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Humans are able to flexibly devise and implement rules to reach their desired goals. For simple situations, we can use single rules, such as “if traffic light is green then cross the street.” In most cases, however, more complex rule sets are required, involving the integration of multiple layers of control. Although it has been shown that prefrontal cortex is important for rule representation, it has remained unclear how the brain encodes more complex rule sets. Here, we investigate how the brain represents the order in which different parts of a rule set are evaluated. Participants had to follow compound rule sets that involved the concurrent application of two single rules in a specific order, where one of the rules always had to be evaluated first. The rules and their assigned order were independently manipulated. By applying multivariate decoding to fMRI data, we found that the identity of the current rule was encoded in a frontostriatal network involving right ventrolateral prefrontal cortex, right superior frontal gyrus, and dorsal striatum. In contrast, rule order could be decoded in the dorsal striatum and in the right premotor cortex. The nonhomogeneous distribution of information across brain areas was confirmed by follow-up analyses focused on relevant regions of interest. We argue that the brain encodes complex rule sets by “decomposing” them in their constituent features, which are represented in different brain areas, according to the aspect of information to be maintained.

Rules are widely used in everyday life to organize actions and thoughts in accordance with our internal goals. At the simplest level, single rules can be used to link individual sensory stimuli to their appropriate responses. However, most tasks are more complex and require the concurrent application of multiple rules. Experiments on humans and monkeys have shown the involvement of a frontoparietal network in rule representation. Yet, a fundamental issue still needs to be clarified: Is the neural representation of multiple rules compositional, that is, built on the neural representation of their simple constituent rules? Subjects were asked to remember and apply either simple or compound rules. Multivariate decoding analyses were applied to functional magnetic resonance imaging data. Both ventrolateral frontal and lateral parietal cortex were involved in compound representation. Most importantly, we were able to decode the compound rules by training classifiers only on the simple rules they were composed of. This shows that the code used to store rule information in prefrontal cortex is compositional. Compositional coding in rule representation suggests that it might be possible to decode other complex action plans by learning the neural patterns of the known composing elements.

Two experiments investigated whether dealing with a homogeneous subset of syllogisms with time-constrained responses encouraged participants to develop and use heuristics for abstract (Experiment 1) and thematic (Experiment 2) syllogisms. An atmosphere-based heuristic accounted for most responses with both abstract and thematic syllogisms. With thematic syllogisms, a weaker effect of a belief heuristic was also observed, mainly where the correct response was inconsistent with the atmosphere of the premises. Analytic processes appear to have played little role in the time-constrained condition, whereas their involvement increased in a self-paced, unconstrained condition. From a dual-process perspective, the results further specify how task demands affect the recruitment of heuristic and analytic systems of reasoning. Because the syllogisms and experimental procedure were the same as those used in a previous neuroimaging study by Goel, Buchel, Frith, and Dolan (2000), the result also deepen our understanding of the cognitive processes investigated by that study.

Elementary deduction is the ability of unreflectively drawing conclusions from explicit or implicit premises, on the basis of their logical forms. This ability is involved in many aspects of human cognition and interactions. To date, limited evidence exists on its cortical bases. We propose a model of elementary deduction in which logical inferences, memory, and meta-logical control are separable subcomponents. We explore deficits in patients with left, medial and right frontal lesions, by both studying patients' deductive abilities and providing measures of their meta-logical sensitivity for proof difficulty. We show that lesions to left lateral and medial frontal cortex impair abilities at solving elementary deductive problems, but not so lesions to right frontal cortex. Furthermore, we show that memory deficits differentially affect patients according to the locus of the lesion. Left lateral patients with working memory deficits had defective deductive abilities, but not so left lateral patients with spared working memory. In contrast, in medial patients both deductive and meta-deductive abilities were affected regardless of the presence of memory deficits. Overall, the results are compatible with a componential view of elementary deduction, and call for the elaboration of more fine-grained models of deductive abilities.

The neural correlates of inductive reasoning are still poorly understood. In order to explore them, we administered a revised version of the Brixton test [Cortex 32 (2) (1996a) 241], a rule attainment task, to a group of 40 patients with a focal frontal brain lesion of mixed aetiology and to 43 control subjects. To interpret an impairment on the test as suggesting an inductive reasoning deficit a number of alternative hypotheses need first to be considered, namely whether the Brixton impairment could be explained by: (i) a working memory deficit; (ii) a monitoring deficit; (iii) a difficulty in applying an already induced rule; (iv) greater impulsivity. The patients with left lateral (LL) frontal lesions were significantly impaired on the Brixton test; more importantly they were the only group in which none of the alternative hypotheses we explored proved able to explain the flawed performance. In sharp contrast, right lateral lesion patients did not make significantly more errors on the Brixton test than controls, but they produced three times more capture errors (a sign of impaired monitoring processes). The results were interpreted as suggesting functional dissociations between inductive reasoning, monitoring and working memory and a localisation of key processes for induction in left lateral frontal cortex and in right lateral cortex for monitoring and checking.

