOP [START_REF] Rips | The Psychology of Proof[END_REF] and the Mental Logic [START_REF] Braine | Mental Logic[END_REF] -posit that the core operations of deduction may rely on a system of contentfree rules. These theories, which are rooted in the Aristotelian idea that the mind possesses some kind of innate mental logic, rely on the assumption that formal rules are used to infer a conclusion from premises in a way that takes into account only their form (not their meaning).

In some ways, these rules can be compared to the grammar of a natural language. In other words, this formal rule approach sees deductive reasoning as emerging from our ability to combine discrete structural elements into sequences, given a limited set of rules. Much like grammatical rules are applied to words to construct sentences, logical rules may be applied to a propositional representation of the premises to infer conclusions [START_REF] Braine | Mental Logic[END_REF][START_REF] Rips | The Psychology of Proof[END_REF]. Basic inferential rules would involve (at least) the basic propositions and, if and or. For example, the 12 elementary rules (also called schemas) proposed by the Mental Logic are represented in Table 2 [START_REF] Braine | Mental Logic[END_REF].

---------------------------- Table 2 about here ----------------------------
How would this system of rules be used to draw deductive inferences? Consider for instance the Modus Ponens argument in Table 1. The rule [If P then Q; P; therefore Q] (schema 7 in Table 2) would be applied to the major premise If there is a circle then there is a triangle and the minor premise There is a circle to infer the conclusion There is a triangle. Similarly, in the case of the disjunction elimination argument in Table 1, the rule [P or Q; not-P; therefore Q] (schema 3 in Table 2) would be applied to the major premise There is a circle or there is a triangle and the minor premise There is not a circle to infer the conclusion There is a triangle.

However, understanding more complex arguments such as Modus Tollens would require several cognitive steps. This is because the rule [If P then Q; not-Q; therefore not-P] is not believed to be part of the basic deductive competence (which is the reason why it is missing from Table 2). In such cases, strategies that are not universally available can be applied so that reasoners can go beyond their basic competence (e.g., strategies involving reductio ad absurdum: If circle were true, then triangle would have to be true, but triangle is false, so circle must be false).

In principle, one can extend this formal rule approach to relational premises as well.

This would require incorporating axioms for transitivity, or meaning postulates, to the set of rules [START_REF] Goodwin | Reasoning about relations[END_REF][START_REF] Hagert | Modeling mental models: experiments in cognitive modeling spatial reasoning[END_REF][START_REF] Johnson-Laird | Against logical form[END_REF]. For example, the relation is larger than might be associated with the transitive inferences below: If x is larger than y, and y is larger than z, then x is larger than z.

Such inferences can easily be applied to premises such as The circle is larger than the triangle and The triangle is larger than the square to derive the conclusion The circle larger the square in Table 1.

Finally, rules could also be applied to categorical arguments. This might be done by assuming that the repertoire of formal rules extend to those that involve quantifiers [START_REF] Braine | Steps towards a mental-predicate logic[END_REF], or by assuming that there are rules that transform categorical premises into quantifierfree representations prior to syntactic manipulation [START_REF] Rips | The Psychology of Proof[END_REF]. Consider for example the categorical argument at the bottom of Table 1. The premise All tables are triangles and All triangles are blue could be transformed into the premises If x is a table then x is a triangle and If x is a triangle then x is blue. Integrating these now-propositional premises would lead to the quantifier-free conclusion If x is a table then x is blue. Another rule might re-introduce the quantifier so that the conclusion would be translated into All tables are blue.

Deductive reasoning and the syntax of language: Common or different mechanisms?

The hypothesis that deductive reasoning may rely on content-free rules prompts an intriguing question: Does deductive reasoning make use of some of the syntactic machinery that is used to produce sentences in natural language? As argued elsewhere, this question is fundamental because it pertains to the long-standing idea that human thought might be embedded in language (e.g., [START_REF] Monti | Logic, language and the brain[END_REF]. It is important to emphasize, however, that this idea is far from trivial in the cognitive literature, at least for two reasons.

First, over the past two decades or so, the idea that deductive reasoning would rely on rules of inference has been seriously challenged. For example, Johnson-Laird and colleagues [START_REF] Johnson-Laird | Formal rules verses mental models in reasoning[END_REF] have famously argued that deductive reasoning is not a rule-based process, but rather a process that involves the manipulation of a representation of the premises in spatial working memory. This popular theory, called the Mental Model Theory of reasoning, does not assume any role for rule-based representations in deduction. More recently, it has also been claimed that people use everyday probabilistic reasoning when making deductive inferences [START_REF] Oaksford | Imaging deductive reasoning and the new paradigm[END_REF][START_REF] Oaksford | The probabilistic approach to human reasoning[END_REF][START_REF] Goel | Anatomy of deductive reasoning[END_REF]. As such, this probabilistic view of deductive reasoning also denies the existence of a content-free rules of inference.

Second, even if one assumes that formal rules may underlie deductive reasoning, this does not necessarily mean that deductive reasoning and language rely on the same syntactic processes. For instance, as argued by Parsons & Osherson (2001, p. 963), "the language that supports deduction […] need not be a natural language like English, burdened as it is by ambiguity and ellipsis. Deduction (as well as other forms of reasoning) might rather be performed in a format that is antecedent to natural language, the latter being acquired for the purpose of expressing meanings that exist prior to their linguistic expression". In other words, it is entirely possible that deductive reasoning may be licensed by content-free rules relying on syntactic processes that are distinct from those supporting natural language. More generally, this harks back to the broader question of whether there exist some generalized mechanisms that govern all syntactically structured domains, such as language, math, music, or reasoning [START_REF] Fadiga | Broca's area in language, action, and music[END_REF][START_REF] Monti | The role of language in structure-dependent cognition[END_REF][START_REF] Tettamanti | Broca's area: a supramodal hierarchical processor?[END_REF]. Therefore, although evidence that deductive reasoning and the syntax of natural language rely on common mechanisms would arguably provide support for the formal rule approach to reasoning, evidence to the contrary would not necessarily mean that deductive reasoning is not a rule-based process.

