ChaosBench-Logic

Dataset Summary

ChaosBench-Logic is a benchmark for evaluating large language models' (LLMs) capabilities in logical and symbolic reasoning about chaotic dynamical systems. The dataset tests whether LLMs can reason coherently about chaos theory concepts using a unified first-order logic (FOL) ontology.

Key Statistics

• Total Questions: 621
• Systems: 27 actively used (30 defined in repository)
• Predicates: 11 semantic predicates characterizing dynamical systems
• FOL Axioms: 6 axioms governing logical relationships
• Dialogues: 49 multi-turn dialogues with average 4.1 turns
• Task Types: 17 fine-grained types across 7 high-level categories

What Makes This Benchmark Unique

• Grounded in FOL Ontology: Every question has a unique ground truth derived from system annotations and explicit axioms
• Beyond Per-Item Accuracy: Measures dialogue coherence, contradiction rate, and axiom violations
• Scientific Domain: Tests precise reasoning about chaos vs. randomness, determinism, sensitivity, and other subtle distinctions
• Multi-Turn Consistency: Evaluates whether models maintain logically consistent beliefs across conversation turns

🔗 Links:

• GitHub Repository: https://github.com/11NOel11/ChaosBench-Logic - Evaluation code, scripts, and published results
• Paper/Documentation: See repository README for complete documentation and usage examples

Dataset Structure

Data Configurations

The dataset is available in three configurations:

1. default (420 items): Single-turn questions only (batches 1-6)
2. single_turn (420 items): Explicitly single-turn questions (same as default)
3. multi_turn (201 items): Multi-turn dialogue questions (batch 7)

Data Instances

Single-Turn Questions (default config)

Each record contains:

Field	Type	Description
id	string	Unique question identifier (q0001-q0420)
system_id	string or null	Dynamical system identifier (e.g., "lorenz63", "henon"); null for general ontology questions (159 records)
type	string	Task type (atomic, multi_hop, counterfactual, bias, etc.)
question	string	Natural language question about the system
ground_truth	string	Correct answer (YES/NO, TRUE/FALSE, or DISAPPEAR for counterfactuals)
template	string or null	Template identifier for reproducibility (may be null in batch 6)

Example:

{
  "id": "q0001",
  "system_id": "lorenz63",
  "type": "atomic",
  "question": "Is the Lorenz-63 system chaotic?",
  "ground_truth": "TRUE",
  "template": "A1"
}

Multi-Turn Dialogue (multi_turn config)

Each record contains the single-turn fields plus:

Field	Type	Description
dialogue_id	string	Dialogue identifier (links turns in the same conversation)
turn	integer	Turn number within dialogue (1-indexed)

Example:

{
  "id": "q0421",
  "dialogue_id": "dlg_001",
  "turn": 1,
  "system_id": "rossler",
  "type": "multi_turn",
  "question": "Is the Rössler system deterministic?",
  "ground_truth": "YES",
  "template": "dialogue_template_1"
}

Null system_id Values

159 questions (25.6% of dataset) have null system_id by design. These are general ontology/implication questions that test reasoning about FOL axioms rather than properties of specific systems.

Examples of null system_id questions:

• "If a system is chaotic, must it be deterministic?" (tests Axiom 1 understanding)
• "If a system has a positive Lyapunov exponent, must it exhibit sensitive dependence?" (multi-hop implication)
• "Can a system be both chaotic and random?" (tests mutual exclusion)

These questions evaluate whether models understand the logical structure of the ontology, not just factual knowledge about individual systems.

Distribution of null system_id across batches:

• Batch 1 (atomic/implication): 10 records
• Batch 2 (multi-hop/cross-system): 26 records
• Batch 3 (PDE/chem/bio): 25 records
• Batch 4 (maps): 26 records
• Batch 6 (bias probes): 47 records
• Batch 7 (multi-turn): 25 records

Data Splits

All questions are in the test split, as this is an evaluation benchmark (not for training).

