NEXPTIME-Completeness of Provability in Continuous Quantitative Equational Logic
Bibliographic record
Abstract
Quantitative equational logic was developed in 2016 in [10] as a natural extension of equational logic.In 2018 in [4], Shael Brown provided a decision procedure for provability in the case where the equations are never exact, which is called continuous quantitative equational logic.In [4] it is proved that the problem is in NEXPTIME.In this thesis, we show that provability in continuous quantitative equational logic is in fact NEXPTIME-complete. RsumLa logique quationnelle quantitative a t dveloppe en 2016 dans [10] comme une extension naturelle de la logique quationnelle.En 2018 dans [4], Shael Brown a fourni une procdure de dcision pour la prouvabilit dans le cas o les quations ne sont jamais exactes, qu'il appelle la logique quationnelle quantitative continue.Il est prouv dans [4] que ce problme est dans NEXPTIME.Dans cette thse, nous montrons que la prouvabilit en logique quationnelle quantitative continue est NEXPTIME-complte.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".