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Capturing Homomorphism-Closed Decidable Queries with Existential Rules [article]

Camille Bourgaux and David Carral and Markus Krötzsch and Sebastian Rudolph and Michaël Thomazo
2021 arXiv   pre-print
In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates.  ...  It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms.  ...  Chase-terminating existential rules capture the class of all decidable homomorphism-closed queries.  ... 
arXiv:2107.07811v1 fatcat:vh7quzegdrhojjuxv6fkcd7aaa

Capturing Homomorphism-Closed Decidable Queries with Existential Rules

Camille Bourgaux, David Carral, Markus Krötzsch, Sebastian Rudolph, Michaël Thomazo
2021 Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning   unpublished
In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates.  ...  It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms.  ...  Chase-terminating existential rules capture the class of all decidable homomorphism-closed queries.  ... 
doi:10.24963/kr.2021/14 fatcat:33n7z26vl5gwxbvwkkj74wsyzu

Expressiveness of guarded existential rule languages

Georg Gottlob, Sebastian Rudolph, Mantas Simkus
2014 Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '14  
We then show that weakly guarded rules extended with stratified negation are expressive enough to capture all database queries decidable in exponential time, without any assumptions on the input databases  ...  We strengthen this completeness result by proving that on ordered databases with input negation available, weakly guarded rules capture all queries computable in exponential time.  ...  Weakly guarded rules do not capture all database queries decidable in exponential (or, even polynomial) time.  ... 
doi:10.1145/2594538.2594556 dblp:conf/pods/GottlobRS14 fatcat:z4wnaqvdijfldovus3iaycc2ga

A Hybrid Approach to Query Answering under Expressive Datalog+/- [article]

Mostafa Milani, Andrea Cali, Leopoldo Bertossi
2016 arXiv   pre-print
Datalog+/- languages are provably able to capture the most relevant Semantic Web languages.  ...  Datalog+/- is a family of ontology languages that combine good computational properties with high expressive power.  ...  Choose a rule σ in Σ P ′ with an existential variable in a position with rank 1.  ... 
arXiv:1604.06770v2 fatcat:wsgohfgyjzftnbnu4q4dl5sc7e

Complexity of Arithmetic in Warded Datalog+- [article]

Lucas Berent, Markus Nissl, Emanuel Sallinger
2022 arXiv   pre-print
Warded Datalog+- extends the logic-based language Datalog with existential quantifiers in rule heads. Existential rules are needed for advanced reasoning tasks, e.g., ontological reasoning.  ...  We close this gap by defining a new language that extends Warded Datalog+- with arithmetic and prove its P-completeness.  ...  ., 2019] is an extension of Datalog ± , which is a family of Datalog languages with existentials in rule heads.  ... 
arXiv:2202.05086v1 fatcat:dnhm5jem2resri7mvrvrm7cssa

The Power of the Terminating Chase (Invited Talk)

Markus Krötzsch, Maximilian Marx, Sebastian Rudolph, Michael Wagner
2019 International Conference on Database Theory  
A "Datalog-first" standard chase that prioritises applications of rules without existential quantifiers makes modelling simpler -and we conjecture: computationally more efficient.  ...  The chase has become a staple of modern database theory with applications in data integration, query optimisation, data exchange, ontology-based query answering, and many other areas.  ...  It is clear that CT sk ∀ does not capture PTime (since existential rules can only express properties that are preserved under homomorphisms), but Theorem 9 further confines CT sk ∀ to the expressiveness  ... 
doi:10.4230/lipics.icdt.2019.3 dblp:conf/icdt/KrotzschMR19 fatcat:t63tgjkpynffxpq366j4wiaiky

Towards Farsighted Dependencies for Existential Rules [chapter]

Jean-Franc̨ois Baget, Marie-Laure Mugnier, Michaël Thomazo
2011 Lecture Notes in Computer Science  
We consider existential rules (also called Tuple-Generating Dependencies or Datalog+/-rules).  ...  It can also be used to compile the rule base, which leads to improve query answering algorithms.  ...  Queries are supposed to be at least as expressive as conjunctive queries in databases, which can be seen as existentially closed conjunctions of atoms.  ... 
doi:10.1007/978-3-642-23580-1_4 fatcat:u635y4mwj5dz5bgaqlzqpsv5ou

Rewriting Guarded Negation Queries [chapter]

Vince Bárány, Michael Benedikt, Balder ten Cate
2013 Lecture Notes in Computer Science  
At the same time, as was recently shown, the syntax of GNFO is restrictive enough so that static analysis problems such as query containment are still decidable.  ...  In this paper we provide further evidence for this, establishing that GNFO queries have distinctive features with respect to rewriting.  ...  We have also benefited from helpful discussions with Maarten Marx.  ... 
doi:10.1007/978-3-642-40313-2_11 fatcat:tzy7n3y6kvexphorspzkohxr74

