Logical Grammar Induction via Graph Kolmogorov Complexity: A Neuro-Symbolic Framework for Self-Healing Clinical Data Integrity

TL;DR

This paper introduces Logic-GNN, a neuro-symbolic framework that models clinical data as a structured language governed by logical rules, enabling effective anomaly detection and self-healing in healthcare data systems.

Contribution

It presents a novel integration of Temporal Graph Neural Networks with Graph Kolmogorov Complexity to induce symbolic grammar for clinical data anomaly detection.

Findings

Achieved an F1-score of 0.94 on the Sina System dataset.

Outperformed state-of-the-art methods by 12% in anomaly detection.

Enabled real-time self-healing and correction of clinical data.

Abstract

The reliability of Healthcare Information Systems (HIS) is frequently compromised by human-induced data entry errors, which existing statistical anomaly detection methods fail to distinguish from legitimate clinical extremes. This paper proposes Logic-GNN, a novel neuro-symbolic framework that treats clinical records as a structured ``private language'' governed by latent logical games. By integrating Temporal Graph Neural Networks (TGNN) with Graph Kolmogorov Complexity, we induce a symbolic grammar that represents the underlying logic of medical interactions. We define anomalies as ``grammatical violations'' that cause a significant expansion in the Minimum Description Length (MDL) of the clinical graph. Evaluated on the Sina System dataset (2M+ records), Logic-GNN achieves an F1-score of 0.94, outperforming state-of-the-art baselines by 12\% in distinguishing between life-threatening medical outliers and data corruption. Our approach introduces a self-healing mechanism that suggests logical corrections to maintain data integrity in real-time HIS environments.