Bearing this context in mind, neuroimaging studies appear uniquely suited to test whether deductive reasoning makes use of some of the syntactic processes supporting natural language. Indeed, there is a long-standing literature investigating the neural bases of syntactic processing in natural language. Perhaps the brain region that has been the most consistently associated with such processing is Broca's area (i.e., the brain region that corresponds to Brodmann areas, or BAs, 45 and 44) [START_REF] Friederici | The brain basis of syntactic processes: functional imaging and lesion studies[END_REF][START_REF] Grodzinsky | The battle for Broca's region[END_REF][START_REF] Ullman | A neurocognitive perspective on language: the declarative/procedural model[END_REF]. For example, studies have demonstrated enhanced activity in Broca's area when syntactically complex sentences (e.g., The juice that the child spilled stained the rug) are compared to syntactically simple sentences (e.g., The child spilled the juice that stained the rug) [START_REF] Ben-Shachar | The neural reality of syntactic transformations: evidence from functional magnetic resonance imaging[END_REF][START_REF] Friederici | Processing linguistic complexity and grammaticality in the left frontal cortex[END_REF][START_REF] Roder | Brain activation modulated by the comprehension of normal and pseudo-word sentences of different processing demands: a functional magnetic resonance imaging study[END_REF][START_REF] Stromswold | Localization of syntactic comprehension by positron emission tomography[END_REF], or when syntactic violations are detected (e.g.,

The shirt was on ironed vs. The shirt was ironed) [START_REF] Friederici | The role of left inferior frontal and superior temporal cortex in sentence comprehension: localizing syntactic and semantic processes[END_REF][START_REF] Meyer | Neurocognition of auditory sentence comprehension: event-related fMRI reveals sensitivity to syntactic violations and task demands[END_REF]. Grodzinsky and colleagues have suggested that activation of Broca's area is sensitive to the amount of syntactic movement (the displacement of an argument from its canonical position) in a sentence. For example, a sentence involving a lot of syntactic movement such as The mother of Jim loves the woman who the mailman and Kate burnt elicits more activity in Broca's area than a sentence associated with less syntactic movement such as The mailman and the mother of Jim love the woman who Kate burnt [START_REF] Ben-Shachar | The neural reality of syntactic transformations: evidence from functional magnetic resonance imaging[END_REF][START_REF] Ben-Shachar | Neural correlates of syntactic movement: converging evidence from two fMRI experiments[END_REF][START_REF] Grodzinsky | The battle for Broca's region[END_REF]. In line with these neuroimaging findings, patients with lesion in Broca's area cannot understand sentences with movement but understand sentences without movement [START_REF] Grodzinsky | The battle for Broca's region[END_REF]. Overall, and although other regions have been associated with syntactic processing in the literature (e.g., the superior temporal gyrus, [START_REF] Friederici | The brain basis of syntactic processes: functional imaging and lesion studies[END_REF], there is ample evidence that syntactic processing in natural language is primarily supported by Broca's area.

This makes this region a prime candidate for a potential overlap between deductive reasoning and the syntax of language.

The goal of the present review is to examine the hypothesis that deductive reasoning is associated with enhanced activity in brain areas that are also involved in the syntactic processing of language (and especially Broca's area). In what follows, I first describe some common features of the paradigms that are typically used to study the neural bases of deductive reasoning. In doing so, I want to draw the reader's attention on some methodological issues and caveats associated with these neuroimaging studies. These issues are important to keep in mind when interpreting the results of neuroimaging studies. I then turn to the neuroimaging literature investigating deductive reasoning in the absence of tasks investigating linguistic processing.

These studies include early investigations focusing on the conclusion processing stage of a deductive argument, as well as a set of more recent studies focusing on the premise processing stage. Finally, I review more recent studies that have focused on directly comparing brain activity associated with deductive reasoning and linguistic processing.

Some issues and caveat when investigating the neural bases of deductive reasoning

In a typical neuroimaging experiment on deductive reasoning, participants are visually or auditorily presented with 2 to 3 premises, followed by a conclusion (see Fig. 1). The task typically requires participants to evaluate whether that conclusion follows out of necessity from the premises. Although such a design might not appear that different from designs that are used in behavioral studies, the neuroimaging environment requires some adaptations to be made to standard paradigms. This may give rise to issues that have to be taken into consideration when assessing results from neuroimaging studies. I will highlight here four of the most important issues (see also [START_REF] Monti | Logic, language and the brain[END_REF][START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF][START_REF] Prado | The brain network for deductive reasoning: a quantitative meta-analysis of 28 neuroimaging studies[END_REF][START_REF] Reverberi | Neural basis of generation of conclusions in elementary deduction[END_REF][START_REF] Reverberi | Response demands and the recruitment of heuristic strategies in syllogistic reasoning[END_REF].

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Figure 1 about here ----------------------------
First, whereas behavioral studies typically present a large number of participants with one (or a few) reasoning problems to solve, neuroimaging experiments typically present a limited number of participants (e.g., between 15 to 20 participants) with a large number of trials (e.g., from 20 to 40 trials). Although this is done to maximize signal-to-noise ratio, this strategy may come with some experimental complications. For instance, by the end of the neuroimaging session, participants may develop strong expectations regarding the task and may employ memory or heuristic strategies to solve problems (rather than genuine reasoning; Reverberi et al., 2009). This confound may be especially prevalent in studies that extensively train participants on the reasoning task before even entering into the scanner (generally to maximize accuracy or to select participants based on their performance). A typical strategy to limit this bias is to make the task as varied as possible. For instance, participants may be presented with filler trials as well as with a variety of logical forms [START_REF] Mathieu | Distributed neural representations of logical arguments in school-age children[END_REF]Prado et al., 2015;[START_REF] Prado | Recomposing a fragmented literature: how conditional and relational arguments engage different neural systems for deductive reasoning[END_REF][START_REF] Schwartz | The neural development of conditional reasoning in children: Different mechanisms for assessing the logical validity and likelihood of conclusions[END_REF].

