On Panini and the Generative Capacity of Contextualized Replacement Systems
Bibliographic record
Abstract
This paper re-examines the widely held belief that the formalism underlying the rule system propounded by the ancient Indian grammarian, Pān. ini (ca. 450–350 BCE), either anticipates or converges upon the same expressive power found in finite state control systems or the context-free languages that are used in programming language theory and computational linguistics. While there is indeed a striking but cosmetic resemblance to the contextualized rewriting systems used by modern morphologists and phonologists, a subtle difference in how rules are prevented from applying cyclically leads to a massive difference in generative capacity. The formalism behind Pān. inian grammar, in fact, generates string languages not even contained within any of the multiple-component tree-adjoining languages, MCTAL(k), for any k. There is ample evidence, nevertheless, that Pān. ini’s grammar itself judiciously avoided the potential pitfalls of this unconstrained formalism to articulate a large-coverage, but seemingly very tractable grammar of the Sanskrit language.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".