AI with Symbolic Empathy: Shannon-Neumann Insight Guided Logic

We present an Artificial Intelligence with Symbolic Empathy, where an agent $$\mathcal {A}$$ cooperatively aligns a person’s cognitive state $$\vec {X}_P(t)$$ with their ideal trajectory $$\vec {X}_{L_P}(t)$$ . Alignment is guided by a context-sensitive, non-monotonic logic $$\mathcal {L}_{\mathcal {A}}$$ implemented as a five-stage Hierarchical FSM: $$\textsf{Identify}$$ (fact structuring), $$\textsf{Classify}$$ (pattern extraction), $$\textsf{Explore}$$ (intervention generation), $$\textsf{Plan}$$ (ontology-based misalignment diagnosis), and $$\textsf{Reason}$$ (abductive hypothesis evaluation). Reasoning is driven by the Shannon-von Neumann insight gain $$I_{SN}(\gamma _i) = \big [ \mathcal {H}(B_P(t)) - \mathcal {H}(B_P^{(i)}(t+1)) \big ] \cdot U(\gamma _i),$$ combining entropy reduction with goal-relevant utility. This metric enables self-supervised abductive learning, refining $$\mathcal {A}$$ ’s theory-of-mind and guiding psychologically meaningful, uncertainty-reducing interventions. The architecture ensures interpretability (I-AI), explainability (X-AI), and trustworthiness (T-AI) via explicit fact-rule tracing. Cognitive-cooperative case studies show that integrating symbolic causal models with utility-guided abductive-deductive reasoning yields transparent, goal-aligned human-AI interaction.