Duality in Rough Set Theory Based on the Square of Opposition
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Bibliographic record
Abstract
In rough set theory, one typically considers pairs of dual entities such as a pair of lower and upper approximations, a pair of indiscernibility and discernibility relations, a pair of sets of core and non-useful attributes, and several more. By adopting a framework known as hypercubes of duality, of which the square of opposition is a special case, this paper investigates the role of duality for interpreting fundamental concepts in rough set analysis. The objective is not to introduce new concepts, but to revisit the existing concepts by casting them in a common framework so that we can obtain more insights into an understanding of these concepts and their relationships. We demonstrate that these concepts can, in fact, be defined and explained in a common framework, although they first appear to be very different and have been studied in somewhat isolated ways.
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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 | 0.001 | 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 | 0.001 |
| Open science | 0.001 | 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