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README.md

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----
-license: cc-by-4.0
----
+---
+dataset_info:
+- config_name: v1-All
+  features:
+  - name: id
+    dtype: int64
+  - name: prompt
+    dtype: string
+  - name: ground-truth rule
+    dtype: string
+  - name: validation program
+    dtype: string
+  - name: symbols
+    dtype: string
+  - name: curriculum level
+    dtype: int64
+  - name: curriculum tier
+    dtype: string
+  - name: rule sampling
+    dtype: string
+  - name: rule complexity
+    dtype: string
+  - name: background sampling
+    dtype: string
+  - name: problem size
+    dtype: int64
+  - name: vocabulary predicates
+    dtype: int64
+  - name: vocabulary car constants
+    dtype: string
+  splits:
+  - name: train
+    num_bytes: 779520787
+    num_examples: 18053
+  - name: validation
+    num_bytes: 7884798
+    num_examples: 200
+  - name: test
+    num_bytes: 39057386
+    num_examples: 1000
+  download_size: 181773027
+  dataset_size: 826462971
+- config_name: v1-Basic
+  features:
+  - name: id
+    dtype: int64
+  - name: prompt
+    dtype: string
+  - name: ground-truth rule
+    dtype: string
+  - name: validation program
+    dtype: string
+  - name: symbols
+    dtype: string
+  - name: curriculum level
+    dtype: int64
+  - name: curriculum tier
+    dtype: string
+  - name: rule sampling
+    dtype: string
+  - name: rule complexity
+    dtype: string
+  - name: background sampling
+    dtype: string
+  - name: problem size
+    dtype: int64
+  - name: vocabulary predicates
+    dtype: int64
+  - name: vocabulary car constants
+    dtype: string
+  splits:
+  - name: train
+    num_bytes: 12702464
+    num_examples: 3053
+  - name: validation
+    num_bytes: 177614
+    num_examples: 50
+  - name: test
+    num_bytes: 884062
+    num_examples: 250
+  download_size: 1750029
+  dataset_size: 13764140
+- config_name: v1-Easy
+  features:
+  - name: id
+    dtype: int64
+  - name: prompt
+    dtype: string
+  - name: ground-truth rule
+    dtype: string
+  - name: validation program
+    dtype: string
+  - name: symbols
+    dtype: string
+  - name: curriculum level
+    dtype: int64
+  - name: curriculum tier
+    dtype: string
+  - name: rule sampling
+    dtype: string
+  - name: rule complexity
+    dtype: string
+  - name: background sampling
+    dtype: string
+  - name: problem size
+    dtype: int64
+  - name: vocabulary predicates
+    dtype: int64
+  - name: vocabulary car constants
+    dtype: string
+  splits:
+  - name: train
+    num_bytes: 46113619
+    num_examples: 5000
+  - name: validation
+    num_bytes: 461812
+    num_examples: 50
+  - name: test
+    num_bytes: 2308963
+    num_examples: 250
+  download_size: 8434162
+  dataset_size: 48884394
+- config_name: v1-Hard
+  features:
+  - name: id
+    dtype: int64
+  - name: prompt
+    dtype: string
+  - name: ground-truth rule
+    dtype: string
+  - name: validation program
+    dtype: string
+  - name: symbols
+    dtype: string
+  - name: curriculum level
+    dtype: int64
+  - name: curriculum tier
+    dtype: string
+  - name: rule sampling
+    dtype: string
+  - name: rule complexity
+    dtype: string
+  - name: background sampling
+    dtype: string
+  - name: problem size
+    dtype: int64
+  - name: vocabulary predicates
+    dtype: int64
+  - name: vocabulary car constants
+    dtype: string
+  splits:
+  - name: train
+    num_bytes: 511706880
+    num_examples: 5000
+  - name: validation
+    num_bytes: 5149291
+    num_examples: 50
+  - name: test
+    num_bytes: 25522109
+    num_examples: 250
+  download_size: 123687304
+  dataset_size: 542378280
+- config_name: v1-Medium
+  features:
+  - name: id
+    dtype: int64
