Kernel Contraction and Base Dependence
Bibliographic record
Abstract
The AGM paradigm of belief change studies the dynamics of belief states in light of new information. Finding, or even approximating, those beliefs that are dependent on or relevant to a change is valuable because, for example, it can narrow the set of beliefs considered during belief change operations. A strong intuition in this area is captured by Gärdenforss preservation criterion (GPC), which suggests that formulas independent of a belief change should remain intact. GPC thus allows one to build dependence relations that are linked with belief change. Such dependence relations can in turn be used as a theoretical benchmark against which to evaluate other approximate dependence or relevance relations. Fariñas and Herzig axiomatize a dependence relation with respect to a belief set, and, based on GPC, they characterize the correspondence between AGM contraction functions and dependence relations. In this paper, we introduce base dependence as a relation between formulas with respect to a belief base, and prove a more general characterization that shows the correspondence between kernel contraction and base dependence. At this level of generalization, different types of base dependence emerge, which we show to be a result of possible redundancy in the belief base. We further show that one of these relations that emerge, strong base dependence, is parallel to saturated kernel contraction. We then prove that our latter characterization is a reversible generalization of Fariñas and Herzigs characterization. That is, in the special case when the underlying belief base is deductively closed (i.e., it is a belief set), strong base dependence reduces to dependence, and so do their respective characterizations. Finally, an intriguing feature of Fariñas and Herzigs formalism is that it meets other criteria for dependence, namely, Keyness conjunction criterion for dependence (CCD) and Gärdenforss conjunction criterion for independence (CCI). We prove that our base dependence formalism also meets these criteria. Even more interestingly, we offer a more specific criterion that implies both CCD and CCI, and show our base dependence formalism also meets this new criterion.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".