| --- |
| 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/). |