Second, it is important to emphasize that any results from a brain imaging experiment need to be interpreted as a difference in activity between two cognitive states. That is, activity associated with deductive reasoning is always measured relative to a control or baseline condition. In some cases, this baseline may be a "low-level" control condition such as a fixation cross (which would then correspond to some sort of resting state). Of course, any activity associated with solving a deductive argument compared to such a resting state may be confounded by activity associated with reading the argument or selecting a response (which are processes that are not controlled for by the simple perception of a fixation cross). Therefore, such contrasts are not particularly useful when evaluating whether deductive reasoning involves linguistic processes that go beyond the mere reading of a triplet of sentences. More informative are undoubtedly contrasts in which activity associated with reading and response selection is subtracted out from activity associated with evaluating a deductive argument. Researchers have used a variety of such "high-level" baseline conditions across studies. For example, some have used arguments in which premises and/or conclusions are not related to one another [START_REF] Goel | Dissociation of mechanisms underlying syllogistic reasoning[END_REF][START_REF] Goel | Functional neuroanatomy of three-term relational reasoning[END_REF], 2004), arguments in which the conclusion is the repetition of one premise [START_REF] Noveck | The neural basis of conditional reasoning with arbitrary content[END_REF], or arguments that are easier to process than the type of arguments that is investigated [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF][START_REF] Prado | Fractionating the Neural Substrates of Transitive Reasoning: Task-Dependent Contributions of Spatial and Verbal Representations[END_REF]. This is not to say that all of these "high-level" control conditions lead to the exact same interpretations regarding the effects observed. Variations in these control conditions also need to be taken into consideration when interpreting results. However, "high-level" baselines controlling for processes such as reading are a bare minimum when assessing the hypothesis that deductive reasoning may rely on the neural substrates of syntactic processing in language.

Third, although behavioral investigations of deductive reasoning are mainly concerned with whether a conclusion is endorsed or not, neuroimaging studies are interested in what type of brain activity is associated with deductive reasoning. Reasoning, however, is a complex process that is diffuse and somewhat difficult to pinpoint temporarily. At what point during the processing of a deductive argument should we expect reasoning-related activity? While most researchers have focused on brain activity associated with the conclusion [START_REF] Goel | Dissociation of mechanisms underlying syllogistic reasoning[END_REF][START_REF] Goel | Functional neuroanatomy of three-term relational reasoning[END_REF], 2003, 2004;[START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF][START_REF] Monti | The boundaries of language and thought in deductive inference[END_REF][START_REF] Noveck | The neural basis of conditional reasoning with arbitrary content[END_REF][START_REF] Stollstorff | Levels of conflict in reasoning modulate right lateral prefrontal cortex[END_REF], others have argued that an inference is made as soon as the second premise appears and can be integrated with the first premise [START_REF] Prado | Recomposing a fragmented literature: how conditional and relational arguments engage different neural systems for deductive reasoning[END_REF][START_REF] Reverberi | Large scale brain activations predict reasoning profiles[END_REF][START_REF] Reverberi | Conditional and syllogistic deductive tasks dissociate functionally during premise integration[END_REF][START_REF] Reverberi | Neural basis of generation of conclusions in elementary deduction[END_REF].

Therefore, some studies have specifically investigated brain activity elicited by the second premise rather than the conclusion. Of course, there is no right or wrong answer to the question of when reasoning occurs. But it is important to keep in mind that studies vary in terms of conceptual choices made by the experimenters.

Fourth, as exemplified in Table 1, deductive argument may come in many forms. While all deductive arguments have in common the central feature that a conclusion follows out of necessity from the premises, multiple logical forms have rarely been used and compared in one single study. In other words, it is possible that the results obtained in one study using a specific logical form (e.g., propositional reasoning) may not translate to another study using a different form (e.g., relational reasoning). The idea that different forms of reasoning would rely on different types of mechanisms was in fact acknowledged by proponents of a formal rule approach of reasoning, who for example argued that "mental models in some form also provide a tool available to the human reasoning. Constructing models seems an intuitively natural way of solving the kind of spatial problems discussed by Johnson-Laird and Byrne" (Braine & O'Brien, 1998, p.193-194). Thus, it is possible that different types of logical arguments may be associated with different types of brain mechanisms. Inter-study variability in terms of logical forms also needs to be kept in mind.

Overall, neuroimaging investigations of deductive reasoning come with a number of methodological and conceptual questions that experimenters have to face. As pointed out by Vinod Goel, a pioneer in the neuroimaging study of deductive reasoning, "there are no absolutely right or wrong answers to these and other similar issues. In making these decisions and compromises it is advisable to pay as much attention to the neuroscience as to the cognitive theory" [START_REF] Goel | Anatomy of deductive reasoning[END_REF]. In the following, I will try to keep these issues in mind when reviewing relevant studies.

Evidence for reliance on linguistic processing in early neuroimaging studies focusing on the conclusion processing stage of a deductive argument

The hypothesis that deductive reasoning may rely on brain regions supporting linguistic processing was already at the center of the very first positron emission tomography (PET) study on deductive reasoning 20 years ago [START_REF] Goel | The seats of reason? An imaging study of deductive and inductive reasoning[END_REF]. At the time, Goel and colleagues posited that, according to a formal rule approach, "deductive reasoning, being a formal, rule-governed process defined over the structure of language, will activate the left hemisphere more than the right hemisphere and will implicate some of the same structures involved in language processing" (p. 1306). Comparing deductive arguments (including categorical and propositional syllogisms) to a baseline condition in which participants had to determine how many of the sentences in an argument had people as subject, the authors did find enhanced activity in Broca's area (BA 45). This was interpreted as evidence for the idea that deductive reasoning may be supported by linguistic mechanisms. However, activity in Broca's area has not systematically been observed in subsequent neuroimaging studies of deductive reasoning.

