Alternating Fixpoint Operator for Hybrid MKNF Knowledge Bases as an\n Approximator of AFT
Bibliographic record
Abstract
Approximation fixpoint theory (AFT) provides an algebraic framework for the\nstudy of fixpoints of operators on bilattices and has found its applications in\ncharacterizing semantics for various classes of logic programs and nonmonotonic\nlanguages. In this paper, we show one more application of this kind: the\nalternating fixpoint operator by Knorr et al. for the study of the well-founded\nsemantics for hybrid MKNF knowledge bases is in fact an approximator of AFT in\ndisguise, which, thanks to the power of abstraction of AFT, characterizes not\nonly the well-founded semantics but also two-valued as well as three-valued\nsemantics for hybrid MKNF knowledge bases. Furthermore, we show an improved\napproximator for these knowledge bases, of which the least stable fixpoint is\ninformation richer than the one formulated from Knorr et al.'s construction.\nThis leads to an improved computation for the well-founded semantics. This work\nis built on an extension of AFT that supports consistent as well as\ninconsistent pairs in the induced product bilattice, to deal with\ninconsistencies that arise in the context of hybrid MKNF knowledge bases. This\npart of the work can be considered generalizing the original AFT from symmetric\napproximators to arbitrary approximators.\n
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.001 | 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 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".