Proving Reachability in B using Substitution Refinement
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Bibliographic record
Abstract
This paper proposes an approach to prove reachability properties of the form AG(ψ⇒EFϕ) using substitution refinement in classical B. Such properties denote that there exists an execution path for each state satisfying ψ to a state satisfying ϕ. These properties frequently occur in security policies and information systems. We show how to use Morganʼs specification statement to represent a property and refinement laws to prove it. The idea is to construct by stepwise refinement a program whose elementary statements are operation calls. Thus, the execution of such a program provides an execution satisfying AG(ψ⇒EFϕ). Proof obligations are represented using assertions (ASSERTIONS clause of B) and can be discharged using Atelier B.
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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 | 0.004 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| 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 it