Disabling conditional inferences: an EEG study

Electrophysiological connectivity of logical deduction: Early cortical MEG study

Complex human reasoning involves minimal abilities to extract conclusions implied in the available information. These abilities are considered "deductive" because they exemplify certain abstract relations among propositions or probabilities called deductive arguments. However, the electrophysiological dynamics which supports such complex cognitive processes has not been addressed yet. In this work we consider typically deductive logico-probabilistically valid inferences and aim to verify or refute their electrophysiological functional connectivity differences from invalid inferences with the same content (same relational variables, same stimuli, same relevant and salient features). We recorded the brain electrophysiological activity of 20 participants (age = 20.35 ± 3.23) by means of an MEG system during two consecutive reasoning tasks: a search task (invalid condition) without any specific deductive rules to follow, and a logically valid deductive task (valid condition) with explicit deductive rules as instructions. We calculated the functional connectivity (FC) for each condition and conducted a seed-based analysis in a set of cortical regions of interest. Finally, we used a cluster-based permutation test to compare the differences between logically valid and invalid conditions in terms of FC. As a first novel result we found higher FC for valid condition in beta band between regions of interest and left prefrontal, temporal, parietal, and cingulate structures. FC analysis allows a second novel result which is the definition of a propositional network with operculo-cingular, parietal and medial nodes, specifically including disputed medial deductive "core" areas. The experiment discloses measurable cortical processes which do not depend on content but on truth-functional propositional operators. These experimental novelties may contribute to understand the cortical bases of deductive processes.

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.

The neural pattern of intuitive and analytical processes in the subliminal environment: N2 responses on the embedded Chinese character task

Dual process theory proposes that there are two different types of human thinking: an intuitive process and an analytical process. However, if these two types of thinking could maintain their characteristics in the subliminal environment, further exploration of their relationship is required. This study used the Embedded Chinese Character Task (ECCT) with event-related potentials to investigate the behavioral and neural patterns of the intuitive and analytical processes in the subliminal environment. In this task, one Chinese character (target character) was extracted from another character (test character) with problem solving that required either an intuitive process (in which the two characters were spatially separated or adjacent) or analytical process (in which the target characters were embedded in the test characters). Participants were asked to judge whether the target character was included or excluded from the test character in the subliminal environment. Results showed that a difference in reaction time occurred between inclusion and exclusion only in the analytical materials, but there was a difference in N2 between the inclusion and exclusion conditions in both intuitive and analytical materials, indicating that participants preferred to choose intuitive processing to solve intuitive and analytical problems in an unconscious environment. These findings support the traditional dual process theory, which states that the intuitive process is unconscious and effortless, while the analytical process may perform like an intuitive process in a subliminal environment.

Specificity effects in reasoning with counterintuitive and arbitrary conditionals

When people have prior knowledge about an inference, they accept conclusions from specific conditionals (e.g., “If Jack does sports, then Jack loses weight”) more strongly than for unspecific conditionals (e.g., “If a person does sports, then the person loses weight”). But can specific phrasings also elevate the acceptance of conclusions from unbelievable conditionals? In Experiment 1, we varied the specificity of counterintuitive conditionals, which described the opposite of what is expected according to everyday experiences (“If Lena/a person studies hard, then Lena/the person will not do well on the test”). In Experiment 2, we varied the specificity of arbitrary conditionals, which had no obvious link between antecedent and consequent (“If Mary/a person goes shopping, then Mary/ the person gets pimples”). All conditionals were embedded in MP and AC inferences. Participants were instructed to reason as in daily life and to evaluate the conclusions on a 7-point Likert scale. Our results showed a specificity effect in both experiments: participants gave higher acceptance ratings for specific than for unspecific conditionals.

Conditional content, explicit information and generating cases: Sources for suppressing inferences

In the present study, we evaluate the suppression effect by asking participants to make inferences with everyday conditionals ("if A, then B"; "if Ana finds a friend, then she will go to the theatre"), choosing between three possible conclusions ("she went to the theatre"; "she did not go to the theatre"; "it cannot be concluded"). We test how these inferences can be influenced by three factors: a) when the content of the conditional induces us to think about disabling conditions that prevent us from accepting the consequent (A and ¬B) or alternative conditions that induce us to think about other antecedents that could also lead to the consequent (¬A and B), b) when explicit information is given about what really happened (e.g. Ana found a friend but they did not go to the theatre; or Ana did not find a friend but she went to the theatre) and c) when participants have to look for concrete disabling (e.g. Ana's friend had to work) and alternative cases (e.g. Ana's sister wanted to go to the theatre) before making the inferences. Previous studies have shown what were called "suppression effects": disabling conditions reduced valid inferences while considering alternatives led to a reduction in fallacies. These two "suppression effects" were shown in Experiment 1: a) in an Implicit condition that included just the content factor of the conditional and b) with a greater magnitude in a second Explicit condition that included the three factors (content, explicit information and search for counterexamples). Experiment 2 compared the same Explicit condition with another in which participants, instead of looking for counterexamples, completed a control task of looking for synonyms. In addition, half the participants looked for a few items (2 cases) and the other half for many items (5 cases). Results again showed the suppressing effect in all the conditions, but the magnitude was greater in the counterexample condition. No relevant differences were obtained according to the number of cases generated; the most relevant result was that the factors provided an additive effect on the suppression.