Optimizing the chase

George Konstantinidis, José Luis Ambite
2014 Proceedings of the VLDB Endowment  
Our second contribution is to use the frugal chase to scale up query answering using views under LAV weakly acyclic target constraints, a useful language capturing RDF/S.  ...  The latter problem can be reduced to query rewriting using views without constraints by chasing the source-to-target mappings with the target constraints.  ...  BACKGROUND Queries. We use rule notation for conjunctive queries.  ... 
doi:10.14778/2733085.2733093 fatcat:rngrlclvbnfcppsbcnpdkqle4a

Conjunctive Artifact-Centric Services [chapter]

Piero Cangialosi, Giuseppe De Giacomo, Riccardo De Masellis, Riccardo Rosati
2010 Lecture Notes in Computer Science  
induced by the conjunctive queries.  ...  The main characteristic of this work is that conditions and actions are based on conjunctive queries.  ...  The most closely related one is [12] ), which shares the general setting with our approach but differs in the conditions required to obtain decidability.  ... 
doi:10.1007/978-3-642-17358-5_22 fatcat:tnoimeljrjfnxcc4qxmyuwt54a

Some Model Theory of Guarded Negation [article]

Vince Barany, Michael Benedikt, Balder ten Cate
2020 arXiv   pre-print
Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large  ...  logics, along with many sentences that arise in databases.  ...  Bárány's work was done while affiliated with TU Darmstadt. The authors gratefully acknowledge their debt to Martin Otto for enlightening discussions.  ... 
arXiv:2005.06299v2 fatcat:awujhhdh6bgrrgs3xu3v7igz4u

Oblivious and Semi-Oblivious Boundedness for Existential Rules

Pierre Bourhis, Michel Leclère, Marie-Laure Mugnier, Sophie Tison, Federico Ulliana, Lily Gallois
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
We show that it is decidable to recognize if a set of rules is bounded for several classes of rules and outline the complexity of the problem.  ...  We study the notion of boundedness in the context positive existential rules, that is, wether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance  ...  The so-chase is very close to the Skolem chase, which relies on a skolemisation of the rules: first, each rule σ is transformed by replacing each occurrence of an existential variable z with a functional  ... 
doi:10.24963/ijcai.2019/219 dblp:conf/ijcai/BourhisLMTUG19 fatcat:hltwg27ahfbo7a7n5mqrvxde4i

Oblivious and Semi-Oblivious Boundedness for Existential Rules [article]

Pierre Bourhis and Michel Leclère and Marie-Laure Mugnier and Sophie Tison and Federico Ulliana and Lily Galois
2020 arXiv   pre-print
We show that it is decidable to recognize if a set of rules is bounded for several classes and outline the complexity of the problem.  ...  We study the notion of boundedness in the context of positive existential rules, that is, whether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance  ...  The so-chase is very close to the Skolem chase, which relies on a skolemisation of the rules: first, each rule σ is transformed by replacing each occurrence of an existential variable z with a functional  ... 
arXiv:2006.08467v1 fatcat:jn7ms57t2rh47f3rmgzqmxchn4

A Single Approach to Decide Chase Termination on Linear Existential Rules

Michel Leclère, Marie-Laure Mugnier, Michaël Thomazo, Federico Ulliana, Michael Wagner
2019 International Conference on Database Theory  
restricted chase, proving that chase termination on linear existential rules with atomic head is decidable for both versions of the problem: Does every chase sequence terminate?  ...  In this work, we consider linear existential rules with atomic head, a simple yet important subclass of existential rules that generalizes inclusion dependencies.  ...  Acknowledgements We thank the reviewers for their insightful comments, as well as Antoine Amarilli for Example 21, which is simpler than a previous example and shows that the fairness issue already occurs with  ... 
doi:10.4230/lipics.icdt.2019.18 dblp:conf/icdt/LeclereMTU19 fatcat:w6ziga2xczbrzfxqknt5gyppou

Scalable containment for unions of conjunctive queries under constraints

George Konstantinidis, Jose Luis Ambite
2013 Proceedings of the Fifth Workshop on Semantic Web Information Management - SWIM '13  
, with applications to data integration, query optimization and minimization.  ...  As a result we couple the phases of both for chase and regular containment and end up with a faster and more scalable algorithm. Our experiments show a speedup of close to two orders of magnitude.  ...  Consider the following rules which capture "domain" and "range" properties in RDF/S, as well as "subclass" relations.  ... 
doi:10.1145/2484712.2484716 dblp:conf/sigmod/KonstantinidisA13 fatcat:oga6fbjtnjcmjogqahecqm7llu
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