A Computational Algebraic Approach to English Grammar
Why this work is in the frame
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Bibliographic record
Abstract
Abstract. Whereas type‐logical grammars treat syntactic derivations as logical proofs, usually represented by two‐dimensional diagrams, I here wish to defend the view that people process linguistic information by one‐dimensional calculations and will explore an algebraic approach based on the notion of a ‘‘pregroup,’’ a partially ordered monoid in which each element has both a left and a right ‘‘adjoint.’’ As a first approximation, say to English, one assigns to each word one or more ‘‘syntactic types,’’ elements of the free pregroup generated by a partially ordered set of ‘‘basic types,’’ in the expectation that the grammaticality of a string of words can be checked by a calculation on the corresponding types. This theoretical framework provides a simple foundation for a kind of feature checking that may be of general interest. According to G. A. Miller, there is a limit to the temporary storage capacity of our short‐term memory, which cannot hold more than seven (plus or minus two) ‘‘chunks’’ of information at any time. I explore here the possibility of identifying these chunks with ‘‘simple types,’’ which are obtained from basic types by forming iterated adjoints. In a more speculative vein, I attempt to find out how so‐called constraints on transformations can be framed in the present algebraic context.
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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 | 0.000 | 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 | 0.001 | 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