Reachability analysis using multiway decision graphs in the HOL theorem prover
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Bibliographic record
Abstract
In this paper, all the necessary infrastructure is provided to define a state exploration approach within the HOL theorem prover. While related work has tackled the same problem by representing primitive Binary Decision Diagram (BDD) operations as inference rules added to the core of the theorem prover, the presented approach is based on the Multiway Decision Graphs (MDGs). MDG generalizes BDD to represent and manipulate a subset of first-order logic formulae. Considering MDG instead of BDD will raise the abstraction level of what can be verified using states exploration within a theorem prover. A canonic MDGs is defined in HOL as well-formed directed formulae. Then, the basic MDG operations is formalized following a deep embedding approach and the correctness proof for each operation is derived. Finally, the reachability analysis is implemented as a tactic that uses the MDG theory within HOL.
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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 | 0.002 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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 it