+  - name: prompt
+    dtype: string
+  - name: ground-truth rule
+    dtype: string
+  - name: validation program
+    dtype: string
+  - name: symbols
+    dtype: string
+  - name: curriculum level
+    dtype: int64
+  - name: curriculum tier
+    dtype: string
+  - name: rule sampling
+    dtype: string
+  - name: rule complexity
+    dtype: string
+  - name: background sampling
+    dtype: string
+  - name: problem size
+    dtype: int64
+  - name: vocabulary predicates
+    dtype: int64
+  - name: vocabulary car constants
+    dtype: string
+  splits:
+  - name: train
+    num_bytes: 208997824
+    num_examples: 5000
+  - name: validation
+    num_bytes: 2096081
+    num_examples: 50
+  - name: test
+    num_bytes: 10342252
+    num_examples: 250
+  download_size: 48068673
+  dataset_size: 221436157
+configs:
+- config_name: v1-All
+  data_files:
+  - split: train
+    path: v1-All/train-*
+  - split: validation
+    path: v1-All/validation-*
+  - split: test
+    path: v1-All/test-*
+- config_name: v1-Basic
+  data_files:
+  - split: train
+    path: v1-Basic/train-*
+  - split: validation
+    path: v1-Basic/validation-*
+  - split: test
+    path: v1-Basic/test-*
+- config_name: v1-Easy
+  data_files:
+  - split: train
+    path: v1-Easy/train-*
+  - split: validation
+    path: v1-Easy/validation-*
+  - split: test
+    path: v1-Easy/test-*
+- config_name: v1-Hard
+  data_files:
+  - split: train
+    path: v1-Hard/train-*
+  - split: validation
+    path: v1-Hard/validation-*
+  - split: test
+    path: v1-Hard/test-*
+- config_name: v1-Medium
+  data_files:
+  - split: train
+    path: v1-Medium/train-*
+  - split: validation
+    path: v1-Medium/validation-*
+  - split: test
+    path: v1-Medium/test-*
+license: cc-by-4.0
+language:
+- en
+tags:
+- logic
+- inductive
+- reasoning
+pretty_name: Scalable Logical Reasoning Benchmark
+size_categories:
+- 1K<n<10K
+---
+
+<div style="display: flex; justify-content: flex-start;"><img src="https://raw.githubusercontent.com/ml-research/ScalableLogicalReasoning/master/images/SLR-Bench2.jpg" alt="Preview" style="width: 40vw; min-width: 300px; max-width: 600px;"> </div>
+
+## Dataset Description
+- **Language(s) (NLP):** English
+- **Point of Contact:** [Lukas Helff](mailto:helff@cs.tu-darmstadt.de)
+- **License:** [CC BY](https://creativecommons.org/licenses/by/4.0/)
+
+# SLR-Bench: Scalable Logical Reasoning Benchmark for LLMs
+[![Eval & Reward Model](https://img.shields.io/badge/%F0%9F%A4%96%20Reward%20Model-HF-blueviolet)](https://huggingface.co/spaces/AIML-TUDA/VerifiableRewardsForScalableLogicalReasoning)
+[![GitHub](https://img.shields.io/badge/Code-GitHub-blue)](https://github.com/ml-research/ScalableLogicalReasoning)
+[![arXiv](https://img.shields.io/badge/arXiv-2506.15787-b31b1b.svg)](https://arxiv.org/abs/2506.15787)
+
+
+
+> **🆕 August 2025: Build your own Reasoning Problems with Verifiable Rewards. Source Code is now available!** 👉 [Generate your own Reasoning Task](https://github.com/ml-research/ScalableLogicalReasoning)
+
+> **🆕 June 2024: Evaluation & RLVR Reward Model Released!** 👉 [Demo on Hugging Face Spaces](https://huggingface.co/spaces/AIML-TUDA/VerifiableRewardsForScalableLogicalReasoning)
+
+**SLR-Bench** is a scalable, fully-automated benchmark designed to systematically evaluate and train Large Language Models (LLMs) in logical reasoning via inductive logic programming (ILP) tasks. Built with the [SLR framework](https://github.com/ml-research/ScalableLogicalReasoning), SLR-Bench presents LLMs with open-ended logic problems of progressively increasing difficulty, assesses their solutions via deterministic symbolic evaluation, and supports both curriculum learning and systematic measurement of reasoning performance.
