Parameterized complexity of abduction in Schaefer’s framework
Bibliographic record
Abstract
Abstract Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version, asking for sets of variables as explanations, we study, besides the problem of wether there exists a set of explanations, two explanation size limited variants of this reasoning problem (less than or equal to, and equal to a given size bound). In this paper, we present a thorough two-dimensional classification of these problems: the first dimension is regarding the parameterized complexity under a wealth of different parameterizations, and the second dimension spans through all possible Boolean fragments of these problems in Schaefer’s constraint satisfaction framework with co-clones (T. J. Schaefer. The complexity of satisfiability problems. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing, May 1–3, 1978, San Diego, California, USA, R.J. Lipton, W.A. Burkhard, W.J. Savitch, E.P. Friedman, A.V. Aho eds, pp. 216–226. ACM, 1978). Thereby, we almost complete the parameterized complexity classification program initiated by Fellows et al. (The parameterized complexity of abduction. In Proceedings of the Twenty-Sixth AAAI Conference on Articial Intelligence, July 22–26, 2012, Toronto, Ontario, Canada, J. Homann, B. Selman eds. AAAI Press, 2012), partially building on the results by Nordh and Zanuttini (What makes propositional abduction tractable. Artificial Intelligence, 172, 1245–1284, 2008). In this process, we outline a fine-grained analysis of the inherent parameterized intractability of these problems and pinpoint their FPT parts. As the standard algebraic approach is not applicable to our problems, we develop an alternative method that makes the algebraic tools partially available again.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.051 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.007 | 0.015 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 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 source (direct Gemma or distilled Codex), 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".