The Suppression of Inferences From Counterfactual Conditionals

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, "if she watered the plants they bloomed," when beliefs about additional background conditions, for example, "if the sun shone they bloomed" decrease the frequency of inferences such as modus tollens (from "the plants did not bloom" to "therefore she did not water them"). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, "if she had watered the plants they would have bloomed," when beliefs about the known or presupposed facts, "she did not water the plants and they did not bloom" increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from "she did not water the plants" to "therefore they did not bloom") is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new "switched-suppression" effect for conditionals with negated components, for example, "if she had not watered the plants they would not have bloomed": modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning.

How do the hierarchical levels of premises affect category-based induction: diverging effects from the P300 and N400

Although a number of studies have explored the time course of category-based induction, little is known about how the hierarchical levels (superordinate, basic, subordinate) of premises affect category-based induction. The EEG data were recorded when nineteen healthy human participants were performing a simplified category-based induction task. The ERP results showed that: in the subordinate conclusion condition, the basic premise elicited a larger N400, versus the superordinate promise; in the basic conclusion condition, the superordinate promise elicited a larger P300 relative to both the basic premise and subordinate premise; in the superordinate conclusion condition, however, no difference was found between different promise. Furthermore, the process that reasoning from a higher level to a lower level evoked a larger P300, compared to it did in the reverse direction. The divergent evidence suggested that category-based induction at superordinate, basic, and subordinate levels might be affected by various factors, such as abstract level, direction, and distance between premise and conclusion, which yielded new insights into the neural underpinnings of category-based induction with different inductive strengths.

Aristotle Meets Zeno: Psychophysiological Evidence

This study, a tribute to Aristotle's 2400 years, used a juxtaposition of valid Aristotelian arguments to the paradoxes formulated by Zeno the Eleatic, in order to investigate the electrophysiological correlates of attentional and /or memory processing effects in the course of deductive reasoning. Participants undertook reasoning tasks based on visually presented arguments which were either (a) valid (Aristotelian) statements or (b) paradoxes. We compared brain activation patterns while participants maintained the premises / conclusions of either the valid statements or the paradoxes in working memory (WM). Event-related brain potentials (ERPs), specifically the P300 component of ERPs, were recorded during the WM phase, during which participants were required to draw a logical conclusion regarding the correctness of the valid syllogisms or the paradoxes. During the processing of paradoxes, results demonstrated a more positive event-related potential deflection (P300) across frontal regions, whereas processing of valid statements was associated with noticeable P300 amplitudes across parieto-occipital regions. These findings suggest that paradoxes mobilize frontal attention mechanisms, while valid deduction promotes parieto-occipital activity associated with attention and/or subsequent memory processing.

How types of premises modulate the typicality effect in category-based induction: diverging evidence from the P2, P3, and LPC effects

Behavioural studies have indicated that semantic typicality influences processing time and accuracy during the performance of inductive reasoning (i.e., the typicality effect). The present study examines this effect by manipulating the types of premises and conclusions (i.e., general, typical, or atypical) at an electrophysiological level using a semantic category-based induction task. With regard to behavioural results, higher inductive strength was found in typical conclusions in all premise conditions, whereas a longer response time for atypical conclusions was only found in general and typical premise conditions. The ERP results had different response patterns: in the general premise condition, a larger P2, as well as a smaller P3 and LPC (500–600 ms), were elicited by atypical conclusions relative to typical ones; in the typical premise condition, a larger P2 and LPC (600–700 ms) were found for atypical conclusions; in the atypical premise condition, however, only a larger P2 was found for atypical conclusions. The divergent evidence for the typicality effect indicated that the processing of the typicality effect in general, and specific premise conditions, might involve different cognitive processes, such as resource allocation and inference violation, which yielded new insights into the neural underpinnings of the typicality effect in a category-based induction.

How can we study reasoning in the brain?

The brain did not develop a dedicated device for reasoning. This fact bears dramatic consequences. While for perceptuo-motor functions neural activity is shaped by the input's statistical properties, and processing is carried out at high speed in hardwired spatially segregated modules, in reasoning, neural activity is driven by internal dynamics and processing times, stages, and functional brain geometry are largely unconstrained a priori. Here, it is shown that the complex properties of spontaneous activity, which can be ignored in a short-lived event-related world, become prominent at the long time scales of certain forms of reasoning. It is argued that the neural correlates of reasoning should in fact be defined in terms of non-trivial generic properties of spontaneous brain activity, and that this implies resorting to concepts, analytical tools, and ways of designing experiments that are as yet non-standard in cognitive neuroscience. The implications in terms of models of brain activity, shape of the neural correlates, methods of data analysis, observability of the phenomenon, and experimental designs are discussed.

