Tableau-based Reasoning for Description Logics with Inverse Roles and Number Restrictions
Bibliographic record
Abstract
The tableaux algorithm is a general technique for deciding concept satisfiability problems in description logics (DLs). It is useful not only for practical implementations, but also for studying the correctness and complexity of concrete decision procedures. There is a family of DLs currently lack appropriate optimization techniques. The research focuses on these DLs which typically have inverse roles and number restrictions (corresponding to ontology languages OWL-lite and OWL-DL respectively). We provide solutions to known problems such as the unsoundness of global tableaux caching, and present new tableau-based algorithms for concept satisfiability problems in these DLs. The research presented in this thesis is significant in several aspects. Firstly, based on an equivalence discovered during the course of the research, we are able to show an elimination of inverse roles for a sub-family of DLs. Our experiments have confirmed the practicality of this technique. Secondly, we provide three sub-tableaux caching techniques that is sound and global (but with different power in caching functionality). Finally, we present two ExpTime tableau-based decision procedures, with the one for SHIQ achieving an improved worst-case upper bound in the strong sense of binary coding of numbers (based on the integer linear programming technique). iii Contents iii
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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 | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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".