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Modal Logical Neural Networks for Financial AI

Antonin Sulc

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 ($A_θ$), 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.

Modal Logical Neural Networks for Financial AI

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 () and Learnable Accessibility (), 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.
Paper Structure (19 sections, 4 equations, 1 figure, 3 tables)

This paper contains 19 sections, 4 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction: The Logic-Learning Gap in Finance
  2. Related Work
  3. The Differentiable Logic Layer in Finance
  4. Scenarios
  5. Scenario 1: Agentic Compliance - The "Wash Sale" Guardrail
  6. Scenario 2: Market Surveillance - The "Collusion Hunter"
  7. Scenario 3: Risk Management - "Crash-Proof" Portfolios
  8. Scenario 4: The Safe Signer - Interpretable Contract Review
  9. Architecture and Setup.
  10. Results.
  11. Interpretability Advantage.
  12. Conclusion
  13. Safe Signer: Architecture Details
  14. Multi-World Kripke Structure.
  15. Dual-Head Architecture.
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Modal Logical Neural Networks for Finance.Left: Kripke semantics with possible worlds (temporal: $t, t+1$; stress: crash world $w_c$). Middle: Two learning modes—(A) Deductive: fixed accessibility $R$ (e.g., time flow), (B) Inductive: learned $A_\theta$ (e.g., trust networks). Modal operators $\Box$ (necessity: all worlds) and $\Diamond$ (possibility: $\geq$1 world) enable differentiable logical reasoning. Right: Four financial applications leveraging these modes for compliance, surveillance, risk management, and interpretability.