We investigated whether two basic forms of deductive inference, Modus Ponens and Disjunctive Syllogism, occur automatically and without awareness. In Experiment 1, we used a priming paradigm with a set of conditional and disjunctive problems. For each trial, two premises were shown. The second premise was presented at a rate designed to be undetectable. After each problem, participants had to evaluate whether a newly-presented target number was odd or even. The target number matched or did not match a conclusion endorsed by the two previous premises. We found that when the target matched the conclusion of a Modus Ponens inference, the evaluation of the target number was reliably faster than baseline even when participants reported that they were not aware of the second premise. This priming effect did not occur for any other valid or invalid inference that we tested, including the Disjunctive Syllogism. In Experiment 2, we used a forced-choice paradigm in which we found that some participants were able to access some information on the second premise when their attention was explicitly directed to it. In Experiment 3, we showed that the priming effect for Modus Ponens was present also in subjects who could not access any information about P 2 . In Experiment 4 we explored whether spatial relations (e.g., “ a before b ”) or sentences with quantifiers (e.g., “all a with b ”) could generate a priming effect similar to the one observed for Modus Ponens. A priming effect could be found for Modus Ponens only, but not for the other relations tested. These findings show that the Modus Ponens inference, in contrast to other deductive inferences, can be carried out automatically and unconsciously. Furthermore, our findings suggest that critical deductive inference schemata can be included in the range of high-level cognitive activities that are carried out unconsciously.

Deduction is the ability to draw necessary conclusions from previous knowledge. Here we propose a novel approach to understanding the neural basis of deduction, which exploits fine-grained inter-participant variability in such tasks. Participants solved deductive problems and were grouped by the behavioral strategies employed, i.e., whether they were sensitive to the logical form of syllogistic premises, whether the problems were solved correctly, and whether heuristic strategies were employed. Differential profiles of neural activity can predict membership of the first two of these groups. The predictive power of activity profiles is distributed non-uniformly across the brain areas activated by deduction. Activation in left ventro-lateral frontal (BA47) and lateral occipital (BA19) cortices predicts whether logically valid solutions are sought. Activation of left inferior lateral frontal (BA44/45) and superior medial frontal (BA6/8) cortices predicts sensitivity to the logical structure of problems. No specific pattern of activation was associated with the use of a non-logical heuristic strategy. Not only do these findings corroborate the hypothesis that left BA47, BA44/45 and BA6/8 are critical for making syllogistic deductions, but they also imply that they have different functional roles as components of a dedicated network. We propose that BA44/45 and BA6/8 are involved in the extraction and representation of the formal structure of a problem, while BA47 is involved in the selection and application of relevant inferential rules. Finally, our findings suggest that deductive reasoning can be best described as a cascade of cognitive processes requiring the concerted operation of several, functionally distinct, brain areas.

This study tested the impact of prefrontal-cortex lesion on learning hierarchically structured action sequences. Using a visual-manual serial reaction time task, we had subjects first perform five blocks of trials with a hierarchically structured 14-element action sequence and then tested for sequence-specific learning by introducing a pseudo-random transfer sequence. Relative to control subjects (N = 39), we found that both lateral frontal (N = 16) and medial frontal (N = 18) patients showed reduced overall performance benefits across the training phase. In contrast, the negative transfer test showed significantly increased reaction times in all patient groups, indicating robust sequence-specific learning. This learning was not significantly different from that of the control group. Taken together, the data suggest that learning hierarchically structured action sequences is unimpaired in patients with prefrontal-cortex lesion.

A recently proposed theory on frontal lobe functions claims that the prefrontal cortex, particularly its dorso-lateral aspect, is crucial in defining a set of responses suitable for a particular task, and biasing these for selection. This activity is carried out for virtually any kind of non-routine tasks, without distinction of content. The aim of this study is to test the prediction of Frith's 'sculpting the response space' hypothesis by means of an 'insight' problem-solving task, namely the matchstick arithmetic task. Starting from Knoblich et al.'s interpretation for the failure of healthy controls to solve the matchstick problem, and Frith's theory on the role of dorsolateral frontal cortex, we derived the counterintuitive prediction that patients with focal damage to the lateral frontal cortex should perform better than a group of healthy participants on this rather difficult task. We administered the matchstick task to 35 patients (aged 26-65 years) with a single focal brain lesion as determined by a CT or an MRI scan, and to 23 healthy participants (aged 34-62 years). The findings seemed in line with theoretical predictions. While only 43% of healthy participants could solve the most difficult matchstick problems ('type C'), 82% of lateral frontal patients did so (Fisher's exact test, P < 0.05). In conclusion, the combination of Frith's and Knoblich et al.'s theories was corroborated.

