An Anytime Deduction Algorithm for the Probabilistic Logic and Entailment Problems
Bibliographic record
Abstract
We study two basic problems of probabilistic reasoning: the probabilistic logic and the probabilistic entailment problems. The first one can be defined as follows. Given a set of logical sentences and probabilities that these sentences are true, the aim is to determine whether these probabilities are consistent or not. Given a consistent set of logical sentences and probabilities, the probabilistic entailment problem consists in determining the range of the possible values of the probability associated with additional sentences while maintaining a consistent set of sentences and probabilities. This paper proposes a general approach based on an anytime deduction method that allows the follow-up of the reasoning when checking consistency for the probabilistic logic problem or when determining the probability intervals for the probabilistic entailment problem. Considering a series of subsets of sentences and probabilities, the approach proceeds by computing increasingly narrow probability intervals that either show a contradiction or that contain the tightest entailed probability interval. Computational experience have been conducted to compare the proposed anytime deduction method, called ad-psat with an exact one, psatcol, using column generation techniques, both with respect to the range of the probability intervals and the computing times.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".