Bibliographic record
Abstract
E.L. Post's study (1941) shows that, although the lattice of clones in 2-valued logic is countably infinite, there exist only finitely many clones which contain both constants, and only finitely many which contain the negation function (neg). There are, however, uncountably many k-valued clones for all k>2; in fact, I. Agoston, et al. (1983) have shown that there are uncountably many containing all constants. One may also regard the set of constant functions of two-valued logic as an instance of the set of all noninvertible, unary functions over any finite domain. We show here that, for all k, there are indeed only finitely many clones containing all such functions. We also generalize those clones in Post's lattice which contain neg to the clones containing all permutation functions. Once again, it can be shown that there are only finitely many such clones. The latter result also serves to characterize the homogeneous relation algebras of R. Poschel (1979).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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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 | 0.000 | 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 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".