# Solving Bongard Problems with a Visual Language and Pragmatic Reasoning

arXiv: https://arxiv.org/abs/1804.04452 · HTML: https://mlsanity.com/paper/1804.04452/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2018.

## Built on by (most cited first, 21 of 21)

- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [VASR: Visual Analogies of Situation Recognition](https://mlsanity.com/paper/2212.04542/) (2022)
- [MEWL: Few-shot multimodal word learning with referential uncertainty](https://mlsanity.com/paper/2306.00503/) (2023)
- [Bongard in Wonderland: Visual Puzzles that Still Make AI Go Mad?](https://mlsanity.com/paper/2410.19546/) (2024)
- [Reasoning Limitations of Multimodal Large Language Models. A Case Study of Bongard Problems](https://mlsanity.com/paper/2411.01173/) (2024)
- [Neural networks for abstraction and reasoning: Towards broad generalization in machines](https://mlsanity.com/paper/2402.03507/) (2024)
- [Are Deep Neural Networks Adequate Behavioural Models of Human Visual Perception?](https://mlsanity.com/paper/2305.17023/) (2023)
- [Benchmarking World-Model Learning with Environment-Level Queries](https://mlsanity.com/paper/2510.19788/) (2025)
- [Multi-Viewpoint and Multi-Evaluation with Felicitous Inductive Bias Boost Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2210.14914/) (2022)
- [Budgeted Online Continual Learning by Adaptive Layer Freezing and Frequency-based Sampling](https://mlsanity.com/paper/2410.15143/) (2024)
- [Bongard-RWR+: Real-World Representations of Fine-Grained Concepts in Bongard Problems](https://mlsanity.com/paper/2508.12026/) (2025)
- [Using Program Synthesis and Inductive Logic Programming to solve Bongard Problems](https://mlsanity.com/paper/2110.09947/) (2021)
- [Geoclidean: Few-Shot Generalization in Euclidean Geometry](https://mlsanity.com/paper/2211.16663/) (2022)
- [Towards a Solution to Bongard Problems: A Causal Approach](https://mlsanity.com/paper/2206.07196/) (2022)
- [Im-Promptu: In-Context Composition from Image Prompts](https://mlsanity.com/paper/2305.17262/) (2023)
- [Who's the Best Detective? LLMs vs. MLs in Detecting Incoherent Fourth Grade Math Answers](https://mlsanity.com/paper/2304.11257/) (2023)
- [Support-Set Context Matters for Bongard Problems](https://mlsanity.com/paper/2309.03468/) (2023)
- [Triple-CFN: Separating Concepts and Features Enhances Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2403.03190/) (2024)
- [Funny-Valen-Tine: Planning Solution Distribution Enhances Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2407.02688/) (2024)
- [D4C: Improving Negative Example Quality to Enhance Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2403.03452/) (2024)
- [Towards a universal language of concepts: A survey](https://mlsanity.com/paper/2609.04528/) (2026)

## Abstract (arXiv)

More than 50 years ago Bongard introduced 100 visual concept learning problems as a testbed for intelligent vision systems. These problems are now known as Bongard problems. Although they are well known in the cognitive science and AI communities only moderate progress has been made towards building systems that can solve a substantial subset of them. In the system presented here, visual features are extracted through image processing and then translated into a symbolic visual vocabulary. We introduce a formal language that allows representing complex visual concepts based on this vocabulary. Using this language and Bayesian inference, complex visual concepts can be induced from the examples that are provided in each Bongard problem. Contrary to other concept learning problems the examples from which concepts are induced are not random in Bongard problems, instead they are carefully chosen to communicate the concept, hence requiring pragmatic reasoning. Taking pragmatic reasoning into account we find good agreement between the concepts with high posterior probability and the solutions formulated by Bongard himself. While this approach is far from solving all Bongard problems, it solves the biggest fraction yet.