---
language:
- en
- zh
license: cc-by-4.0
size_categories:
- 1K<n<10K
task_categories:
- question-answering
- multiple-choice
pretty_name: LogiHard-2k
tags:
- logical-reasoning
- benchmark
- evaluation
- combinatorial-logic
- irt-cat
---

# LogiHard-2k Dataset Card

## Dataset Description

LogiHard-2k is a native logical reasoning benchmark constructed from high-stakes human examinations. It comprises 2,000 rigorously stratified multiple-choice questions designed to evaluate combinatorial propositional reasoning in large language models.

- **Curated atomic questions (LogiHard-Base)**: 1,461 items requiring 0-order natural language inference.
- **Combinatorial questions (LogiHard-C)**: 539 items deterministically transformed into 2-order propositional judgment tasks via the LogiHard protocol.

Each item includes 9-dimensional cognitive features, IRT 3PL parameters (discrimination, difficulty, pseudo-guessing), source attribution, and reasoning type labels.

## Dataset Structure

```json
{
  "id": "string",
  "subset": "base | combinatorial",
  "tier": "Easy | Medium | Hard | Expert | null",
  "language": "en | zh",
  "source": "string",
  "context": "string",
  "options": ["string"],
  "correct_answer": ["string"],
  "propositional_statements": ["string"],
  "formulas": ["string"],
  "cognitive_features": {
    "oscillation_points": "float",
    "logic_density": "float",
    "abductive_depth": "float",
    "dialectic_tension": "float",
    "dimensional_awareness": "float",
    "inference_chain_length": "float",
    "uncertainty_entropy": "float",
    "pivot_count": "float",
    "conceptual_abstraction": "float"
  },
  "gold_score": "float",
  "irt_3pl": {
    "a": "float",
    "b": "float",
    "c": "float"
  },
  "reasoning_type": "syllogistic | analogical | propositional"
}
```

## Data Splits

| Split | Count | Description |
|-------|-------|-------------|
| `base` | 1,461 | Atomic multiple-choice questions (single-select) |
| `combinatorial` | 539 | Propositional combinatorial variants (multi-select) |
| — Easy | 108 | Exactness only |
| — Medium | 215 | + Disjunction |
| — Hard | 162 | + Negation |
| — Expert | 54 | + Compound negations |

## Source Data

Questions were curated from publicly available high-stakes examination preparation materials:
- Chinese Civil Service Examination
- LSAT (Law School Admission Test)
- GMAT (Graduate Management Admission Test)
- IBPS (Institute of Banking Personnel Selection)
- CAT (Common Admission Test)
- Raven's Progressive Matrices

**Languages**: 45% English, 55% Chinese.

## Annotations

Cognitive features were extracted via automated pattern-matching from long chain-of-thought reasoning traces generated by a frontier reasoning model (temperature 1.0, max 16,000 tokens). The Gold Score aggregates these 9 metrics via a weighted linear combination with z-normalization and logical-fallacy penalization.

IRT 3PL parameters were calibrated empirically from cognitive features:
- Difficulty $b_j$ derived from Gold Score, logic density, and reasoning length.
- Discrimination $a_j$ mapped from operator complexity tier.

## Bias, Risks, and Limitations

- **Language imbalance**: 55% Chinese and 45% English; typologically distant languages are not represented.
- **Cultural scope**: Sources are concentrated in East Asian and North American examination traditions.
- **Model dependency**: Cognitive scoring relies on a single reasoning model's trace patterns; rankings may not generalize to other model families.
- **No PII**: All items are abstract logical reasoning problems; no personal or sensitive information is present.
- **Domain restriction**: The benchmark isolates pure logical deduction and does not assess perceptual reasoning, procedural execution, or open-ended generation.

## Intended Use

LogiHard-2k is intended for:
- Evaluating combinatorial reasoning capabilities of large language models.
- Calibrating difficulty in computerized adaptive testing (CAT) frameworks.
- Research on validity-guaranteed benchmark hardening and contamination resistance.

It is **not** intended for high-stakes human assessment, hiring, or admissions screening without domain-specific validation.

## Citation

If you use this dataset, please cite the associated paper (citation to be added upon publication).

## License

This dataset is released under [CC-BY 4.0](https://creativecommons.org/licenses/by/4.0/).