Multiple neural representations of elementary logical connectives - Suppl. Mat.

Giosué Baggio, Paolo Cherubini, Doris Pischedda, Anna Blumenthal, John-Dylan Haynes, Carlo Reverberi*
*carlo.reverberi@unimib.it

Abstract

A defining trait of human cognition is the capacity to form compounds out of simple thoughts. This ability relies on the logical connectives AND, OR and IF. Simple propositions, e.g., ‘There is a fork’ and ‘There is a knife’, can be combined in alternative ways using logical connectives: e.g., ‘There is a fork AND there is a knife’, ‘There is a fork OR there is a knife’, ‘IF there is a fork, there is a knife’. How does the brain represent compounds based on different logical connectives, and how are compounds evaluated in relation to new facts? In the present study, participants had to maintain and evaluate conjunctive (AND), disjunctive (OR) or conditional (IF) compounds while undergoing functional MRI. Our results suggest that, during maintenance, the left posterior inferior frontal gyrus (pIFG, BA44, or Broca’s area) represents the surface form of compounds. During evaluation, the left pIFG switches to processing the full logical meaning of compounds, and two additional areas are recruited: the left anterior inferior frontal gyrus (aIFG, BA47) and the left intraparietal sulcus (IPS, BA40). The aIFG shows a pattern of activation similar to pIFG, and compatible with processing the full logical meaning of compounds, whereas activations in IPS differ with alternative interpretations of conditionals: logical vs conjunctive. These results uncover the functions of a basic cortical network underlying human compositional thought, and provide a shared neural foundation for the cognitive science of language and reasoning.

Supplementary Results

Statistical tables of the main analyses

We report here the statistical tables of the analyses described in the main text for the maintenance phase (Table \ref{table:p_mvpa_m}) and for the evaluation phase (Table \ref{table:p_anova_eval}).

\label{table:p_mvpa_m}Peak activations for the MVPA analysis exploring which brain regions encode logical connectives during the maintenance phase. For details see main text. Coordinates [x, y, z] are in the space of the Montreal Neurological Institute (MNI) template and the selection of cluster maxima is according to the conventions of SPM12. All the reported main effects are significant p <0.05 FWE-corrected for multiple comparisons at cluster level.
MNI Peak Z Cluster size Cluster p (FWE)
-54 11 20 4.05 240 <.001
-48 8 44 3.48
-45 2 38 3.42

\label{table:p_anova_eval}Peak activations for the analysis testing activation differences between logical connectives during the evaluation phase. For details see main text. Coordinates [x, y, z] in space of Montreal Neurological Institute (MNI) template and selection of cluster maxima according to conventions of SPM12. All the reported main effects are significant p <0.05 FWE corrected for multiple comparisons at cluster level.
MNI Peak Z Cluster size Cluster p (FWE)
-30 23 -4 6.03 230 <.001
-45 23 -10 5.36
-48 35 -10 5.32
-42 -64 50 4.65 194 <.001
-48 -52 47 4.59
-39 -61 41 4.19
-45 23 41 4.2 202 <.001
-42 23 29 4.09
-42 5 32 3.66


Evaluation phase: whole-brain simple effects

We report the results of the pairwise comparisons underlying the ANOVA reported in the main text. In the ANOVA we described the brain regions showing different levels of activations between AND, OR and IF during the evaluation phase. For the simple effects, six pairwise comparisons are possible (IF \(>\) AND, IF \(>\) OR, OR \(>\) AND, AND \(>\) IF, OR \(>\) IF, AND \(>\) OR). Only two out of these six produce significant results. The results are largely overlapping with those from the ANOVA. The findings here also show that the effect reported in the ANOVA is driven by a higher activation while processing IF and OR compared to AND.

Peak activations for the analysis testing pairwise activation differences between IF and AND processing during the evaluation phase.