Horn clause belief change: contraction functions
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Bibliographic record
Abstract
The standard (AGM) approach to belief change assumes that the underlying logic is at least as strong as classical propositional logic. This paper investigates an account of belief change, specifically contraction, where the underlying logic is that governing Horn clauses. Thus this work sheds light on the theoretical underpinnings of belief change by weakening a fundamental assumption of the area. This topic is also of independent interest since Horn clauses have been used in areas such as deductive databases and logic programming. It proves to be the case that there are two distinct classes of contraction functions for Horn clauses: e-contraction, which applies to entailed formulas, and i-contraction, which applies to formulas leading to inconsistency. E-contraction is applicable in yet weaker systems where there may be no notion of negation (such as in definite clauses). I-contraction on the other hand has severe limitations, which makes it of limited use as a belief change operator. In both cases we explore the class of maxichoice functions which, we argue, is the appropriate approach for contraction in Horn clauses theories.
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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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it