Multiple neural representations of elementary logical connectives

The role of memory in affirming-the-consequent fallacy

People tend to recognize that a transitive relation remains true even when its order is reversed. This affirming-the-consequent fallacy is thought to be uniquely related to human intelligence. It is generally thought that this fallacy is a byproduct of explicit reasoning at the moment of recognition of the reversed order. Here, we provide evidence suggesting a reconsideration of this account using an implicit memory paradigm, which minimizes the involvement of explicit reasoning. Specifically, we tested a two-stage memory model: (1) when a sequence of events is encoded, the memory of the reversed sequence is formed, resulting in the affirming-the-consequent fallacy, and (2) the memories of the forward and reversed sequences are integrated over time, reinforcing the fallacy. Results of behavioral and functional magnetic resonance imaging experiments were consistent with this memory-based model. Our findings suggest that the affirming-the-consequent fallacy may begin unwittingly when individuals memorize a transitive relation.

Distinctive Delta and Theta Responses in Deductive and Probabilistic Reasoning

INTRODUCTION

The neural substrates of reasoning, a cognitive ability we use constantly in daily life, are still unclear. Reasoning can be divided into two types according to how the inference process works and the certainty of the conclusions. In deductive reasoning, certain conclusions are drawn from premises by applying the rules of logic. On the other hand, in probabilistic reasoning, possible conclusions are drawn by interpreting the semantic content of arguments.

METHODS

We examined event-related oscillations associated with deductive and probabilistic reasoning. To better represent the natural use of reasoning, we adopted a design that required participants to choose what type of reasoning they would use. Twenty healthy participants judged the truth values of alternative conclusion propositions following two premises while the EEG was being recorded. We then analyzed event-related delta and theta power and phase-locking induced under two different conditions.

RESULTS

We found that the reaction time was shorter and the accuracy rate was higher in deductive reasoning than in probabilistic reasoning. High delta and theta power in the temporoparietal, parietal, and occipital regions of the brain were observed in deductive reasoning. As for the probabilistic reasoning, prolonged delta response in the right hemisphere and high frontal theta phase-locking were noted.

CONCLUSION

Our results suggest that the electrophysiological signatures of the two types of reasoning have distinct characteristics. There are significant differences in the delta and theta responses that are associated with deductive and probabilistic reasoning. Although our findings suggest that deductive and probabilistic reasoning have different neural substrates, consistent with most of the studies in the literature, there is not yet enough evidence to make a comprehensive claim on the subject. There is a need to diversify the growing literature on deductive and probabilistic reasoning with different methods and experimental paradigms.

Electrical analysis of logical complexity: an exploratory eeg study of logically valid/invalid deducive inference

INTRODUCTION

Logically valid deductive arguments are clear examples of abstract recursive computational procedures on propositions or on probabilities. However, it is not known if the cortical time-consuming inferential processes in which logical arguments are eventually realized in the brain are in fact physically different from other kinds of inferential processes.

METHODS

In order to determine whether an electrical EEG discernible pattern of logical deduction exists or not, a new experimental paradigm is proposed contrasting logically valid and invalid inferences with exactly the same content (same premises and same relational variables) and distinct logical complexity (propositional truth-functional operators). Electroencephalographic signals from 19 subjects (24.2 ± 3.3 years) were acquired in a two-condition paradigm (100 trials for each condition). After the initial general analysis, a trial-by-trial approach in beta-2 band allowed to uncover not only evoked but also phase asynchronous activity between trials.

RESULTS

showed that (i) deductive inferences with the same content evoked the same response pattern in logically valid and invalid conditions, (ii) mean response time in logically valid inferences is 61.54% higher, (iii) logically valid inferences are subjected to an early (400 ms) and a late reprocessing (600 ms) verified by two distinct beta-2 activations (p-value < 0,01, Wilcoxon signed rank test).

CONCLUSION

We found evidence of a subtle but measurable electrical trait of logical validity. Results put forward the hypothesis that some logically valid deductions are recursive or computational cortical events.

Seeing inferences: brain dynamics and oculomotor signatures of non-verbal deduction

We often express our thoughts through words, but thinking goes well beyond language. Here we focus on an elementary but basic thinking process, disjunction elimination, elicited by elementary visual scenes deprived of linguistic content, describing its neural and oculomotor correlates. We track two main components of a nonverbal deductive process: the construction of a logical representation (A or B), and its simplification by deduction (not A, therefore B). We identify the network active in the two phases and show that in the latter, but not in the former, it overlaps with areas known to respond to verbal logical reasoning. Oculomotor markers consistently differentiate logical processing induced by the construction of a representation, its simplification by deductive inference, and its maintenance when inferences cannot be drawn. Our results reveal how integrative logical processes incorporate novel experience in the flow of thoughts induced by visual scenes.