Event-related potential parameters of category and property violations during semantic category-based induction

Previous studies have failed to clarify the event-related potentials (ERPs) that occur in response to categorization and property inferences during category-based induction. The present study examined ERP differences among acceptable-induction conclusions, unrelated-category conclusions, and unrelated-property conclusions to dissociate categorization and property-inference processing during category-based induction. The results showed that: (a) conclusions with categories that were unrelated to the premise evoked greater frontal N2 amplitudes, smaller P3b amplitudes, and greater N400 amplitudes, compared to conclusions with categories that were logically related to the premise; and (b) conclusions with unrelated properties evoked larger late positive components (LPCs) during the 700-800ms time interval compared to conclusions with related properties. These results suggest that the N2-P3b-N400 effects reflect categorization violations, while the LPCs are related to property violations during category-based induction, therefore, the ERP responses to category-related and property-related processes are dissociated respectively during category-based induction.

Imaging deductive reasoning and the new paradigm

There has been a great expansion of research into human reasoning at all of Marr’s explanatory levels. There is a tendency for this work to progress within a level largely ignoring the others which can lead to slippage between levels (Chater et al., 2003). It is argued that recent brain imaging research on deductive reasoning—implementational level—has largely ignored the new paradigm in reasoning—computational level (Over, 2009). Consequently, recent imaging results are reviewed with the focus on how they relate to the new paradigm. The imaging results are drawn primarily from a recent meta-analysis by Prado et al. (2011) but further imaging results are also reviewed where relevant. Three main observations are made. First, the main function of the core brain region identified is most likely elaborative, defeasible reasoning not deductive reasoning. Second, the subtraction methodology and the meta-analytic approach may remove all traces of content specific System 1 processes thought to underpin much human reasoning. Third, interpreting the function of the brain regions activated by a task depends on theories of the function that a task engages. When there are multiple interpretations of that function, interpreting what an active brain region is doing is not clear cut. It is concluded that there is a need to more tightly connect brain activation to function, which could be achieved using formalized computational level models and a parametric variation approach.

Event-related potential responses to letter-string comparison analogies

Previous studies have used analogy completion tasks (e.g., abe is to abf as ijk is to what?) to examine the event-related potential (ERP) parameters of analogical reasoning. In the present study, ERP responses to analogies were investigated using an analogy comparison task (e.g., is abe to abf as ijk is to ijl?), with a focus on structural evaluation. The results showed that the identical match task elicited an N2 component with smaller amplitude than that of the N2 component in the zero- and one-step consistent analogies, reflecting automatic match detection. The data also showed that there were significant differences in the N400 during the consistent and inconsistent analogies, which may reflect a delayed perceptual mismatch with semantic strategies. Moreover, one-step consistent analogies evoked smaller late positive component (LPC) amplitudes than that evoked by identical match or zero-step consistent analogies in the 500- to 800-ms time interval, and one-step inconsistent analogies elicited smaller amplitude LPCs than that elicited by zero-step inconsistent analogies in the 500- to 750-ms time interval, which suggested that LPCs reflected structure evaluation in analogy comparison tasks.

Neural correlates of causal power judgments

Causal inference is a fundamental component of cognition and perception. Probabilistic theories of causal judgment (most notably causal Bayes networks) derive causal judgments using metrics that integrate contingency information. But human estimates typically diverge from these normative predictions. This is because human causal power judgments are typically strongly influenced by beliefs concerning underlying causal mechanisms, and because of the way knowledge is retrieved from human memory during the judgment process. Neuroimaging studies indicate that the brain distinguishes causal events from mere covariation, and also distinguishes between perceived and inferred causality. Areas involved in error prediction are also activated, implying automatic activation of possible exception cases during causal decision-making.

Reasoning from transitive premises: an EEG study

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

The difference in spatiotemporal dynamics between modus ponens and modus tollens in the Wason selection task: an event-related potential study

High-density, event-related brain potentials (ERPs) were recorded to explore differences in spatiotemporal dynamics between modus ponens (MP) and modus tollens (MT) in the Wason selection task. Results showed that MP elicits a more positive P3b-like component than MT from 400 to 800 ms. MP appeared to occur earlier than MT in various stages of proposition testing, such as stimulus processing and response selection. ERP results showed that MT has a longer duration and more negative later negative component (LNC) than MP at 2,000 ms. This result suggests that MT occupies more cognitive resources than MP in the final stages of proposition testing. The short and small left frontal LNC obtained by MP implies examination of the expectable conclusion, whereas the long and large left frontal LNC elicited by MT may be involved in the retention operation of the card in working memory from the monitoring and inspecting putative conclusion in the later stages of proposition testing.