On the one hand, while employing relatively similar experimental materials, Goel and colleagues replicated this engagement of Broca's area in deductive reasoning in follow-up studies using PET [START_REF] Goel | Neuroanatomical correlates of human reasoning[END_REF] and functional magnetic resonance imaging (fMRI) [START_REF] Goel | Dissociation of mechanisms underlying syllogistic reasoning[END_REF]. On the other hand, several other studies have failed to uncover activity in Broca's area during deductive reasoning. For example, comparing deductive reasoning to a language comprehension task involving the exact same arguments, neither [START_REF] Osherson | Distinct brain loci in deductive versus probabilistic reasoning[END_REF] nor [START_REF] Parsons | New Evidence for Distinct Right and Left Brain Systems for Deductive versus Probabilistic Reasoning[END_REF] reported activity in either left BA 45 or BA 44. Using relational arguments such as "Karen is in front of Larry, Larry is in front of Jane, Is Karen in front of Jane?", [START_REF] Goel | Functional neuroanatomy of three-term relational reasoning[END_REF] and [START_REF] Goel | The hippocampal system mediates logical reasoning about familiar spatial environments[END_REF] found enhanced activity in the parietal cortex but not in Broca's area. Other neuroimaging studies employing relational arguments have also failed to find involvement of Broca's area, instead reporting activity in the posterior parietal cortices [START_REF] Knauff | Reasoning, models, and images: behavioral measures and cortical activity[END_REF][START_REF] Knauff | Spatial imagery in deductive reasoning: a functional MRI study[END_REF][START_REF] Prado | Recomposing a fragmented literature: how conditional and relational arguments engage different neural systems for deductive reasoning[END_REF][START_REF] Ruff | Reasoning and working memory: common and distinct neuronal processes[END_REF]. Given the role of the posterior parietal cortex in spatial processing, these results are more consistent with the idea that relational premises are mapped onto spatial mental models than with the idea that it relies on formal rules (which was a possibility acknowledged by Mental Logic theorists, [START_REF] Braine | Mental Logic[END_REF]. But perhaps more surprising were the results of the first fMRI study that specifically investigated the neural bases of conditional arguments, such as Modus Ponens and Modus Tollens (see Table 1). [START_REF] Noveck | The neural basis of conditional reasoning with arbitrary content[END_REF] did not report any activity in either left BA 44 or 45 when such conditional arguments (arguably at the heart of the Mental Logic theory, see Table 2) were compared to baseline arguments in which the conclusion was the repetition of a non-overlapping premise (If P then Q, R, therefore R). Instead, enhanced activity was found in more dorsal fronto-parietal regions [START_REF] Noveck | The neural basis of conditional reasoning with arbitrary content[END_REF].

Overall, early neuroimaging studies provide equivocal evidence for the involvement of Broca's area in deductive reasoning. It is clear that there is some variability between studies, which may come from a number of different sources. First, the type of deductive argument appears to matter. For example, relational arguments are less likely to activate Broca's area that other types of arguments. This was confirmed by a quantitative meta-analysis of the neuroimaging literature on deductive reasoning performed a few years ago [START_REF] Prado | The brain network for deductive reasoning: a quantitative meta-analysis of 28 neuroimaging studies[END_REF].

Compared to studies that specifically investigated the neural bases of categorical or propositional arguments, studies that focused on relational arguments tended to find consistent activation in the posterior parietal cortex rather than Broca's area. In contrast, this meta-analysis found consistent activation of Broca's area across studies that investigated categorical arguments (propositional arguments were found to involve a more dorsal fronto-parietal network).

Second, the studies discussed here all employ control conditions in which sentences are presented to participants. However, as argued elsewhere [START_REF] Monti | Logic, language and the brain[END_REF], the amount of linguistic processing required to process these "control" sentences may not always be similar to the amount of linguistic processing that is required when participants have to carefully read premises and conclusions to determine the logical validity of an argument. For instance, early studies in which involvement of Broca's area has been found employed baseline tasks in which participants simply had to determine how many sentences have people as subjects [START_REF] Goel | The seats of reason? An imaging study of deductive and inductive reasoning[END_REF][START_REF] Goel | Neuroanatomical correlates of human reasoning[END_REF]. Other studies have used conclusions that were entirely unrelated to the previous premises [START_REF] Goel | Dissociation of mechanisms underlying syllogistic reasoning[END_REF]. Because sentences in all of those tasks may not be read with the same depth as deductive arguments, any activity observed in Broca's area may be related to differences in terms of reading demands rather than in terms of reasoning per se [START_REF] Monti | Logic, language and the brain[END_REF].

Third, as mentioned earlier, reasoning is a diffuse process that is difficult to isolate temporarily. Studies have relied on different assumptions regarding the exact moment an inference may be best captured. For instance, some studies have used block designs capturing brain activity throughout an entire argument (and even a set of arguments) [START_REF] Goel | The seats of reason? An imaging study of deductive and inductive reasoning[END_REF][START_REF] Goel | Neuroanatomical correlates of human reasoning[END_REF][START_REF] Osherson | Distinct brain loci in deductive versus probabilistic reasoning[END_REF][START_REF] Parsons | New Evidence for Distinct Right and Left Brain Systems for Deductive versus Probabilistic Reasoning[END_REF], whereas others have modeled brain activity starting from the onset of the conclusion [START_REF] Goel | Dissociation of mechanisms underlying syllogistic reasoning[END_REF][START_REF] Goel | Functional neuroanatomy of three-term relational reasoning[END_REF][START_REF] Noveck | The neural basis of conditional reasoning with arbitrary content[END_REF] or halfway between the onset of the conclusion and the response [START_REF] Goel | Explaining modulation of reasoning by belief[END_REF], 2004). It is even possible that studies have missed the critical moment an inference is made. Specifically, Carlo Reverberi and his colleagues argued that, in theory, an inference can be drawn as soon as the second premise is available and can be integrated with the first premise [START_REF] Reverberi | Neural basis of generation of conclusions in elementary deduction[END_REF]. For example, the conclusion There is triangle can be inferred as soon as the premises If there is a square then there is triangle and There is square are available to a reasoner. Reverberi and colleagues conducted a series of recent studies based on this assumption.