A Cortical Surface-Based Meta-Analysis of Human Reasoning

Recent advances in neuroimaging have augmented numerous findings in the human reasoning process but have yielded varying results. One possibility for this inconsistency is that reasoning is such an intricate cognitive process, involving attention, memory, executive functions, symbolic processing, and fluid intelligence, whereby various brain regions are inevitably implicated in orchestrating the process. Therefore, researchers have used meta-analyses for a better understanding of neural mechanisms of reasoning. However, previous meta-analysis techniques include weaknesses such as an inadequate representation of the cortical surface’s highly folded geometry. Accordingly, we developed a new meta-analysis method called Bayesian meta-analysis of the cortical surface (BMACS). BMACS offers a fast, accurate, and accessible inference of the spatial patterns of cognitive processes from peak brain activations across studies by applying spatial point processes to the cortical surface. Using BMACS, we found that the common pattern of activations from inductive and deductive reasoning was colocalized with the multiple-demand system, indicating that reasoning is a high-level convergence of complex cognitive processes. We hope surface-based meta-analysis will be facilitated by BMACS, bringing more profound knowledge of various cognitive processes.

Compositionality in a Parallel Architecture for Language Processing

Compositionality has been a central concept in linguistics and philosophy for decades, and it is increasingly prominent in many other areas of cognitive science. Its status, however, remains contentious. Here, I reassess the nature and scope of the principle of compositionality (Partee, 1995) from the perspective of psycholinguistics and cognitive neuroscience. First, I review classic arguments for compositionality and conclude that they fail to establish compositionality as a property of human language. Next, I state a new competence argument, acknowledging the fact that any competent user of a language L can assign to most expressions in L at least one meaning which is a function only of the meanings of the expression's parts and of its syntactic structure. I then discuss selected results from cognitive neuroscience, indicating that the human brain possesses the processing capacities presupposed by the competence argument. Finally, I outline a language processing architecture consistent with the neuroscience results, where semantic representations may be generated by a syntax-driven stream and by an "asyntactic" processing stream, jointly or independently. Compositionality is viewed as a constraint on computation in the former stream only.

Brain electrical traits of logical validity

Neuroscience has studied deductive reasoning over the last 20 years under the assumption that deductive inferences are not only de jure but also de facto distinct from other forms of inference. The objective of this research is to verify if logically valid deductions leave any cerebral electrical trait that is distinct from the trait left by non-valid deductions. 23 subjects with an average age of 20.35 years were registered with MEG and placed into a two conditions paradigm (100 trials for each condition) which each presented the exact same relational complexity (same variables and content) but had distinct logical complexity. Both conditions show the same electromagnetic components (P3, N4) in the early temporal window (250-525 ms) and P6 in the late temporal window (500-775 ms). The significant activity in both valid and invalid conditions is found in sensors from medial prefrontal regions, probably corresponding to the ACC or to the medial prefrontal cortex. The amplitude and intensity of valid deductions is significantly lower in both temporal windows (p = 0.0003). The reaction time was 54.37% slower in the valid condition. Validity leaves a minimal but measurable hypoactive electrical trait in brain processing. The minor electrical demand is attributable to the recursive and automatable character of valid deductions, suggesting a physical indicator of computational deductive properties. It is hypothesized that all valid deductions are recursive and hypoactive.

The Effect of Counterfactual Information on Outcome Value Coding in Medial Prefrontal and Cingulate Cortex: From an Absolute to a Relative Neural Code

Adaptive coding of stimuli is well documented in perception, where it supports efficient encoding over a broad range of possible percepts. Recently, a similar neural mechanism has been reported also in value-based decision, where it allows optimal encoding of vast ranges of values in PFC: neuronal response to value depends on the choice context (relative coding), rather than being invariant across contexts (absolute coding). Additionally, value learning is sensitive to the amount of feedback information: providing complete feedback (both obtained and forgone outcomes) instead of partial feedback (only obtained outcome) improves learning. However, it is unclear whether relative coding occurs in all PFC regions and how it is affected by feedback information. We systematically investigated univariate and multivariate feedback encoding in various mPFC regions and compared three modes of neural coding: absolute, partially-adaptive and fully-adaptive.Twenty-eight human participants (both sexes) performed a learning task while undergoing fMRI scanning. On each trial, they chose between two symbols associated with a certain outcome. Then, the decision outcome was revealed. Notably, in one-half of the trials participants received partial feedback, whereas in the other half they got complete feedback. We used univariate and multivariate analysis to explore value encoding in different feedback conditions.We found that both obtained and forgone outcomes were encoded in mPFC, but with opposite sign in its ventral and dorsal subdivisions. Moreover, we showed that increasing feedback information induced a switch from absolute to relative coding. Our results suggest that complete feedback information enhances context-dependent outcome encoding.SIGNIFICANCE STATEMENT This study offers a systematic investigation of the effect of the amount of feedback information (partial vs complete) on univariate and multivariate outcome value encoding, within multiple regions in mPFC and cingulate cortex that are critical for value-based decisions and behavioral adaptation. Moreover, we provide the first comparison of three possible models of neural coding (i.e., absolute, partially-adaptive, and fully-adaptive coding) of value signal in these regions, by using commensurable measures of prediction accuracy. Taken together, our results help build a more comprehensive picture of how the human brain encodes and processes outcome value. In particular, our results suggest that simultaneous presentation of obtained and foregone outcomes promotes relative value representation.

