Modal Logical Neural Networks for Financial AI

TL;DR

This paper introduces Modal Logical Neural Networks (MLNNs) that integrate modal logic with neural networks to enhance interpretability and reasoning in financial AI applications, addressing regulatory and robustness challenges.

Contribution

The paper presents MLNNs as a differentiable logic layer for finance, combining Kripke semantics with neural architectures to improve compliance, transparency, and robustness in financial AI systems.

Findings

MLNNs promote regulatory compliance in trading agents.

MLNNs help recover latent trust networks for market surveillance.

MLNNs improve robustness under stress scenarios.

Abstract

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 ($A_\theta$), 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.