Bibliographic record
Abstract
One of the authors introduced in [1] a calculus of circular proofs for studying the computability arising from the following categorical operations: finite products and coproducts, initial algebras, final coalgebras. The calculus of [1] is cut-free; yet, even if sound and complete for provability, it lacks an important property for the semantics of proofs, namely fullness w.r.t. the class of natural categorical models called μ-bicomplete category in [2]. We fix, with this work, this problem by adding the cut rule to the calculus. To this goal, we need to modifying the syntactical constraints on the cycles of proofs so to ensure soundness of the calculus and at same time local termination of cut-elimination. The enhanced proof system fully represents arrows of the intended model, a free μ-bicomplete category. We also describe a cut-elimination procedure as a model of computation arising from the above mentioned categorical operations. The procedure constructs a cut-free proof-tree with infinite branches out of a finite circular proof with cuts. [1] Luigi Santocanale. A calculus of circular proofs and its categorical semantics. In Mogens Nielsen and Uffe Engberg, editors, FoSSaCS, volume 2303 of Lecture Notes in Computer Science, pages 357–371. Springer, 2002. [2] Luigi Santocanale. μ-bicomplete categories and parity games. Theoretical Informatics and Applications, 36:195–227, September 2002.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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 source (direct Gemma or distilled Codex), 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".