Enhancing a theorem prover by delayed clause-construction and attribute sequences
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Bibliographic record
Abstract
The performance of a resolution-based automated theorem prover (ATP) depends on the speed at which clauses are derived and the efficiency at pruning the search space. The speed at which clauses are derived depends in part on the number of operations performed to construct derived clauses. Depth-first search based ATPs derive clauses in a linear manner. In linear derivations, a large percentage of the derived clauses are intermediate conclusions that are discarded shortly after they are derived. Therefore, the time spent constructing those clauses is wasted. In this thesis we present a stalling strategy, called delayed clause-construction (DCC), that reduces this wasted time by delaying the construction of intermediate conclusions until they are needed. Top-down depth-first search algorithms have the disadvantage of deriving the same clauses over and over again. Bottom-up best-first search approaches solve this problem by redundancy elimination, but their disadvantages are the lack of goal-orientation and the large memory requirements. In this thesis we introduce semi-linear resolution (SLR), a top-down bottom-up search procedure that combines advantageous characteristics found in best-first search and depth-first search algorithms. It requires a modest amount of memory and includes redundancy control. SLR relies on DCC for speed. DCC also provides SLR with ability to perform large inference steps through the use of a mega-inference rule. In order to improve the efficiency of SLR, we developed a restriction strategy, called attribute sequences (ATS), that uses sequences of clause characteristics as a guide to limit the participation of clauses in a linear derivation, thereby reducing the explorable search space . ATS does not compromise completeness. The performance enhancements ensuing from the use of DCC and ATS in SLR are shown in this thesis to be quite significant in theory, through mathematical analysis, and in practice, through the results obtained from CARINE; an implementation of SLR.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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