Woolgar et al provide a meta-analysis of experiments using multivoxel pattern analysis in FMRI.  They show that cortical areas traditionally though to be visual, auditory or motor, primarily (though not exclusively) code visual, auditory, and motor information.  However, the frontoparietal cortex is hypothesized to a multiple-demand network and it shows domain generality, coding multisensory and rule information.

Woolgar, Alexandra, Jade Jackson, and John Duncan. “Coding of visual, auditory, rule, and response information in the brain: 10 years of multivoxel pattern analysis.” Journal of cognitive neuroscience (2016).

Tsutsui et al shows how the prefrontal cortex integrates rule and category information for a behavioral decision.

Tsutsui, Ken-Ichiro, et al. “Representation of Functional Category in the Monkey Prefrontal Cortex and Its Rule-Dependent Use for Behavioral Selection.” The Journal of Neuroscience 36.10 (2016): 3038-3048.

This paper reports FMRI in humans performing a task requiring first-order rules (S-R associations with a specific motor output) and second order rules that govern the use of the first-order rules.  Cerebellum lobules that project to the prefrontal cortex show activation for both types of rules.  This suggests that the cerebellum contributes to rule-based behaviors even when the rules are higher-order and don’t directly involve a motor command.

For further reading on the role of rules in cognition and their neural implementation see:
Miller, E.K. and Cohen, J.D. (2001) An integrative theory of prefrontal cortex function. Annual Review of Neuroscience, 24:167-202.  View PDF »

Buschman, T.J., Denovellis, E.L., Diogo, C., Bullock, D. and Miller, E.K. (2012) Synchronous oscillatory neural ensembles for rules in the prefrontal cortex. Neuron, 76: 838-846.  View PDF

Wallis, J.D., Anderson, K.C., and Miller, E.K. (2001) Single neurons in the prefrontal cortex encode abstract rules. Nature, 411:953-956. View PDF »