+
+
+## DS Overview
+- **Curriculum:** 20 complexity levels, grouped into 4 broad tiers (basic, easy, medium, hard)
+- **Tasks:** >19,000, each comprising: A *natural language* prompt, an executable *validation program* for automatic evaluation, and a *latent ground-truth rule*.
+- **Application:** SLR-Bench can used to evaluate conventional and reasoning LLMs (e.g., GPT-4o, Llama-3, Gemini, DeepSeek-R1) and to train models via curriculum learning.
+
+
+## Key Features of SLR
+
+- 🔨 **Automatic Task Generation:** Synthesize new inductive reasoning tasks with controllable complexity, novel logic rules, and natural language prompts—no need for human annotation.
+- 🧩 **Programmable & Scalable:** Specify your own logic vocabulary, grammar, rule distributions, and task parameters; supports curriculum-style scaling and out-of-distribution task creation.
+- 🧠 **Symbolic, Automated Evaluation:** Deterministically verify LLM outputs via the validation program, not MCQA, LLM judge, or exact matching.
+- 📈 **Curriculum Learning:** Use SLR-Bench, a structured 20-level benchmark, for evaluating and training models across a span of logical challenges.
+
+---
+
+## Quick Start
+
+### Loading the Dataset
+```python
+from datasets import load_dataset
+# Load SLR-Bench test split
+ds = load_dataset("AIML-TUDA/SLR-Bench", "v1-All", split="test")
+```
+### Evaluate using SLR-Bench
+Requires the [`evaluate`](https://huggingface.co/docs/evaluate/) library and a Prolog interpreter installed on your system (e.g., [SWI-Prolog](https://www.swi-prolog.org/)).
+Install the required dependencies via:
+
+```bash
+pip install evaluate
+sudo apt-get install swi-prolog
+```
+
+#### Example Usage
+
+```python
+from evaluate import load
+symbolic_judge = load("AIML-TUDA/VerifiableRewardsForScalableLogicalReasoning")
+rules = ds["ground-truth rule"]  # For demo only—use model predictions in practice
+references = [
+    {
+        "validation_program": p,
+        "evaluation_config": {
+            "positive_predicate": "eastbound",
+            "negative_predicate": "westbound"
+        }
+    } for p in ds["validation program"]
+]
+
+results = symbolic_judge.compute(predictions=rules, references=references)
+print(results)
+```
+
+*Note: For real evaluation, replace `rules` with your model's predicted rules. Here, we use ground-truth rules for demonstration only.*
+
+Example results:
+```python
+{'accuracy': 1.0,
+ 'partial_score': 1.0,
+ 'syntax_score': 1.0,
+ 'detailed_results': [{'is_correct': True,'partial_score': 1.0,'syntax_valid': True,'error': None,'exec_time1': 0.014362812042236328},
+                      {'is_correct': True,'partial_score': 1.0,'syntax_valid': True,'error': None,'exec_time1': 0.012364625930786133}]
+}
+```
+
+---
+
+## **Dataset Columns**
+
+| Column Name                 | Type      | Description                                                                                                                 |
+|-----------------------------|-----------|-----------------------------------------------------------------------------------------------------------------------------|
+| **id**                      | `int64`   | Unique identifier for each dataset entry (row).                                                                             |
+| **prompt**                  | `string`  | The instruction prompt of the logical reasoning task.                                                                       |
+| **ground-truth rule**       | `string`  | The latent logical rule that solves the given task.                                                                         |
+| **validation program**      | `string`  | The executable logic program used by the symbolic judge to verify candidate model solutions for the task.                   |
+| **symbols**                 | `string`  | Symbolic representation of the bckground knowledge                                                                          |