Evidence for reliance on linguistic processing in neuroimaging studies focusing on the premise processing stage of a deductive argument

In two studies in which fMRI activity was measured from the onset of this second premise (and compared to activity associated with a premise that could not be integrated), Reverberi and colleagues found enhanced activity in Broca's area (left BAs 44 and 45), both in the case of propositional [START_REF] Reverberi | Neural basis of generation of conclusions in elementary deduction[END_REF] and categorical arguments [START_REF] Reverberi | Conditional and syllogistic deductive tasks dissociate functionally during premise integration[END_REF]. In another study focusing on inter-individual differences, [START_REF] Reverberi | Large scale brain activations predict reasoning profiles[END_REF] further found that activity in Broca's area predicted participants' sensitivity to the logical structure of a problem (i.e., how consistent participants were when responding to problems that were superficially different but logically similar). These results led Reverberi and colleagues to suggest that Broca's area (together with more dorsal and medial frontal regions) may be "involved in extraction and representation of the formal structure of problems" (p. 1763).

Importantly, the authors did not suggest that this region would act in isolation, but rather in cooperation with a more ventral area (left BA 47) that would be involved in selecting and applying logical rules.

Recently, the involvement of Broca's area in the fundamental operations of deduction has further been corroborated by [START_REF] Baggio | Multiple neural representations of elementary logical connectives[END_REF]. In that study, the authors used multivariate pattern analysis to uncover the neural representation of compounds based on the logical connectives and, if, and or. The results show that Broca's area is involved in representing both the surface form and the full logical meaning of these compounds. This led [START_REF] Baggio | Multiple neural representations of elementary logical connectives[END_REF] to suggest that there is a "shared neural foundation for the cognitive science of language and reasoning" (p. 309).

Results from this set of studies are certainly intriguing and lend some support for the idea that Broca's area may be involved in some aspects of deductive reasoning. However, they suffer from an important caveat. In none of these studies were the brain mechanisms supporting syntactic processing in language formally identified. This is problematic because, even if there is little doubt that Broca's area is involved in syntactic processing [START_REF] Friederici | The cortical language circuit: from auditory perception to sentence comprehension[END_REF][START_REF] Friederici | The brain basis of syntactic processes: functional imaging and lesion studies[END_REF][START_REF] Grodzinsky | Neuroimaging of syntax and syntactic processing[END_REF], it is also involved in other linguistic functions such as phonological and semantic processing [START_REF] Vigneau | Meta-analyzing left hemisphere language areas: phonology, semantics, and sentence processing[END_REF] 1 . In fact, Broca's area may even support functions that appear unrelated to linguistic or syntactic processing, such as visual search [START_REF] Manjaly | Context-dependent interactions of left posterior inferior frontal gyrus in a local visual search task unrelated to language[END_REF], action recognition [START_REF] Hamzei | The human action recognition system and its relationship to Broca's area: an fMRI study[END_REF], movement preparation [START_REF] Thoenissen | Differential involvement of parietal and precentral regions in movement preparation and motor intention[END_REF], verbal working-memory [START_REF] Chein | Functional heterogeneity within Broca's area during verbal working memory[END_REF][START_REF] Rogalsky | Broca's area, sentence comprehension, and working memory: an fMRI Study[END_REF], and the processing of ordered information (Van 1 Note, however, that the semantic complexity of a sentence is typically related to its syntactic complexity [START_REF] Pylkkänen | Grounding the cognitive neuroscience of semantics in linguistic theory[END_REF]. Therefore, studies focusing on semantic processing might have syntactic confounds. [START_REF] Van Opstal | The neural representation of extensively trained ordered sequences[END_REF]. Therefore, before drawing any conclusion about a link between linguistic processing and deductive reasoning in Broca's area, it is important to formally compare both types of processing within the same participants. I will now turn to studies that precisely investigated this overlap (or lack thereof).

Evidence for reliance on linguistic processing in neuroimaging studies directly comparing brain activity associated with deductive reasoning and linguistic processing [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF] were the first to examine brain activity associated with deductive reasoning and brain activity associated with linguistic processing within the same study. To identify the neural correlates of deductive reasoning, the authors compared fMRI activity associated with evaluating propositional arguments in the form of Modus Tollens to activity associated with evaluating propositional arguments in the form of Modus Ponens (see Table 1). Because conclusions in Modus Tollens arguments are typically more difficult to evaluate than conclusions in Modus Ponens arguments, the authors argued that such a contrast provides an index of "reasoning load" that can be used to identify brain regions supporting deductive reasoning. To uncover the neural correlates of linguistic processing, activity associated with reading the first premise of each argument was contrasted to fixation. As expected, this latter contrast was associated with enhanced activity in several frontal, temporal and parietal regions typically associated with reading (including Broca's area). More surprising, however, was the fact that very little overlap was observed between these reading-related brain regions and the brain network identified in the contrast of Modus Tollens versus Modus Ponens arguments.

That is, more activity for Modus Tollens than Modus Ponens was found in a fronto-parietal network that included the rostrolateral prefrontal cortex (RLPFC), the medial frontal gyrus, and the posterior parietal cortex. In none of these regions did the authors observed reading-related activity. Overall, these findings (which were replicated across different versions of the task and different participants in [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF] appear to provide some evidence for a dissociation between reasoning and linguistic processing. 2This dissociation between reasoning and linguistic processing was also partially observed in [START_REF] Prado | Fractionating the Neural Substrates of Transitive Reasoning: Task-Dependent Contributions of Spatial and Verbal Representations[END_REF]. In that study, we also aimed to formally identify the brain regions subserving linguistic processing and deductive reasoning within the same participants.

Unlike [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF], however, we used an independent word rhyming task as a localizer of the neural mechanisms underlying linguistic processing. For each subject, we identified the specific voxels of Broca's area in which enhanced activity was observed in the rhyming task.

