Disjunctive logic programs with existential quantification in rule heads
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We consider disjunctive logic programs without function symbols but with existential quantification in rule heads, under the semantics of general stable models. There are at least two interesting prospects in these programs. The first is that a program can be made more succinct by using existential variables, and the second is on the potential in representing defeasible ontological knowledge by these logic programs. This paper studies some of the properties of these programs. First, we show a simple yet intuitive definition of stable models for these programs that does not resort to second-order logic. Second, the stable models of these programs can be characterized by an extension of progression for disjunctive programs, which provides a native characterization of justification for stable models. We then study the decidability issue. While the stable model existence problem for safe disjunctive programs is decidable, with existential quantification allowed in rule heads the problem becomes undecidable. We identify an interesting decidable fragment by exploring a new notion of stratification over existential quantification.
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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 | 0.003 | 0.001 |
| 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 | 0.002 |
| 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 it