# Modal Logical Neural Networks for Financial AI

arXiv: https://arxiv.org/abs/2603.12487 · HTML: https://mlsanity.com/paper/2603.12487/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [CUAD: An Expert-Annotated NLP Dataset for Legal Contract Review](https://mlsanity.com/paper/2103.06268/) (2021)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Modal Logic Neural Networks](https://mlsanity.com/paper/2512.03491/) (2025)

## Abstract (arXiv)

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 (Aθ), 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.