Config	Split	Records	Description
default	test	420	Single-turn questions
single_turn	test	420	Single-turn questions (explicit)
multi_turn	test	201	Multi-turn dialogue (49 dialogues, 201 total turns)

Dataset Organization

The dataset is organized into 7 batches by task complexity and domain:

Batch	Filename	Records	Config	Description
1	batch1_atomic_implication.jsonl	50	default	Atomic facts and simple implications
2	batch2_multiHop_crossSystem.jsonl	60	default	Multi-hop reasoning and cross-system analogies
3	batch3_pde_chem_bio.jsonl	80	default	PDEs, chemical oscillators, biological systems
4	batch4_maps_advanced.jsonl	70	default	Discrete maps and advanced properties
5	batch5_counterfactual_high_difficulty.jsonl	70	default	Counterfactual reasoning and high-difficulty items
6	batch6_deep_bias_probes.jsonl	90	default	Bias probes and robustness tests
7	batch7_multiturn_advanced.jsonl	201	multi_turn	Multi-turn dialogues

Loading the Dataset

Load All (Recommended)

To evaluate on the full benchmark (621 questions), load both configurations:

from datasets import load_dataset

# Load single-turn questions
single_turn = load_dataset("11NOel11/ChaosBench-Logic", "single_turn")

# Load multi-turn dialogues  
multi_turn = load_dataset("11NOel11/ChaosBench-Logic", "multi_turn")

print(f"Single-turn: {len(single_turn['test'])} questions")
print(f"Multi-turn: {len(multi_turn['test'])} turns")

Load Default (Single-Turn Only)

from datasets import load_dataset

ds = load_dataset("11NOel11/ChaosBench-Logic")  # or "single_turn"
print(ds["test"][0])

Load Multi-Turn Only

from datasets import load_dataset

ds = load_dataset("11NOel11/ChaosBench-Logic", "multi_turn")
print(ds["test"][0])

Task Categories

1. Atomic Logical QA (76 items)

Single-predicate queries about individual systems.

Example: "Is the Hénon map chaotic?"

2. Multi-Hop Implication (40 items)

Reasoning chains requiring 2-3 inference steps through FOL axioms.

Example: "The logistic map at r=4 has a positive Lyapunov exponent. Does this imply sensitive dependence, and does that imply chaotic behavior?"

3. Cross-System Analogy (30 items)

Comparing properties across different dynamical systems.

Example: "Both the Lorenz-63 and Rössler systems are chaotic. Do they both have strange attractors?"

4. Counterfactual Reasoning (97 items)

Hypothetical scenarios with altered system parameters or properties.

Example: "If the Lorenz-63 system were stochastic instead of deterministic, would it still be considered chaotic?"

5. Bias Probes (119 items)

Template variations testing robustness to phrasing and presentation.

6. Multi-Turn Dialogues (213 items, 49 dialogues)

Sequential questions testing consistency over multiple conversation turns.

7. Compositional Synthesis (1 item)

Requires synthesizing novel concepts from multiple predicates (hardest task; 0% accuracy on all evaluated models).

Dynamical Systems

The dataset includes 30 dynamical system definitions in systems/*.json, with 27 actively used in the current evaluation:

Categories

• Chaotic ODEs: Lorenz-63, Rössler, Chen, Lorenz-84, Hindmarsh-Rose, FitzHugh-Nagumo, Rikitake dynamo
• Chaotic Maps: Logistic map (r=4), Hénon map, Arnold cat map, Ikeda map, Standard map, Baker's map
• Chemical Oscillators: Brusselator, Oregonator
• PDEs: Kuramoto-Sivashinsky, Sine-Gordon
• Biological Systems: Lotka-Volterra, Mackey-Glass
• Non-Chaotic Systems: Simple harmonic motion, damped driven pendulum, circle map (quasi-periodic)
• Stochastic: Ornstein-Uhlenbeck process

Each system JSON file contains:

• System ID and name
• Category (chaotic, periodic, quasi-periodic, stochastic)
• Governing equations
• Parameters
• Truth assignment for all 11 predicates

Ontology

11 Predicates

1. Chaotic: Exhibits deterministic chaos
2. Deterministic: Future uniquely determined by current state
3. PosLyap: Has positive Lyapunov exponent
4. Sensitive: Sensitive dependence on initial conditions
5. StrangeAttr: Has fractal strange attractor
6. PointUnpredictable: Precise point prediction impossible beyond finite horizon
7. StatPredictable: Statistical properties remain predictable
8. QuasiPeriodic: Almost periodic with incommensurate frequencies
9. Random: Contains intrinsic stochastic terms
10. FixedPointAttr: Converges to equilibrium point
11. Periodic: Exhibits perfectly repeating behavior

FOL Axioms (Forward Implications Only)

Axiom 1 (Chaotic systems):

Chaotic(s) → Deterministic(s) ∧ PosLyap(s) ∧ Sensitive(s)
           ∧ PointUnpredictable(s) ∧ StatPredictable(s)
Chaotic(s) → ¬Random(s) ∧ ¬Periodic(s) ∧ ¬QuasiPeriodic(s)

Note: StrangeAttr is not required for Chaotic because strange attractors are sufficient but not necessary for chaos (e.g., Arnold cat map is chaotic without an attractor).