Similar to [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF], we used a "reasoning load" approach to test whether enhanced activity could be observed in those voxels during a reasoning task. Specifically, we compared brain activity associated with evaluating a conclusion relying on 3 categorical premises (e.g., All As are Bs, All Bs are Cs, All Cs are Ds, therefore All As are Ds) to brain activity associated with evaluating a conclusion relying on 2 categorical premises (e.g., All As are Bs, All Bs are Cs, All Cs are Ds, therefore All As are Cs). When only considering the voxels that were activated in the rhyming task in Broca's area, we did find more activity for conclusions relying on 3 premises as compared to conclusion relying on 2 premises. In other words, there was some overlap between the rhyming and the reasoning task in Broca's area. However, there was also some important differences between the brain systems supporting reasoning and linguistic processing. First, more activity for conclusions relying on 3 categorical premises as compared to conclusion relying on 2 categorical premises was found in a region of the RLPFC that was not involved in the rhyming task. Second, no overlap between the rhyming and the reasoning task was observed in Broca's area when categorical relations were replaced by linear relations (e.g., A is taller than B, B is taller than C, C is taller than D, therefore A is taller than D). For both categorical and relational arguments, however, the number of premises did modulate activity in the RLPFC. Therefore, it is possible that the involvement of Broca's area in deductive reasoning may have more to do with task-specific demands than with the recruitment of content-free rules of inference. For example, it has been argued that categorical relations may rely to a greater extent on verbal working-memory than linear relations because categories are more difficult to map onto a unified representation [START_REF] Favrel | On the Relation Between Representations Constructed From Text Comprehension and Transitive Inference Production* 1[END_REF]. To some extent, it is possible that a greater reliance on verbal working memory accounts for the enhanced activity in Broca's area in categorical reasoning tasks (see also [START_REF] Mathieu | Distributed neural representations of logical arguments in school-age children[END_REF], for a replication of the association between categorical argument and verbal processing in children).

It is important to point out, however, that neither [START_REF] Prado | Fractionating the Neural Substrates of Transitive Reasoning: Task-Dependent Contributions of Spatial and Verbal Representations[END_REF] nor [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF] provide a straightforward test of whether deductive reasoning relies on formal rules of inference similar to those underlying natural language. This is because these studies identified the regions involved in linguistic processing, but not the neural mechanisms specifically supporting syntactic processing in language. A more direct comparison between deductive reasoning and the syntax of language was provided by another study from Monti and colleagues, using a particularly clever design [START_REF] Monti | The boundaries of language and thought in deductive inference[END_REF]. In that study, participants were presented with arguments that the authors classified as either 'logical' or 'linguistic'. Both types of arguments involved a premise and a conclusion. They also contained the same 3 elements (X, Y and Z). However, logical and linguistic arguments differed with regards to the kind of inference that was required to assess whether the conclusion was valid or not. Logical arguments were deductive arguments relying on propositional logic. For example, a logical argument was "If both X and Z then not Y, therefore If Y then either not X or not Z". Evaluating the validity of such an argument requires participants to make a logical inference based on an understanding of the meaning of the sentential connectives if … then, and, or, and not. Linguistic arguments, however, were based on ditransitive verbs such as give, say or take. For example, a linguistic argument was "It was X that Y saw Z take, therefore Z was seen by Y taking X". Evaluating the validity of such an argument does not rely on a logical inference.

Rather, it requires participants to perform a syntactic transformation of the sentences. In sum, comparing brain activity associated with logical and linguistic arguments provides a fairly direct test of whether logical inferences and syntactic processing in language rely on the same set of brain regions. The results indicate that, compared to similar arguments evaluated for grammatical correctness, linguistic and logical arguments elicited enhanced activity in largely separated brain networks. On the one hand, linguistic arguments relied on frontal, temporal and parietal brain regions encompassing Broca's area and Wernicke's area. On the other hand, logical arguments relied on a more restricted sets of brain regions that included the RLPFC and the medial frontal gyrus. Notably, logical arguments were not associated with any specific activity in clusters of the Broca's area that were involved in linguistic arguments. Thus, the authors concluded that "logical inference is not embedded in natural language" (Monti et al., 2009, p. 12554).

The interaction between deductive reasoning and linguistic processing: Putting the pieces of the puzzle together

It appears relatively clear from the studies above that deductive reasoning does not always rely on the brain regions supporting linguistic (and especially syntactic) processing. At the very least, several studies show that dissociations can be found between the mechanisms underlying some deductive tasks and those supporting language processing. This arguably weakens the claim that deductive reasoning relies on the neural machinery supporting syntactic processing in natural language. Instead, it supports the view that deductive reasoning can operate independently from linguistic mechanisms [START_REF] Monti | Logic, language and the brain[END_REF]. Nevertheless, several studies reviewed here have found Broca's area to be involved in some deductive reasoning tasks [START_REF] Goel | Dissociation of mechanisms underlying syllogistic reasoning[END_REF][START_REF] Goel | The seats of reason? An imaging study of deductive and inductive reasoning[END_REF][START_REF] Goel | Neuroanatomical correlates of human reasoning[END_REF][START_REF] Reverberi | Large scale brain activations predict reasoning profiles[END_REF][START_REF] Reverberi | Conditional and syllogistic deductive tasks dissociate functionally during premise integration[END_REF][START_REF] Reverberi | Neural basis of generation of conclusions in elementary deduction[END_REF]. Although some of these results may be driven by baseline issues (e.g., some studies may have employed control conditions that are not entirely matched with experimental conditions in terms of reading demands, see [START_REF] Monti | Logic, language and the brain[END_REF], not all studies have experimental shortcomings and their findings have to be taken into account.

Overall, I would argue that there are two main ways to explain the involvement of Broca's area in these studies.

