On the Formalization of Importance Measures Using HOL Theorem Proving
Bibliographic record
Abstract
Importance measures provide a systematic approach to scrutinize critical system components, which are extremely beneficial in making important decisions, such as prioritizing reliability improvement activities, identifying weak-links and effective usage of given resources. The importance measures are then in turn used to obtain a criticality value for each system component and to rank the components in descending manner. Simulations tools are generally used to perform importance measure based analysis, but they require expensive computations and thus they are not suitable for large systems. A more scalable approach is to utilize the importance measures to obtain all the necessary conditions by proving a generic relationship describing the relative importance between any pair of components in a system. In this paper, we propose to use higher-order-logic (HOL) theorem proving to verify such relationships and thus making sure that all the essential conditions are accompanied by the proven property. In particular, we formalize the commonly used importance measures, such as Birnbaum and Fussell-Vesely, and conduct a formal importance measure analysis of a railway signaling system at a Moroccan level crossing as an application for illustration purpose.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".