{
 "body": "\nPart of the [MMLU](mmlu.md) family.\n\n## What it measures\n\nPropositional and predicate logic, validity and inference rules, as taught in a philosophy department. Like the rest of MMLU, each question gives four labelled options and the model is\ngraded on picking the single correct one, typically evaluated 5-shot. The benchmark's own\ncategorisation places this subject in the \"philosophy\" subcategory, within the \"humanities\" group of\nMMLU's four broad areas (STEM, humanities, social sciences, and other).\n\n## Reading the numbers\n\nThe Hugging Face mirror of this subject holds 126 test questions (used for scoring), plus 14\nvalidation and 5 dev questions for few-shot prompting. With well under a thousand items, a\nhandful of questions can shift the reported percentage by several points, so treat small\ndifferences between models on this subject alone as noisy rather than meaningful. Read it against\na model's overall MMLU score and against other subjects in the \"humanities\" group rather than in\nisolation, and see\nthe [MMLU](mmlu.md) family page for the shared scoring protocol, saturation and contamination notes\nthat apply here too.\n",
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 ],
 "page": {
  "category": "knowledge",
  "dataset": {
   "languages": [
    "en"
   ],
   "license": "MIT",
   "modalities": [
    "text"
   ],
   "public_test_set": true,
   "size": 126,
   "size_note": "126 test questions (used for scoring), plus 14 validation and 5 dev (few-shot prompt) questions, per the Hugging Face parquet mirror of cais/mmlu, config 'formal_logic'.",
   "splits": "dev (5), validation (14), test (126)",
   "url": "https://huggingface.co/datasets/cais/mmlu"
  },
  "freshness": {
   "researched": "2026-09-07",
   "researched_by": "sonnet-5 agent, batch 1, slice A"
  },
  "harness": {
   "helm": "mmlu:subject=formal_logic",
   "lm_eval": "mmlu_formal_logic",
   "other": "hendrycksTest-formal_logic in the pre-2024 Open LLM Leaderboard v1 harness fork"
  },
  "id": "mmlu_formal_logic",
  "leaderboard_url": "https://github.com/hendrycks/test",
  "lineage": {
   "family": "mmlu"
  },
  "measures": "Propositional and predicate logic, validity and inference rules, as taught in a philosophy department. Questions are four-option multiple-choice, drawn from the MMLU test set's \"philosophy\" subcategory within the benchmark's \"humanities\" top-level group, and are graded on the single correct labelled option.",
  "metric": {
   "baseline_note": "25% is the four-option random-guess rate. No subject-specific human baseline is given by the paper for this subject; see the mmlu family page for the benchmark-wide human baselines.",
   "direction": "higher_is_better",
   "max_score": 100,
   "name": "accuracy",
   "random_baseline": 25,
   "unit": "%"
  },
  "name": "MMLU: Formal Logic",
  "page_kind": "subset",
  "paper": {
   "arxiv": "2009.03300",
   "title": "Measuring Massive Multitask Language Understanding",
   "url": "https://arxiv.org/abs/2009.03300",
   "year": 2021
  },
  "publisher": {
   "authors": [
    "Dan Hendrycks",
    "Collin Burns",
    "Steven Basart",
    "Andy Zou",
    "Mantas Mazeika",
    "Dawn Song",
    "Jacob Steinhardt"
   ],
   "org": "UC Berkeley (original); Center for AI Safety (current host)",
   "url": "https://github.com/hendrycks/test"
  },
  "released": "2020-09",
  "repo_url": "https://github.com/hendrycks/test",
  "sources": [
   {
    "accessed": "2026-09-07",
    "title": "Measuring Massive Multitask Language Understanding (Hendrycks et al., arXiv:2009.03300)",
    "url": "https://arxiv.org/abs/2009.03300"
   },
   {
    "accessed": "2026-09-07",
    "title": "hendrycks/test GitHub repository (MMLU reference implementation)",
    "url": "https://github.com/hendrycks/test"
   },
   {
    "accessed": "2026-09-07",
    "title": "cais/mmlu dataset card, Hugging Face",
    "url": "https://huggingface.co/datasets/cais/mmlu"
   }
  ],
  "status": "active",
  "subcategory": "philosophy",
  "summary": "MMLU subject subset: Propositional and predicate logic, validity and inference rules, as taught in a philosophy department.",
  "tags": [
   "knowledge",
   "multiple-choice",
   "mmlu-subset",
   "humanities"
  ],
  "task_format": "Four-option multiple-choice questions, graded on the single correct labelled option; commonly evaluated 5-shot, consistent with the rest of MMLU."
 }
}