First, it is possible that any activity in Broca's area during deductive reasoning may reflect some domain-general processes that are not necessarily related to syntactic processing per se. For example, deductive reasoning is likely to rely on verbal working-memory or the processing of ordered information, two cognitive skills that have been associated with Broca's area [START_REF] Chein | Functional heterogeneity within Broca's area during verbal working memory[END_REF][START_REF] Chein | Using neuroimaging to evaluate models of working memory and their implications for language processing[END_REF][START_REF] Van Opstal | The neural representation of extensively trained ordered sequences[END_REF]. This may explain the increased activity in Broca's area observed as a function of the number of premises in [START_REF] Prado | Fractionating the Neural Substrates of Transitive Reasoning: Task-Dependent Contributions of Spatial and Verbal Representations[END_REF]. The fact that deductive reasoning may tax some domain-general mechanisms that are also be involved in linguistic processing has been acknowledged by Monti and colleagues [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF]. Specifically, these authors have argued that deductive reasoning is supported by a brain network that can be decomposed into core (i.e., domainspecific) and support (i.e., domain-general) areas. Even though Broca's area is not necessarily part of the support network highlighted by [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF], it remains possible that reasoning-related activity in that region reflects such a support role in making deductive inferences.

A second possibility is that the involvement of Broca's area in reasoning studies reflects activity related to syntactic processing that may be task-dependent. In fact, an examination of the type of deductive tasks used in studies that did versus did not find involvement of Broca's area suggests some interesting differences in experimental materials. On the one hand, most of the studies that have found involvement of Broca's area tend to have used arguments that are relatively simple and would require the application of one or two basic rules of inference according to the Mental Logic (see Table 2 and red focii in Fig. 2). For instance, [START_REF] Reverberi | Neural basis of generation of conclusions in elementary deduction[END_REF] presented participants with simple arguments based on the forms Modus Ponens and disjunction elimination. [START_REF] Reverberi | Conditional and syllogistic deductive tasks dissociate functionally during premise integration[END_REF] also used simple conditional and categorical arguments that could be solved by the application of basic schemas [START_REF] Braine | Mental Logic[END_REF].

----------------------------Figure 2 about here ----------------------------On the other hand, studies that have found reasoning-related activity outside of Broca's area tend to have used tasks that are more complex and would require the application and coordination of several rules of inference (see Table 2 and blue focii in Fig. 2). For instance, [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF] investigated Modus Tollens arguments. As mentioned earlier, Modus Tollens is not an inference that is believed to be part of the basic deductive competence according to the Mental Logic (see Table 2). Understanding such arguments would thus call upon a reasoning strategy involving the coordination of several cognitive steps, known as reduction ad absurdum. [START_REF] Monti | The boundaries of language and thought in deductive inference[END_REF] used even more complex arguments embedding disjunctions within Modus Tollens forms. Finally, [START_REF] Prado | Fractionating the Neural Substrates of Transitive Reasoning: Task-Dependent Contributions of Spatial and Verbal Representations[END_REF] found reasoning-related activity outside of Broca's area while using arguments that required the coordination of 3 premises (as compared to 2). In sum, it may be that the complexity of the deductive task is a relevant factor when explaining different patterns of activations in the literature. From a neurocognitive point of view, an increase in the complexity of a deductive argument is associated with an increase in at least 2 components: the number of relations that have to be considered simultaneously and the working memory load. For example, Modus Tollens arguments typically require reasoners to maintain and manipulate several relations in working memory.

Arguments with 3 premises also arguably require reasoners to consider and maintain in working memory more relations than arguments with 2 premises. 3 Recently, [START_REF] Coetzee | At the core of reasoning: Dissociating deductive and non-deductive load[END_REF] tested whether activity outside of Broca's area (e.g., in the RLPFC) during deductive reasoning could be attributed to an increase in working memory load. That is, the authors set out to compare the brain regions sensitive to an increase in deductive complexity to the brain regions sensitive to an increase in working memory demands. Participants were presented with propositional arguments that were either of the Modus Tollens or Modus Ponens form (see Table 1). In the deductive task, arguments had to be evaluated for logical validity. Similar to [START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF], the contrast of Modus Tollens arguments (i.e., complex deductive trials) versus Modus Ponens arguments (i.e., simple deductive trials) provided an index of deductive complexity. In the working memory task, premises and conclusion either had to be maintained in memory (i.e., simple working memory trials) or mentally manipulated (i.e., complex working memory trials) for a subsequent recognition test. The contrast of complex versus simple working memory trials provided an index of working memory demands. The results indicated a crossover interaction between complexity (simple versus complex) and task (deductive versus working memory). That is, whereas deductive complexity modulated activity outside of Broca's area (i.e, in the RLPFC) to a greater extent than working memory complexity, working memory complexity modulated activity in the posterior parietal cortex to a greater extent than deductive complexity. In other 3 This notion of complexity in the domain of reasoning (e.g., an increase in number of logical relations to be considered) differs from the notion of complexity in the linguistic domain. For example, syntactic complexity in the linguistic domain typically refers to factors such as number of embeddings and number of movement operations [START_REF] Santi | fMRI adaptation dissociates syntactic complexity dimensions[END_REF]. Importantly, studies have found that increasing the syntactic complexity of sentences is associated with changes of activity within (rather than outside of) Broca's area. Therefore, the notion of complexity itself is unlikely to generalize over language and reasoning.

words, increased activity in the RLPFC as a function of deductive complexity does not appear to be accounted for by an increase in working-memory demands. These findings suggest that activation outside of Broca's area in deductive reasoning studies cannot be merely explained by the complexity of stimuli in terms of working memory.

Coetzee & Monti (2018)'s results may rule out one important hypothesis concerning the involvement of regions outside of Broca's area (and notably the RLPFC) in some deductive reasoning studies (i.e., the idea that these regions may respond to working memory load).

However, the fact remains that an increase in deductive reasoning complexity is typically associated with an increase in the number of logical relations that have to be considered.

