The Dialectica interpretation of first-order classical affine logic
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Bibliographic record
Abstract
We give a Dialectica-style interpretation of first-order classical affine logic.By moving to a contraction-free logic, the translation (a.k.a.D-translation) of a firstorder formula into a higher-type -formula can be made symmetric with respect to duality, including exponentials.It turned out that the propositional part of our Dtranslation uses the same construction as de Paiva's dialectica category GC and we show how our D-translation extends GC to the first-order setting in terms of an indexed category.Furthermore the combination of Girard's ?!-translation and our D-translation results in the essentially equivalent -formulas as the double-negation translation and Gdel's original D-translation.I would like to thank Valeria de Paiva and anonymous referees for their helpful comments.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it