article

Logical definability and query languages over ranked and unranked trees

Authors:

Michael Benedikt,

Frank NevenAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 8, Issue 2

Pages 11 - es

https://doi.org/10.1145/1227839.1227843

Published: 01 April 2007 Publication History

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 (NC¹) data complexity which still express properties important for database and document applications. We also give normal forms for safe queries in the calculus.

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Hellings JGyssens MVan Den Bussche JVan Gucht D(2023)Expressive Completeness of Two-Variable First-Order Logic with Counting for First-Order Logic Queries on Rooted Unranked Trees2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175828(1-13)Online publication date: 26-Jun-2023
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Logical definability and query languages over ranked and unranked trees

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 8, Issue 2

April 2007

196 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1227839

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Copyright © 2007 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 2007

Published in TOCL Volume 8, Issue 2

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Cited By

Hellings JGyssens MVan Den Bussche JVan Gucht D(2023)Expressive Completeness of Two-Variable First-Order Logic with Counting for First-Order Logic Queries on Rooted Unranked Trees2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175828(1-13)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175828
Arenas MBarceló PLibkin L(2018)Regular Languages of Nested Words: Fixed Points, Automata, and SynchronizationTheory of Computing Systems10.1007/s00224-010-9292-549:3(639-670)Online publication date: 25-Dec-2018
https://dl.acm.org/doi/10.1007/s00224-010-9292-5
Kuhtz LFinkbeiner B(2011)Weak Kripke structures and LTLProceedings of the 22nd international conference on Concurrency theory10.5555/2040235.2040272(419-433)Online publication date: 6-Sep-2011
https://dl.acm.org/doi/10.5555/2040235.2040272
Gauwin ONiehren JTison S(2011)Queries on Xml streams with bounded delay and concurrencyInformation and Computation10.1016/j.ic.2010.08.003209:3(409-442)Online publication date: 1-Mar-2011
https://dl.acm.org/doi/10.1016/j.ic.2010.08.003
Kuhtz LFinkbeiner B(2011)Weak Kripke Structures and LTLCONCUR 2011 – Concurrency Theory10.1007/978-3-642-23217-6_28(419-433)Online publication date: 2011
https://doi.org/10.1007/978-3-642-23217-6_28
Molyneux RSazonov V(2009)Hyperset Approach to Semi-structured DatabasesProceedings of the 26th British National Conference on Databases: Dataspace: The Final Frontier10.1007/978-3-642-02843-4_10(78-90)Online publication date: 30-Jun-2009
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To ALibkin L(2008)Recurrent Reachability Analysis in Regular Model CheckingProceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning10.1007/978-3-540-89439-1_15(198-213)Online publication date: 22-Nov-2008
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Arenas MBarceló PLibkin L(2007)Regular languages of nested wordsProceedings of the 34th international conference on Automata, Languages and Programming10.5555/2394539.2394642(888-900)Online publication date: 9-Jul-2007
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