Modal Logic Neural Networks
cs.LG, cs.LO, cs.MA
Submitted: 2025-12-03
Updated: 2026-09-05
Journal ref: 20th Conference on Neurosymbolic Learning and Reasoning, 2026
Code: https://github.com/sulcantonin/MLNN
License: http://creativecommons.org/licenses/by/4.0/
The gist: Neural Networks are indispensable to natural sciences and society.
Terminology
Abstract
Neural Networks are indispensable to natural sciences and society. Their impact extends from applications in public health to workforce productivity. Here, we introduce Modal Logic Neural Networks (MLNNs) -- an end-to-end differentiable logical neural network realisation of modal logic which evaluates a learnable truth function across possible-world semantics. This neural architecture handles para-consistency and inconsistency via a learnable world accessibility relation and valuation function. Because the modality is fixed by which frame axioms the relation satisfies rather than by the operator, one differentiable engine covers the epistemic, doxastic, deontic and temporal readings, with applications from verification of reactive and distributed systems to legal discourse and microeconomic utility models. In this paper, we introduce a model of differentiable Kripke semantics, and establish their soundness, convergence, and structural guarantees. We show four applications, in which the learned relation reads as a trust matrix, an operating-regime embedding with safety bounds, a temporal precedence order, and a recovered constraint graph.
Sources
- A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification
- A Modal Logic for Explaining some Graph Neural Networks
- Logical Neural Networks
- Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge
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