Ranges: composite measure phrases, modified numerals, and choice functions
Bibliographic record
Abstract
Range expressions such as between 3 and 8, from 3 to 8, and 3 through 8 resemble modified numerals such as at least 3 and have sometimes been mentioned under that rubric. This paper shows that they are crucially different in their distribution, the readings available to them, and their behavior with respect to quantifiers, and more generally that they have an intricate grammar of their own. We distinguish three classes of readings they can receive: singleton punctual readings, on which they often give rise to ignorance inferences; set punctual readings, which arise chiefly in the scope of quantifiers; and interval readings, where the range is interpreted exhaustively. We propose an analysis on which range expressions denote choice functions over degrees, which can in the right circumstances be parameterized.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.002 | 0.015 |
| Scholarly communication | 0.007 | 0.024 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 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 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".