A generalized gelfond-lifschitz transformation for logic programs with abstract constraints
Bibliographic record
Abstract
We present a generalized Gelfond-Lifschitz transformation in order to define stable models for a logic program with arbitrary abstract constraints on sets (c-atoms). The generalization is based on a formal semantics and a novel abstract representation of c-atoms, as opposed to the commonly used power set form representation. In many cases, the abstract representation of a c-atom results in a substantial reduction of size from its power set form representation. We show that any c-atom A =(Ad,Ac) in the body of a clause can be characterized using its satisfiable sets, so that given an interpretation I the c-atom can be handled simply by introducing a special atom θA together with a new clause θA ← A1,..., An for each satisfiable set {A1,..., An} of A. We also prove that the latest fixpoint approach presented by Son et al. and our approach using the generalized Gelfond-Lifschitz transformation are semantically equivalent in the sense that they define the same set of stable models.
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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".