# Differentiable Inductive Logic Programming for Structured Examples

arXiv: https://arxiv.org/abs/2103.01719 · HTML: https://mlsanity.com/paper/2103.01719/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 9 of 9)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Synthesizing Datalog Programs Using Numerical Relaxation](https://mlsanity.com/paper/1906.00163/) (2019)
- [Relational Neural Machines](https://mlsanity.com/paper/2002.02193/) (2020)
- [Structure Learning of Probabilistic Logic Programs by Searching the Clause Space](https://mlsanity.com/paper/1309.2080/) (2013)

## Built on by (most cited first, 26 of 26)

- [Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstraction](https://mlsanity.com/paper/2306.01439/) (2023)
- [Neuro-Symbolic Forward Reasoning](https://mlsanity.com/paper/2110.09383/) (2021)
- [PyReason: Software for Open World Temporal Logic](https://mlsanity.com/paper/2302.13482/) (2023)
- [BlendRL: A Framework for Merging Symbolic and Neural Policy Learning](https://mlsanity.com/paper/2410.11689/) (2024)
- [Neuro-Symbolic Learning of Answer Set Programs from Raw Data](https://mlsanity.com/paper/2205.12735/) (2022)
- [Learning Differentiable Logic Programs for Abstract Visual Reasoning](https://mlsanity.com/paper/2307.00928/) (2023)
- [pix2rule: End-to-end Neuro-symbolic Rule Learning](https://mlsanity.com/paper/2106.07487/) (2021)
- [Extensions to Generalized Annotated Logic and an Equivalent Neural Architecture](https://mlsanity.com/paper/2302.12195/) (2023)
- [EXPIL: Explanatory Predicate Invention for Learning in Games](https://mlsanity.com/paper/2406.06107/) (2024)
- [Compositional Generalization Across Distributional Shifts with Sparse Tree Operations](https://mlsanity.com/paper/2412.14076/) (2024)
- [Neural Meta-Symbolic Reasoning and Learning](https://mlsanity.com/paper/2211.11650/) (2022)
- [Using Logic Programming and Kernel-Grouping for Improving Interpretability of Convolutional Neural Networks](https://mlsanity.com/paper/2310.13073/) (2023)
- [Neural DNF-MT: A Neuro-symbolic Approach for Learning Interpretable and Editable Policies](https://mlsanity.com/paper/2501.03888/) (2025)
- [Learning from Less: Guiding Deep Reinforcement Learning with Differentiable Symbolic Planning](https://mlsanity.com/paper/2505.11661/) (2025)
- [NeSyFOLD: Neurosymbolic Framework for Interpretable Image Classification](https://mlsanity.com/paper/2301.12667/) (2023)
- [Inductive Learning of Robot Task Knowledge from Raw Data and Online Expert Feedback](https://mlsanity.com/paper/2501.07507/) (2025)
- [Differentiable Inductive Logic Programming in High-Dimensional Space](https://mlsanity.com/paper/2208.06652/) (2022)
- [OCALM: Object-Centric Assessment with Language Models](https://mlsanity.com/paper/2406.16748/) (2024)
- [Neuro-symbolic Weak Supervision: Theory and Semantics](https://mlsanity.com/paper/2503.18509/) (2025)
- [Disentangling Neural Disjunctive Normal Form Models](https://mlsanity.com/paper/2507.10546/) (2025)
- [Lattice Annotated Temporal (LAT) Logic for Non-Markovian Reasoning](https://mlsanity.com/paper/2509.02958/) (2025)
- [Satisfiability Modulo Theory Meets Inductive Logic Programming](https://mlsanity.com/paper/2512.12918/) (2025)
- [Boosting deep Reinforcement Learning using pretraining with Logical Options](https://mlsanity.com/paper/2603.06565/) (2026)
- [GRAIL: Autonomous Concept Grounding for Neuro-Symbolic Reinforcement Learning](https://mlsanity.com/paper/2604.16871/) (2026)
- [ANDRE: An Attention-based Neuro-symbolic Differentiable Rule Extractor for Inductive Logic Programming](https://mlsanity.com/paper/2605.04193/) (2026)
- [Weakly supervised concept Bottleneck Learning for Robust Two stage Object centric visual reasoning](https://mlsanity.com/paper/2608.22584/) (2026)

## Abstract (arXiv)

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire reasonable solutions from noisy datasets. However, this framework severely limits expressions for solutions, e.g., no function symbols are allowed, and the shapes of clauses are fixed. As a result, the framework cannot deal with structured examples. Therefore we propose a new framework to learn logic programs from noisy and structured examples, including the following contributions. First, we propose an adaptive clause search method by looking through structured space, which is defined by the generality of the clauses, to yield an efficient search space for differentiable solvers. Second, we propose for ground atoms an enumeration algorithm, which determines a necessary and sufficient set of ground atoms to perform differentiable inference functions. Finally, we propose a new method to compose logic programs softly, enabling the system to deal with complex programs consisting of several clauses. Our experiments show that our new framework can learn logic programs from noisy and structured examples, such as sequences or trees. Our framework can be scaled to deal with complex programs that consist of several clauses with function symbols.