Logical definability and query languages over ranked and unranked trees
Bibliographic record
Abstract
We study relations on trees defined by first-order constraints over a vocabulary that includes the tree extension relation T ≺ T ′ (holding if and only if every branch of T extends to a branch of T ′), unary node-tests, and a binary relation checking whether the domains of two trees are equal. We consider both ranked and unranked trees. These are trees with and without a restriction on the number of children of nodes. We adopt the model-theoretic approach to tree relations and study relations definable over the structure consisting of the set of all trees and the aforementioned predicates. We relate definability of sets and relations of trees to computability by tree automata. We show that some natural restrictions correspond to familiar logics in the more classical setting where every tree is a structure over a fixed vocabulary, and to logics studied in the context of XML pattern languages. We then look at relational calculi over collections of trees, and obtain quantifier-restriction results that give us bounds on the expressive power and complexity. As unrestricted relational calculi can express problems that are complete for each level of the polynomial hierarchy, we look at their restrictions, corresponding to the restricted logics over the family of all unranked trees, and find several calculi with low (NC 1 ) data complexity which still express properties important for database and document applications. We also give normal forms for safe queries in the calculus.
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 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 | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.005 | 0.015 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".