Introduces Modal Logical Neural Networks (MLNNs) as a differentiable logic layer that bridges deep learning with symbolic Kripke semantics for regulated AI.
arXiv · March 16, 2026 · 2603.12487
Why it matters
It moves beyond simple 'constrained optimization' by embedding necessity, possibility, and temporal logic directly into the neural architecture. This provides a new way to enforce regulatory compliance and safety guardrails in black-box models without sacrificing differentiability.
From the 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