A Random Model for Argumentation Framework: Phase Transitions, Empirical Hardness, and Heuristics
Bibliographic record
Abstract
We propose and study, theoretically and empirically, a new random model for the abstract argumentation framework (AF). Our model overcomes some intrinsic difficulties of the only random model of directed graphs in the literature that is relevant to AFs, and makes it possible to study the typical-case complexity of AF instances in terms of threshold behaviours and phase transitions. We proved that the probability for a random AF instance to have a stable/preferred extension goes through a sudden change (from 1 to 0) at the threshold of the parameters of the new model D(n, p, q), satisfying the equation 4q/((1 + q)(1+q)) = p. We showed, empirically, that in this new model, there is a clear easy-hard-easy pattern of hardness (for a typical backtracking-style exact solvers) associated with the phase transition. Our empirical studies indicated that instances from the new model at phase transitions are much harder than those from an Erdos-Renyi-style model with equal edge density. In addition to being an analytically tractable model for understanding the interplay between problems structures and effectiveness of (branching) heuristics used in practical argumentation solvers, the model can also be used to generate, in a systematic way, non-trivial AF instances with controlled features to evaluate the performance of other AF solvers.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 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 | 0.001 |
| 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".