# Neurosymbolic Deep Learning Semantics

arXiv: https://arxiv.org/abs/2511.02825 · HTML: https://mlsanity.com/paper/2511.02825/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 13 of 13)

- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [A Logic for Expressing Log-Precision Transformers](https://mlsanity.com/paper/2210.02671/) (2022)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [Integrating Learning and Reasoning with Deep Logic Models](https://mlsanity.com/paper/1901.04195/) (2019)
- [Convolutional Neural Networks Are Not Invariant to Translation, but They Can Learn to Be](https://mlsanity.com/paper/2110.05861/) (2021)
- [Neuro-Symbolic Reasoning Shortcuts: Mitigation Strategies and their Limitations](https://mlsanity.com/paper/2303.12578/) (2023)
- [From Neural Networks to Logical Theories: The Correspondence between Fibring Modal Logics and Fibring Neural Networks](https://mlsanity.com/paper/2509.23912/) (2025)

## Abstract (arXiv)

Artificial Intelligence (AI) is a powerful new language of science as evidenced by recent Nobel Prizes in chemistry and physics that recognized contributions to AI applied to those areas. Yet, this new language lacks semantics, which makes AI's scientific discoveries unsatisfactory at best. With the purpose of uncovering new facts but also improving our understanding of the world, AI-based science requires formalization through a framework capable of translating insight into comprehensible scientific knowledge. In this paper, we argue that logic offers an adequate framework. In particular, we use logic in a neurosymbolic framework to offer a much needed semantics for deep learning, the neural network-based technology of current AI. Deep learning and neurosymbolic AI lack a general set of conditions to ensure that desirable properties are satisfied. Instead, there is a plethora of encoding and knowledge extraction approaches designed for particular cases. To rectify this, we introduced a framework for semantic encoding, making explicit the mapping between neural networks and logic, and characterizing the common ingredients of the various existing approaches. In this paper, we describe succinctly and exemplify how logical semantics and neural networks are linked through this framework, we review some of the most prominent approaches and techniques developed for neural encoding and knowledge extraction, provide a formal definition of our framework, and discuss some of the difficulties of identifying a semantic encoding in practice in light of analogous problems in the philosophy of mind.