The Neurocognitive Correlates of Human Reasoning: A Meta-analysis of Conditional and Syllogistic Inferences

Inferring knowledge is a core aspect of human cognition. We can form complex sentences connecting different pieces of information, such as in conditional statements like "if someone drinks alcohol, then they must be older than 18." These are relevant for causal reasoning about our environment and allow us to think about hypothetical scenarios. Another central aspect to forming complex statements is to quantify about sets, such as in "some apples are green." Reasoning in terms of the ability to form these statements is not yet fully understood, despite being an active field of interdisciplinary research. On a theoretical level, several conceptual frameworks have been proposed, predicting diverging brain activation patterns during the reasoning process. We present a meta-analysis comprising the results of 32 neuroimaging experiments about reasoning, which we subdivided by their structure, content, and requirement for world knowledge. In conditional tasks, we identified activation in the left middle and rostrolateral pFC and parietal regions, whereas syllogistic tasks elicit activation in Broca's complex, including the BG. Concerning the content differentiation, abstract tasks exhibit activation in the left inferior and rostrolateral pFC and inferior parietal regions, whereas content tasks are in the left superior pFC and parieto-occipital regions. The findings clarify the neurocognitive mechanisms of reasoning and exhibit clear distinctions between the task's type and content. Overall, we found that the activation differences clarify inconsistent results from accumulated data and serve as useful scaffolding differentiations for theory-driven interpretations of the neuroscientific correlates of human reasoning.

Logical negation mapped onto the brain

High-level cognitive capacities that serve communication, reasoning, and calculation are essential for finding our way in the world. But whether and to what extent these complex behaviors share the same neuronal substrate are still unresolved questions. The present study separated the aspects of logic from language and numerosity-mental faculties whose distinctness has been debated for centuries-and identified a new cytoarchitectonic area as correlate for an operation involving logical negation. A novel experimental paradigm that was implemented here in an RT/fMRI study showed a single cluster of activity that pertains to logical negation. It was distinct from clusters that were activated by numerical comparison and from the traditional language regions. The localization of this cluster was described by a newly identified cytoarchitectonic area in the left anterior insula, ventro-medial to Broca's region. We provide evidence for the congruence between the histologically and functionally defined regions on multiple measures. Its position in the left anterior insula suggests that it functions as a mediator between language and reasoning areas.

Evidence Linking Brain Activity Modulation to Age and to Deductive Training

Electrical brain activity modulation in terms of changes in its intensity and spatial distribution is a function of age and task demand. However, the dynamics of brain modulation is unknown when it depends on external factors such as training. The aim of this research is to verify the effect of deductive reasoning training on the modulation in the brain activity of healthy younger and older adults (N = 47 (mean age of 21 ± 3.39) and N = 38 (mean age of 68.92 ± 5.72)). The analysis reveals the benefits of training, showing that it lowers cerebral activation while increasing the number of correct responses in the trained reasoning task (p < 0.001). The brain source generators were identified by time-averaging low-resolution brain electromagnetic tomography (sLORETA) current density images. In both groups, a bilateral overactivation associated with the task and not with age was identified. However, while the profile of bilateral activation in younger adults was symmetrical in anterior areas, in the older ones, the profile was located asymmetrically in anterior and posterior areas. Consequently, bilaterality may be a marker of how the brain adapts to maintain cognitive function in demanding tasks in both age groups. However, the differential bilateral locations across age groups indicate that the tendency to brain modulation is determined by age.

Just above Chance: Is It Harder to Decode Information from Prefrontal Cortex Hemodynamic Activity Patterns?

