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Artificial neural networks (ANNs) have frequently been deployed for classification objectives within functional magnetic resonance imaging (fMRI) research, though such analyses traditionally isolate only specific regional sub-volumes of the brain. Recent methodology has integrated shallow neural networks (SNNs) with explainable artificial intelligence (xAI) frameworks to uncover underlying mechanisms of neural processing. Although prior research validated this paradigm utilizing fMRI data from motor execution tasks, the current investigation implements this framework on Theory of Mind (ToM) cognitive tasks, leveraging data extracted from the Human Connectome Project (HCP) Young Adult repository. Cognitive paradigms introduce greater computational complexity due to the fundamentally non-linear dynamics of neural functions. The HCP multimodal parcellation brain atlas is utilized to partition the cortex, thereby guiding the systematic training, pruning, and subsequent retraining of an SNN. Shapley values are subsequently computed to decode the retrained architecture, with the resulting outputs benchmarked against a General Linear Model (GLM) analysis for empirical validation. The baseline network demonstrated a classification accuracy of 88.2%, which decreased to 80.0% following network pruning, and subsequently recovered to 84.7% after the retraining phase. The SHAP-derived explanations demonstrated strong convergence with both GLM observations and established neuroanatomical regions associated with ToM. This fMRI investigation effectively navigated a highly complex cognitive paradigm, illustrating the efficacy of explainability techniques in deciphering non-linear neurological dynamics. These outcomes indicate that xAI platforms, particularly knowledge extraction frameworks, offer substantial utility for progressing mental health research and neural state decoding applications.