Cognitive problem-solving benefits from cognitive maps aiding navigation and planning. Previous studies revealed that cognitive maps for physical space navigation involve hippocampal (HC) allocentric codes, while cognitive maps for abstract task space engage medial prefrontal cortex (mPFC) task-specific codes. Solving challenging cognitive tasks requires integrating these two types of maps. This is exemplified by spatial alternation tasks in multi-corridor settings, where animals like rodents are rewarded upon executing an alternation pattern in maze corridors. Existing studies demonstrated the HC – mPFC circuit’s engagement in spatial alternation tasks and that its disruption impairs task performance. Yet, a comprehensive theory explaining how this circuit integrates task-related and spatial information is lacking. We advance a novel hierarchical active inference model clarifying how the HC – mPFC circuit enables the resolution of spatial alternation tasks, by merging physical and task-space cognitive maps. Through a series of simulations, we demonstrate that the model’s dual layers acquire effective cognitive maps for navigation within physical (HC map) and task (mPFC map) spaces, using a biologically-inspired approach: a clone-structured cognitive graph. The model solves spatial alternation tasks through reciprocal interactions between the two layers. Importantly, disrupting inter-layer communication impairs difficult decisions, consistent with empirical findings. The same model showcases the ability to switch between multiple alternation rules. However, inhibiting message transmission between the two layers results in perseverative …