A new perspective on neural networks: using modal logic to complement linear algebra and explore how AI preserves meaning across layers.

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Modern neural networks are typically explained through optimization, statistics, and linear algebra, which describe how models learn and transform tensors. This article argues that modal logic offers a complementary mathematical framework for interpreting what those transformations represent. Using Layer Normalization, embeddings, attention, residual connections, and hidden representations as examples, it explores how different numerical states can preserve the same semantic structure and how neural networks may be viewed as progressively refining possible representations rather than simply performing numerical operations. Rather than replacing existing mathematics, modal logic provides another lens for studying representation learning, interpretability, and semantic invariants. This perspective may help explain why neural networks preserve meaning across layers and suggests new directions for understanding and potentially designing future AI architectures.