Exact ASP Counting with Compact Encodings
Bibliographic record
Abstract
Answer Set Programming (ASP) has emerged as a promising paradigm in knowledge representation and automated reason- ing owing to its ability to model hard combinatorial problems from diverse domains in a natural way. Building on advances in propositional SAT solving, the past two decades have wit- nessed the emergence of well-engineered systems for solv- ing the answer set satisfiability problem, i.e., finding mod- els or answer sets for a given answer set program. In re- cent years, there has been growing interest in problems be- yond satisfiability, such as model counting, in the context of ASP. Akin to the early days of propositional model count- ing, state-of-the-art exact answer set counters do not scale well beyond small instances. Exact ASP counters struggle with handling larger input formulas. The primary contribu- tion of this paper is a new ASP counting framework, called sharpASP, which counts answer sets avoiding larger input formulas. This relies on an alternative way of defining answer sets that allows lifting of key techniques developed in the con- text of propositional model counting. Our extensive empirical analysis over 1470 benchmarks demonstrates significant per- formance gain over current state-of-the-art exact answer set counters. Specifically, by using sharpASP, we were able to solve 1062 benchmarks with PAR2 score of 3082 whereas using prior state-of-the-art, we could only solve 895 bench- marks with PAR2 score of 4205, all other experimental con- ditions being the same.
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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 | 0.003 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.006 | 0.010 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
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".