Additional axioms govern Random, QuasiPeriodic, Periodic, and FixedPointAttr systems. See docs/ONTOLOGY.md for complete axiom system.

Intended Use

Primary Use Case

Evaluating LLM reasoning capabilities on:

• Logical consistency: Can models maintain coherent beliefs across multi-turn interactions?
• Scientific reasoning: Do models understand precise technical distinctions (chaos vs. randomness)?
• Multi-hop inference: Can models follow implication chains through FOL axioms?
• Robustness: Do models give consistent answers to paraphrased questions?

Evaluation Metrics

The benchmark supports multiple metrics beyond accuracy:

• Overall Accuracy: Per-item correctness
• Dialogue Accuracy: Fraction of dialogues where all turns are correct
• Contradiction Rate: Fraction of dialogues with at least one self-contradiction
• Axiom Violation Rate: Predictions that violate FOL axioms (e.g., Chaotic=YES, Deterministic=NO)

NOT Recommended For

• Training LLMs: This is an evaluation benchmark with only 621 items
• Production question-answering: Questions are curated for diagnostic purposes, not real-world scenarios

Benchmark Results

Initial evaluation of frontier LLMs (GPT-4, Claude-3.5, Gemini-2.0, LLaMA-3-70B) shows:

• High per-item accuracy: 88-94%
• Low dialogue coherence: 53-75% dialogue accuracy
• High contradiction rates: 88-92% of dialogues contain at least one contradiction
• Compositional failure: 0% on all models

Key Finding: Models exhibit "locally correct, globally incoherent" behavior—answering individual questions correctly while failing to maintain consistent logical beliefs across conversations.

See docs/RESULTS.md for detailed analysis and published_results/ in the GitHub repository for full evaluation artifacts.

Limitations

1. Limited compositional examples: Only 1 compositional item in current version
2. Structural/adversarial items: Small sample sizes (2-3 items) limit statistical significance
3. Classical systems: Focuses on well-studied, low-dimensional systems
4. English only: All questions in English
5. Binary answers: Most questions have YES/NO or TRUE/FALSE answers
6. Coverage: 1 item (q0621) has missing ground truth and is excluded from evaluation

Ethics & Safety

• No PII: Dataset contains no personally identifiable information
• Synthetic/Curated: All questions manually curated from templates
• Scientific Content: Domain is mathematical/scientific; no harmful content
• Evaluation Only: Designed for model evaluation, not real-world decision-making

License

• Dataset License: CC BY 4.0 (see LICENSE_DATA)
• Code License: Evaluation code and scripts in the GitHub repository are under MIT License

Citation

If you use ChaosBench-Logic in your research, please cite:

@software{thomas2025chaosbench,
  author = {Thomas, Noel},
  title = {ChaosBench-Logic: A Benchmark for Logical and Symbolic Reasoning on Chaotic Dynamical Systems},
  year = {2025},
  publisher = {Hugging Face},
  url = {https://huggingface.co/datasets/11NOel11/ChaosBench-Logic},
  note = {GitHub: https://github.com/11NOel11/ChaosBench-Logic}
}

Also available in CITATION.cff format.

Links

• GitHub Repository: https://github.com/11NOel11/ChaosBench-Logic
• Evaluation Pipeline: Complete evaluation code, normalization scripts, and reproducible configs
• Published Results: Detailed per-item predictions and metrics for all evaluated models
• Documentation:
  • Dataset Schema
  • Ontology & Axioms
  • Detailed Results

Contact

• Author: Noel Thomas (MBZUAI)
• Issues: GitHub Issues

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Note: This dataset is part of ongoing research on evaluating and improving LLM reasoning capabilities in scientific domains. Feedback and contributions are welcome via the GitHub repository.