Participants experience difficulty detecting that an item depicting an H-in-a-square confirms the logical rule, “If there is not a T then there is not a circle.” Indeed, there is a perceptual conflict between the items mentioned in the rule (T and circle) and in the test item (H and square). Much evidence supports the claim that correct responding depends on detecting and resolving such conflicts. One aim of this study is to find more precise neurological evidence in support of this claim by using a parametric event-related functional magnetic resonance imaging (fMRI) paradigm. We scanned 20 participants while they were required to judge whether or not a conditional rule was verified (or falsified) by a corresponding target item. We found that the right middorsolateral prefrontal cortex (mid-DLPFC) was specifically engaged, together with the medial frontal (anterior cingulate and presupplementary motor area [pre-SMA]) and parietal cortices, when mismatching was present. Activity in these regions was also linearly correlated with the level of mismatch between the rule and the test item. Furthermore, a psychophysiological interaction analysis revealed that activation of the mid-DLPFC, which increases as mismatching does, was accompanied by a decrease in functional integration with the bilateral primary visual cortex and an increase in functional integration with the right parietal cortex. This indicates a need to break away from perceptual cues in order to select an appropriate logical response. These findings strongly indicate that the regions involved in inhibitory control (including the right mid-DLPFC and the medial frontal cortex) are engaged when participants have to overcome perceptual mismatches in order to provide a logical response. These findings are also consistent with neuroimaging studies investigating the belief bias, where prior beliefs similarly interfere with logical reasoning.