Cognitive control allows behavior to be guided according to environmental contexts and internal goals. During cognitive control tasks, fMRI analyses typically reveal increased activation in frontal and parietal networks, and EEG analyses reveal increased amplitude of neural oscillations in the delta/theta band (2–3, 4–7 Hz) in frontal electrodes. Previous studies proposed that theta-band activity reflects the maintenance of rules associating stimuli to appropriate actions (i.e., the rule set), whereas delta synchrony is specifically associated with the control over the context for when to apply a set of rules (i.e., the rule abstraction). We tested these predictions using EEG and fMRI data collected during the performance of a hierarchical cognitive control task that manipulated the level of abstraction of task rules and their set-size. Our results show a clear separation of delta and theta oscillations in the control of rule abstraction and of stimulus–action associations, respectively, in distinct frontoparietal association networks. These findings support a model by which frontoparietal networks operate through dynamic, multiplexed neural processes.

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