The Left Lateral cortex is known to have a role in inductive reasoning tasks. A more specific hypothesis on its role is that it is crucial in the generation of new abstract rules, rather than in the selection and implementation of a specific rule among a set of previously learned ones. Two new tests – the Generation of Hypotheses test and the Recognition of the Rule test – were administered to 46 patients with focal damage to the frontal cortex. Patients were divided in three frontal subgroups: Left Lateral, Right Lateral and Medial. On the basis of the new hypothesis, it was predicted that (i) the Left Lateral subgroup would fail in the Generation of Hypotheses test but would show spared performance on the Recognition of the Rule test and that (ii) the other frontal subgroups would perform normally on both tests. The findings on the Left Lateral and Right Lateral frontal subgroup were consistent with the predictions. This suggests that the Left Lateral frontal cortex is critical specifically for the generation of hypotheses in inductive reasoning. The Medial frontal subgroup, in contrast with our expectations, was impaired on Generation test; two hypotheses have been raised to explain this finding.

Semantic verbal fluency is widely used in clinical and experimental studies. This task is highly sensitive to the presence of brain pathology and is frequently impaired after frontal lesions. Besides the total number of words generated, a qualitative analysis of their sequence can add valuable information about the impaired cognitive components. Thirty-four frontal patients and a group of matched controls were examined. Besides the number of words and subcategories retrieved by each group, we analysed two distinct aspects of the word sequence: the search strategy through a semantically organised store and the ability to switch from one subcategory to another. We checked whether the pattern of impairment changed according to the lesion site within the frontal lobe. Overall, patients produced fewer words than controls. However, only lateral frontal patients presented a reduced semantic relatedness between contiguously produced words and a specifically increased proportion of switches to different subcategories. The performance of lateral frontal patients was in line with the hypothesis of a search strategy impairment and cannot be attributed to a switching deficit. The performance of mesial frontal patients could be ascribed to a general deficit of activation.

In everyday life, people untrained in formal logic draw simple deductive inferences from linguistic material (i.e., elementary propositional deductions). Presently, we have limited information on the brain areas implicated when such conclusions are drawn. We used event-related fMRI to identify these brain areas. A set of multiple and independent criteria was derived from the two main theories in the field of reasoning to maximize the reliability of detection of areas in which activity is specifically associated with deductive inferences. Two left lateralized clusters of areas, one in frontal cortex (Brodmann Area 44 and 6) and one in parietal lobe (BA 40), satisfied all criteria; activation was present at the moment of inference, it was shared by both conditional ("if-based") and disjunctive ("or-based") inferences but was greater for disjunctive clauses. Identification of the reasoning network was corroborated by the observation that activity in these areas was greater the longer the reasoning time. Taken together with results from preceding studies, our findings suggest possible theoretically relevant dissociations between elementary propositional deductions and other types of deductive reasoning.

Deduction allows us to draw consequences from previous knowledge. Deductive reasoning can be applied to several types of problem, for example, conditional, syllogistic, and relational. It has been assumed that the same cognitive operations underlie solutions to them all; however, this hypothesis remains to be tested empirically. We used event‐related fMRI, in the same group of subjects, to compare reasoning‐related activity associated with conditional and syllogistic deductive problems. Furthermore, we assessed reasoning‐related activity for the two main stages of deduction, namely encoding of premises and their integration. Encoding syllogistic premises for reasoning was associated with activation of BA 44/45 more than encoding them for literal recall. During integration, left fronto‐lateral cortex (BA 44/45, 6) and basal ganglia activated with both conditional and syllogistic reasoning. Besides that, integration of syllogistic problems additionally was associated with activation of left parietal (BA 7) and left ventro‐lateral frontal cortex (BA 47). This difference suggests a dissociation between conditional and syllogistic reasoning at the integration stage. Our finding indicates that the integration of conditional and syllogistic reasoning is carried out by means of different, but partly overlapping, sets of anatomical regions and by inference, cognitive processes. The involvement of BA 44/45 during both encoding (syllogisms) and premise integration (syllogisms and conditionals) suggests a central role in deductive reasoning for syntactic manipulations and formal/linguistic representations. Hum Brain Mapp, 2010. © 2010 Wiley‐Liss, Inc.