## Logical definability and query languages over ranked and unranked trees (2007)

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Venue: | ACM Trans. on Comput. Logic |

Citations: | 7 - 4 self |

### BibTeX

@ARTICLE{Benedikt07logicaldefinability,

author = {Michael Benedikt and Leonid Libkin and Frank Neven},

title = {Logical definability and query languages over ranked and unranked trees},

journal = {ACM Trans. on Comput. Logic},

year = {2007},

volume = {2006}

}

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### 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 if 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 above 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 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, while still expressing properties important for database and