+| **curriculum level**        | `int64`   | The specific level (1-20) in the SLR-Bench curriculum that this task belongs to, reflecting difficulty.                     |
+| **curriculum tier**         | `string`  | The broader difficulty tier grouping multiple levels (e.g., "basic", "easy", "medium", "hard").                             |
+| **rule sampling**           | `string`  | The policy or method used to generate the ground-truth rule (e.g., "uniform", "llm-guided").                                |
+| **rule complexity**         | `string`  | The length of the logic rule, counting the number of used predicates without the has_car predicate.                         |
+| **background sampling**     | `string`  | The policy used to sample background knowledge for the task (e.g., "mirror", "uniform").                                    |
+| **problem size**            | `int64`   | Total number of labeled examples (positive + negative) provided in the task instance.                                       |
+| **vocabulary predicates**   | `int64`   | Number of unique predicate symbols available in the vocabulary for constructing rules and background knowledge.             |
+| **vocabulary car constants**| `string`  | List of car constant symbols (e.g., "car1", "car2", ...) available in the vocabulary for the task. |
+
+
+---
+## SLR-Bench Curriculum
+
+| Stage     | Level | #Consts | #Preds | κ (Problem Size) | Bπ (Background) | Rlen (Rule len) | Rsample (Rule Sample) | Comb. Size       |
+| --------- | ----- | ------- | ------ | ---------------- | --------------- | --------------- | --------------------- | ---------------- |
+| **Basic** | 1     | 1       | 5      | 2                | mirror          | 1               | uniform               | 10³              |
+|           | 2     | 1       | 5      | 2                | mirror          | 1-2             | uniform               | 10³              |
+|           | 3     | 1       | 5      | 4                | mirror          | 1-2             | uniform               | 10⁵              |
+|           | 4     | 2       | 5      | 4                | mirror          | 1-2             | uniform               | 10¹⁰             |
+|           | 5     | 2       | 5      | 6                | mirror          | 1-2             | uniform               | 10¹⁶             |
+| **Easy**  | 6     | 2       | 5      | 6                | uniform         | 1-2             | uniform/llm           | 10¹⁶             |
+|           | 7     | 2       | 6      | 6                | uniform         | 1-2             | uniform/llm           | 10²⁴             |
+|           | 8     | 2-3     | 6      | 8                | uniform         | 1-2             | uniform/llm           | 10³²             |
+|           | 9     | 2-3     | 6      | 10               | uniform         | 2-3             | uniform/llm           | 10⁴⁰             |
+|           | 10    | 2-3     | 7      | 12               | uniform         | 2-3             | uniform/llm           | 10⁵⁵             |
+| **Medium**| 11    | 2-4     | 7      | 14               | uniform         | 2-3             | uniform/llm           | 10⁶⁵             |
+|           | 12    | 2-4     | 9      | 16               | uniform         | 3-4             | uniform/llm           | 10¹²⁰            |
+|           | 13    | 4-6     | 9      | 18               | uniform         | 3-4             | uniform/llm           | 10²⁷¹            |
+|           | 14    | 4-6     | 9      | 20               | uniform         | 4-5             | uniform/llm           | 10³⁰⁰            |
+|           | 15    | 4-6     | 9      | 22               | uniform         | 4-5             | uniform/llm           | 10³³⁰            |
+| **Hard**  | 16    | 5-6     | 10     | 24               | uniform         | 4-5             | uniform/llm           | 10⁵⁰⁷            |
