Bibliographic record
Abstract
Applicative structures In first-order logic, a common question to ask about a formal theory is ‘what are its models like?’. For the theories λβ and CL w the first person to ask this was Dana Scott in the 1960s, while he was working on extending the concept of ‘computable’ from functions of numbers to functions of functions. The first non-trivial model, D ∞ , was constructed by Scott in 1969. Since then many other models have been made. The present chapter will set the scene by introducing a few basic general properties of models of CL w , and the next will do the same for λβ, whose concept of model is more complicated. Then Chapter 16 will describe the model D ∞ in detail and give outlines and references for some other models. Scott's D ∞ is not the simplest model known, but it is a good introduction, as the concepts used in building it are also involved in discussions of other models. But first, a comment: although λ-calculus and combinatory logic were invented as long ago as the 1920s, there was a 40-year gap before their first model was constructed; why was there this long delay? There are two main reasons. The first is the origin of λβ and CL w . Both Church and Curry viewed these theories, not from within the semantics that most post-1950 logicians were trained in, but from the alternative viewpoint described in Discussion 3.27.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.011 | 0.015 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.033 | 0.006 |
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".