mjbommar/openlemma-v0.1-items

OpenLemma v0.1: task items

One row per task item: the item behind the documents in openlemma-v0.1-pretrain, for your own packing, fine-tuning or analysis.

• input and answer are text, or JSON for structured inputs;
• options lists the choices of multiple-choice items;
• tier, label_source and audit_accuracy say how the answer was checked;
• record keeps the full source record, as JSON.

default

Source	Rows	Tokens	What
constructs-1	205,741		Construct generation run 1: all 180 reasoning constructs (inference rules, equivalences, fallacies, schemes, techniques, quantifier, deontic and legal reasoning) as natural, varied arguments: identify, identify-and-correct, what-follows, valid-or-not.
gloss-run2	184,133		OpenGloss task run 2: F1 mapping-rule induction, F2 label-set induction, F3 knowledge frames, F4 reverse dictionary, F5 passage QA.
gloss-run3	318,557		OpenGloss task run 3: extraction, document QA, question generation, word problems, rewriting, error correction, instruction following, and the lexical T-families.
gloss-run4	577,301		OpenGloss task run 4: 11K more F1/F2 induction task types (F1 after a gpt-6-sol pass over every rule).
gloss-run5	876,144		OpenGloss task run 5: the high-value families on 12,005 new headwords, plus 10K more F1/F2 task types.
lemma-v0	430,697		OpenLemma batch v0: procedural logic, structure, algorithms; CAS-checked math; certified puzzles. Label families repacked at the base rate.
lemma-v1	643,421		OpenLemma batch v1: function induction, data structures and algorithms with traces, code (Python, SQL, regex), formats, word problems, the full logic and reasoning catalog. Label families repacked at the base rate.

extended

Source	Rows	Tokens	What
gloss-run2	73,692		OpenGloss task run 2: F1 mapping-rule induction, F2 label-set induction, F3 knowledge frames, F4 reverse dictionary, F5 passage QA.
gloss-run3	192,770		OpenGloss task run 3: extraction, document QA, question generation, word problems, rewriting, error correction, instruction following, and the lexical T-families.
gloss-run5-a	14,216
gloss-run5-b	20,959
gloss-run5-pilot	4,244

Provenance and verification

Every row comes from OpenLemma (code: MIT; the documentation in docs/ covers every source).

• Generation: procedural generators and gpt-6-luna (OpenAI, flex, reasoning effort low). Some upstream retrieval material was written by gpt-5.4-mini.
• Auditing only: gpt-6-sol.
• Checks:
  • verified: an independent checker, solver (axeyum), CAS route or truth table recomputed the answer;
  • constructed: the label is fixed by how the item was built (planted values, code corruptions, the sense a sentence was written for);
  • agreed: a model-proposed label that independent blind model checks agreed with, in a family whose gpt-6-sol audit is >= 95% (default) or 80-95% (extended, with audit_accuracy on every row);
  • prose: model-written explanatory text about verified facts.

Anti-copy packing. k-shot documents (k in {0, 1, 3, 8}) never reward copying the previous answer:

• open answers are pairwise distinct;
• label answers repeat the last demonstration's label only at the base rate 1/n, with labels balanced over the demonstrations;
• copy traps and symbol labels appear on 10% of documents each.

Batches v0/v1 were originally packed so that "any label but the last one" was always right; this release repacks those families.

Plain text. Documents in default/extended contain no control tokens. ALEA-style <|start|>/<|end|> boundaries are added at tokenization. Reasoning glyphs (① ∴ ∵ ⊢ ● ⚠ …) are ordinary characters. The special_tokens config keeps the original ALEA control-token renderings for replication.

Token counts use the ALEA tokenizer alea-p1-prefix-16k.

Licence and attribution

CC-BY-4.0. Attribute OpenLemma (https://github.com/mjbommar/openlemma). Upstream sources:

• axeyum (MIT OR Apache-2.0): curriculum, facts, scenarios, CAS and solver checks;
• OpenGloss v2.4 (CC-BY-4.0): lexical seeds and grounding;
• WordNet 3.0: rows derived from WordNet senses carry the WordNet licence, included as LICENSE-WordNet.txt;
• alea-quality-model: the 93 foundational reasoning constructs.

Generated text was produced with OpenAI models and is subject to the provider's terms.

Known limitations

• agreed labels are model-checked, not proven; read audit_accuracy and the per-family audits in the repository docs.
• OpenGloss v2.4 has known defects (about 10% of common senses invalid, unreliable etymologies). Etymology tasks are excluded, and seed senses were validity-checked for the newer runs.
• Two deontic constructs are thin (Permission Operator, Prohibition Operator).
• This release was published before any model was trained on it. It makes no claim about downstream gains.

Citation

@misc{openlemma2026,
  title  = {OpenLemma: verified, bottom-up synthetic data for logic, reasoning, algorithms and language},
  author = {Bommarito, Michael J.},
  year   = {2026},
  note   = {Version 0.1},
  url    = {https://github.com/mjbommar/openlemma}
}