Modal Logical Neural Networks for Financial AI
This addresses the problem of AI adoption in the financial industry, where interpretability and rule adherence are critical for regulated settings, though it appears incremental as it builds on existing neural and logical methods.
The paper tackles the challenge of combining deep learning's performance with symbolic logic's interpretability in financial AI by introducing Modal Logical Neural Networks (MLNNs), which integrate Kripke semantics into neural architectures to enable differentiable reasoning about necessity, possibility, time, and knowledge, as demonstrated through four case studies in regulatory compliance, market surveillance, stress testing, and mitigating robo-advisory hallucinations.
The financial industry faces a critical dichotomy in AI adoption: deep learning often delivers strong empirical performance, while symbolic logic offers interpretability and rule adherence expected in regulated settings. We use Modal Logical Neural Networks (MLNNs) as a bridge between these worlds, integrating Kripke semantics into neural architectures to enable differentiable reasoning about necessity, possibility, time, and knowledge. We illustrate MLNNs as a differentiable ``Logic Layer'' for finance by mapping core components, Necessity Neurons ($\Box$) and Learnable Accessibility ($A_θ$), to regulatory guardrails, market stress testing, and collusion detection. Four case studies show how MLNN-style constraints can promote compliance in trading agents, help recover latent trust networks for market surveillance, encourage robustness under stress scenarios, and distinguish statistical belief from verified knowledge to help mitigate robo-advisory hallucinations.