Interestingly, even though the role of the RLPFC in high-order cognition remains unclear, two major theories posit that this region supports the integration of multiple relations when making a decision [START_REF] Bunge | Left, but not right, rostrolateral prefrontal cortex meets a stringent test of the relational integration hypothesis[END_REF][START_REF] Krawczyk | A hierarchy for relational reasoning in the prefrontal cortex[END_REF][START_REF] Wendelken | Brain is to thought as stomach is to ??": investigating the role of rostrolateral prefrontal cortex in relational reasoning[END_REF], as well as the ability to maintain in mind a main goal while working towards secondary goals [START_REF] Koechlin | Dissociating the role of the medial and lateral anterior prefrontal cortex in human planning[END_REF][START_REF] Koechlin | The architecture of cognitive control in the human prefrontal cortex[END_REF][START_REF] Ramnani | Anterior prefrontal cortex: insights into function from anatomy and neuroimaging[END_REF]. Complex deductive arguments often involve dealing with multiple logical relations while working towards finding a valid conclusion. In other words, complex deductive arguments often require greater relational integration and cognitive branching than simple arguments. This may explain the involvement of the RLPFC in those tasks. In contrast, simple deductive arguments (e.g., Modus Ponens) are straightforward and should rely on the instantiation of one single rule according to the Mental Logic (see Table 2). Unlike the kind of arguments that are typically used in studies that focus on deductive complexity (and in which activity in the RLPFC is often found), simple deductive arguments are also routinely used in verbal and written discourse. It is possible that these arguments might have gained -either through ontogeny or phylogeny --a form of automaticity that makes their underlying syntax similar to that of a natural language. In other words, it is possible that simple and complex deductive arguments may rely on qualitatively different mechanisms, with only the former involving the neural substrates of linguistic syntax. This, however, remains to be formally demonstrated.

Conclusion

The question of whether language and deductive reasoning rely on similar syntactic mechanisms is fascinating because it informs on the broader and fundamental question of whether human thought is embedded in natural language [START_REF] Monti | The role of language in structure-dependent cognition[END_REF]. It is also relevant to the reasoning literature because theories have long posited that deductive reasoning might rely on a system of formal rules of inference that can be compared to the linguistic syntax. This probably explains why the study of the relationship between deductive reasoning and language has been at the heart of the neuroimaging literature on reasoning. To date, however, there is no clear evidence that deductive reasoning relies on the neural mechanisms supporting the syntax of language. That is, even though there is support for the idea that some deductive tasks may recruit Broca's area, experimental shortcomings (e.g., baseline conditions that are not matched for reading demands and lack of independent localization of mechanisms supporting the syntax of language) makes it difficult to clearly interpret these findings in terms of overlap between the neural mechanisms for deduction and language. On the contrary, the few studies that have explicitly compared the neural correlates of deductive reasoning to that of language have found largely separated neural networks. It is interesting to note, however, that studies that have found reasoning-related activity outside of Broca's area have largely investigated deductive arguments that are more complex (e.g., involves the integration of more logical relations) than studies that have found reasoning-related activity in Broca's area. Thus, it is possible that the involvement of the neural mechanisms supporting linguistic syntax in deductive reasoning may be task-dependent and restricted to simple inferences such as those highlighted in Table 2. A potentially fruitful approach in future studies may then be to investigate the interaction between deductive reasoning and linguistic processing in Broca's area while (i) systematically varying the complexity of the deductive argument and (ii) independently localizing the syntactic mechanisms of language. [START_REF] Baggio | Multiple neural representations of elementary logical connectives[END_REF][START_REF] Reverberi | Large scale brain activations predict reasoning profiles[END_REF][START_REF] Reverberi | Conditional and syllogistic deductive tasks dissociate functionally during premise integration[END_REF][START_REF] Reverberi | Neural basis of generation of conclusions in elementary deduction[END_REF] while coordinates of studies employing relatively complex arguments are taken from Monti and colleagues [START_REF] Coetzee | At the core of reasoning: Dissociating deductive and non-deductive load[END_REF][START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF][START_REF] Monti | The boundaries of language and thought in deductive inference[END_REF]. A yellow outline delineates Broca's area, defined as Brodmann areas 44 and 45 according to the cytoarchitectonic map of [START_REF] Amunts | Broca's region revisited: cytoarchitecture and intersubject variability[END_REF].

Tables Table 1. Examples of deductive arguments as a function of their logical form

Logical form Example

Modus Ponens Premise 1: If there is a circle then there is a triangle

FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. Distribution of activation peaks in studies employing relatively simple propositional

  If there is a circle then there is a triangle Premise 2: There is not a triangle Conclusion: Therefore, there is not a circleDisjunction eliminationPremise 1: There is a circle or there is a triangle Premise 2: There is not a circle Conclusion: Therefore, there is a triangle Relational argument Premise 1: The circle is larger the triangle Premise 2: The triangle is larger the square Conclusion: Therefore, the circle is larger than the square Categorical Argument Premise 1: All tables are triangles Premise 2: All triangles are blue Conclusion: Therefore, all tables are blue

Table 2 . The 12 elementary rules (i.e., schemas) from the Mental Logic

 2

	Schema	Premises	Conclusion
	1	Not not-P	P
	2	If P or Q then R; P	P
	3	P or Q; not P	Q
	4	Not both P and Q; P	Not-Q
	5	P or Q; If P then R; If Q then R	R
	6	P or Q; If P then R; If Q then S	R or S
	7	If P then Q; P	Q
	8	P; Q	P and Q
	9	P and Q	P
	10	P and (Q or R)	(P and Q) or (P and R)
	11	P and not-P	Incompatibility
	12	P or Q; Not-P; Not-Q	Incompatibility

Activity in a brain network similar to that uncovered in[START_REF] Monti | Functional neuroanatomy of deductive inference: a language-independent distributed network[END_REF] was also found in[START_REF] Rodriguez-Moreno | The dynamics of deductive reasoning: an fMRI investigation[END_REF]. In particular, using categorical syllogisms instead of propositional statements, the authors did not find reasoning-related activity in left BA 44 or 45. However, there was not task aimed at localizing linguistic processing in that study.

This research was supported by a grant from the Agence Nationale de la Recherche (ANR-14-CE30-0002).