+|           | 17    | 5-6     | 10     | 26               | uniform         | 4-5             | uniform/llm           | 10⁵⁴⁹            |
+|           | 18    | 5-6     | 12     | 28               | uniform         | 4-5             | uniform/llm           | 10⁸⁰⁵            |
+|           | 19    | 5-6     | 12     | 30               | uniform         | 5               | uniform/llm           | 10⁸⁶¹            |
+|           | 20    | 5-6     | 12     | 32               | uniform         | 5               | uniform/llm           | 10⁹¹⁹            |
+
+*SLR-Bench Curriculum: level-wise configurations, detailing language and task parameters for each difficulty stage. Language complexity is systematically increased by expanding the number of car constants and predicates. Task configuration grows via adapting problem size, background sampling, rule length, and rule sampling strategy. The final column reports the approximate combinatorial size of unique tasks available at each level.*
+
+---
+
+## Example
+
+```
+You are a train classifier who is observing trains that are traveling either east- or westbound. Each train is composed of one or more cars, and each car is characterized by a set of properties, represented as ground atoms over a fixed set of predicates. The direction (eastbound or westbound) of a train is to be determined from its composition. To describe the trains we define a set of predicates and grounding domains:
+
+'has_car(Train, Car)': Specifies that 'Car' is part of the train 'Train'.
+'car_num(Car, CarNumber)': Specifies the position of the car within its train. 'CarNumber' is a positive integer.
+'car_color(Car, Color)': Specifies the color of the car. 'Color' can be 'red', 'blue', 'green', 'yellow', or 'white'.
+'car_len(Car, Length)': Specifies the length of the car. 'Length' can be either 'short' or 'long'.
+'has_wall(Car, WallType)': Specifies the wall type of a car. 'WallType' can be either 'full' or a 'railing'.
+
+You are provided with positive and negative examples in the form of eastbound(t) or westbound(t) for each train t, together with background knowledge consisting of ground facts over the above predicates which describe its composition.
+
+eastbound(train0).
+has_car(train0, car0_1).								 		
+car_num(car0_1, 1).          				 					   
+car_color(car0_1, red).										 					   
+car_len(car0_1, long).										 					    
+has_wall(car0_1, railing).
+
+westbound(train1).
+has_car(train1, car1_1).
+car_num(car1_1, 1).
+car_color(car1_1, red).
+car_len(car1_1, short).
+has_wall(car1_1, railing).
+
+Your task is to formulate a hypothesis, i.e. a prolog rule of the form 'eastbound(Train) :- Body.' that correctly distinguishes eastbound from westbound trains. The hypothesis must be true for all positive examples (i.e., eastbound trains) and false for all negative examples (i.e., westbound trains). Aim to find the shortest correct rule, that is, one that uses the fewest possible body literals subject to the prior constraints. Your rule must use only predicates defined above and must perfectly separate eastbound from westbound trains.
+```
+
+Solution:
+```prolog
+eastbound(Train) :- has_car(Train,Car), car_len(Car,long)
+```
+
+---
+
+
+## Licensing Information
+
+SLR-Bench is made available under the [CC BY](https://creativecommons.org/licenses/by/4.0/) license.
+
+
+## Citation
+
+If you use this dataset or framework, please cite:
+
+```bibtex
+@incollection{helff2025slrautomatedsynthesisscalable,
+      title={SLR: Automated Synthesis for Scalable Logical Reasoning}, 
+      author={Lukas Helff and Ahmad Omar and Felix Friedrich and Antonia Wüst and Hikaru Shindo and Rupert Mitchell and Tim Woydt and Patrick Schramowski and Wolfgang Stammer and Kristian Kersting},
+      year={2025},
+      booktitle ={Working Notes of the NeurIPS Workshop on Foundations of Reasoning in Language Models},
+      url={https://arxiv.org/abs/2506.15787}, 
+}
+```
+
+---

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