The prefrontal cortex (PFC) is central to flexible, goal-directed cognition, and understanding its representational code is an important problem in cognitive neuroscience. In humans, multivariate pattern analysis (MVPA) of fMRI blood oxygenation level-dependent (BOLD) measurements has emerged as an important approach for studying neural representations. Many previous studies have implicitly assumed that MVPA of fMRI BOLD is just as effective in decoding information encoded in PFC neural activity as it is in visual cortex. However, MVPA studies of PFC have had mixed success. Here we estimate the base rate of decoding information from PFC BOLD activity patterns from a meta-analysis of published MVPA studies. We show that PFC has a significantly lower base rate (55.4%) than visual areas in occipital (66.6%) and temporal (71.0%) cortices and one that is close to chance levels. Our results have implications for the design and interpretation of MVPA studies of PFC and raise important questions about its functional organization.

Differential roles of polar orbital prefrontal cortex and parietal lobes in logical reasoning with neutral and negative emotional content

To answer the question of how brain pathology affects reasoning about negative emotional content, we administered a disjunctive logical reasoning task involving arguments with neutral content (e.g. Either there are tigers or women in NYC, but not both; There are no tigers in NYC; There are women in NYC) and emotionally laden content (e.g. Either there are pedophiles or politicians in Texas, but not both; There are politicians in Texas; There are no pedophiles in Texas) to 92 neurological patients with focal lesions to various parts of the brain. A Voxel Lesion Symptom Mapping (VLSM) analysis identified 16 patients, all with lesions to the orbital polar prefrontal cortex (BA 10 & 11), as being selectively impaired in the emotional reasoning condition. Another 17 patients, all with lesions to the parietal cortex, were identified as being impaired in the neutral content condition. The reasoning scores of these two patient groups, along with 23 matched normal controls, underwent additional analysis to explore the effect of belief bias. This analysis revealed that the differences identified above were largely driven by trials where there was an incongruency between the believability of the conclusion and the validity of the argument (i.e. valid argument/false conclusion or invalid argument/true conclusion). Patients with lesions to polar orbital prefrontal cortex underperformed in incongruent emotional content trials and over performed in incongruent neutral content trials (compared to both normal controls and patients with parietal lobe lesions). Patients with lesions to parietal lobes underperformed normal controls (at a trend level) in neutral trials where there was a congruency between the believability of the conclusion and the validity of the argument (i.e. valid argument/true conclusion or invalid argument/false conclusion). We conclude that lesions to the polar orbital prefrontal cortex (i) prevent these patients from enjoying any emotionally induced cognitive boost, and (ii) block the belief bias processing route in the neutral condition. Lesions to parietal lobes result in a generalized impairment in logical reasoning with neutral content.

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Polar/orbital PFC lesions result in impaired reasoning in emotional content reasoning.

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Polar/orbital PFC lesion patients overperform in neutral content reasoning trials.

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These differences were driven by incongruent reasoning trials.

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Parietal lesions result in impaired reasoning with neutral but not emotional content.

At the core of reasoning: Dissociating deductive and non-deductive load

In recent years, neuroimaging methods have been used to investigate how the human mind carries out deductive reasoning. According to some, the neural substrate of language is integral to deductive reasoning. According to others, deductive reasoning is supported by a language-independent distributed network including left frontopolar and frontomedial cortices. However, it has been suggested that activity in these frontal regions might instead reflect non-deductive factors such as working memory load and general cognitive difficulty. To address this issue, 20 healthy volunteers participated in an fMRI experiment in which they evaluated matched simple and complex deductive and non-deductive arguments in a 2 × 2 design. The contrast of complex versus simple deductive trials resulted in a pattern of activation closely matching previous work, including frontopolar and frontomedial "core" areas of deduction as well as other "cognitive support" areas in frontoparietal cortices. Conversely, the contrast of complex and simple non-deductive trials resulted in a pattern of activation that does not include any of the aforementioned "core" areas. Direct comparison of the load effect across deductive and non-deductive trials further supports the view that activity in the regions previously interpreted as "core" to deductive reasoning cannot merely reflect non-deductive load, but instead might reflect processes specific to the deductive calculus. Finally, consistent with previous reports, the classical language areas in left inferior frontal gyrus and posterior temporal cortex do not appear to participate in deductive inference beyond their role in encoding stimuli presented in linguistic format.

Decoding rule search domain in the left inferior frontal gyrus

Traditionally, the left hemisphere has been thought to extract mainly verbal patterns of information, but recent evidence has shown that the left Inferior Frontal Gyrus (IFG) is active during inductive reasoning in both the verbal and spatial domains. We aimed to understand whether the left IFG supports inductive reasoning in a domain-specific or domain-general fashion. To do this we used Multi-Voxel Pattern Analysis to decode the representation of domain during a rule search task. Thirteen participants were asked to extract the rule underlying streams of letters presented in different spatial locations. Each rule was either verbal (letters forming words) or spatial (positions forming geometric figures). Our results show that domain was decodable in the left prefrontal cortex, suggesting that this region represents domain-specific information, rather than processes common to the two domains. A replication study with the same participants tested two years later confirmed these findings, though the individual representations changed, providing evidence for the flexible nature of representations. This study extends our knowledge on the neural basis of goal-directed behaviors and on how information relevant for rule extraction is flexibly mapped in the prefrontal cortex.

Neural Representations of Hierarchical Rule Sets: The Human Control System Represents Rules Irrespective of the Hierarchical Level to Which They Belong

Humans use rules to organize their actions to achieve specific goals. Although simple rules that link a sensory stimulus to one response may suffice in some situations, often, the application of multiple, hierarchically organized rules is required. Recent theories suggest that progressively higher level rules are encoded along an anterior-to-posterior gradient within PFC. Although some evidence supports the existence of such a functional gradient, other studies argue for a lesser degree of specialization within PFC. We used fMRI to investigate whether rules at different hierarchical levels are represented at distinct locations in the brain or encoded by a single system. Thirty-seven male and female participants represented and applied hierarchical rule sets containing one lower-level stimulus-response rule and one higher-level selection rule. We used multivariate pattern analysis to investigate directly the representation of rules at each hierarchical level in absence of information about rules from other levels or other task-related information, thus providing a clear identification of low- and high-level rule representations. We could decode low- and high-level rules from local patterns of brain activity within a wide frontoparietal network. However, no significant difference existed between regions encoding representations of rules from both levels except for precentral gyrus, which represented only low-level rule information. Our findings show that the brain represents conditional rules regardless of their level in the explored hierarchy, so the human control system did not organize task representation according to this dimension. Our paradigm represents a promising approach to identifying critical principles that shape this control system.SIGNIFICANCE STATEMENT Several recent studies investigating the organization of the human control system propose that rules at different control levels are organized along an anterior-to-posterior gradient within PFC. In this study, we used multivariate pattern analysis to explore independently the representation of formally identical conditional rules belonging to different levels of a cognitive hierarchy and provide for the first time a clear identification of low- and high-level rule representations. We found no major spatial differences between regions encoding rules from different hierarchical levels. This suggests that the human brain does not use levels in the investigated hierarchy as a topographical organization principle to represent rules controlling our behavior. Our paradigm represents a promising approach to identifying which principles are critical.

Real Objects Can Impede Conditional Reasoning but Augmented Objects Do Not

In this study, Knauff and Johnson-Laird's (2002) visual impedance hypothesis (i.e., mental representations with irrelevant visual detail can impede reasoning) is applied to the domain of external representations and diagrammatic reasoning. We show that the use of real objects and augmented real (AR) objects can control human interpretation and reasoning about conditionals. As participants made inferences (e.g., an invalid one from "if P then Q" to "P"), they also moved objects corresponding to premises. Participants who moved real objects made more invalid inferences than those who moved AR objects and those who did not manipulate objects (there was no significant difference between the last two groups). Our results showed that real objects impeded conditional reasoning, but AR objects did not. These findings are explained by the fact that real objects may over-specify a single state that exists, while AR objects suggest multiple possibilities.

Lesions to polar/orbital prefrontal cortex selectively impair reasoning about emotional material

While it is widely accepted that lesions to orbital prefrontal cortex lead to emotion related disruptions and poor decision-making, there is very little patient data on this issue involving actual logical reasoning tasks. We tested patients with circumscribed, focal lesions largely confined to polar/orbital prefrontal cortex (BA 10 & 11) (N=17) on logical reasoning tasks involving neutral and emotional content, and compared their performance to that of an age and education-matched normal control group (N=22) and a posterior lesion control group (N=24). Our results revealed a significant group by content interaction driven by a selective impairment in the polar/orbital prefrontal cortex group compared to healthy normal controls and to the parietal patient group, in the emotional content reasoning trials. Subsequent analyses of congruent and incongruent reasoning trials indicated that this impairment was driven by the poor performance of patients with polar/orbital lesions in the incongruent trials. We conclude that the polar/orbital prefrontal cortex plays a critical role in filtering emotionally charged content from the material before it is passed on to the reasoning system in lateral/dorsal regions of prefrontal cortex. Where unfiltered content is passed to the reasoning engine, either as a result of pathology (as in the case of our patients) or as a result of individual differences, reasoning performance suffers.