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Checking Chase Termination over Ontologies of Existential Rules with Equality [article]

David Carral, Jacopo Urbani
2019 arXiv   pre-print
The chase is a sound and complete algorithm for conjunctive query answering over ontologies of existential rules with equality.  ...  Therefore, one can apply existing acyclicity notions to check chase termination over an axiomatisation of an ontology and then use the original ontology for reasoning.  ...  Introduction Answering conjunctive queries (CQs) over ontologies of existential rules with equality is a relevant reasoning task, which is undecidable (Beeri and Vardi 1981) .  ... 
arXiv:1911.10981v1 fatcat:x2tspmgp4bhdpj4k4bqalh5fvy

Checking Chase Termination over Ontologies of Existential Rules with Equality

David Carral, Jacopo Urbani
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
The chase is a sound and complete algorithm for conjunctive query answering over ontologies of existential rules with equality.  ...  Therefore, one can apply existing acyclicity notions to check chase termination over an axiomatisation of an ontology and then use the original ontology for reasoning.  ...  Acknowledgments This work is funded by Deutsche Forschungsgemeinschaft (DFG) grant 389792660 as part of TRR 248 (see www.perspicuous-computing.science) and by the NWO research programme 400.17.605 (VWData  ... 
doi:10.1609/aaai.v34i03.5663 fatcat:4ynvaohuyndqvlcdokmmhjjzuq

Efficient Model Construction for Horn Logic with VLog [chapter]

Jacopo Urbani, Markus Krötzsch, Ceriel Jacobs, Irina Dragoste, David Carral
2018 Lecture Notes in Computer Science  
Horn ontologies consisting of existential rules are used in various fields ranging from reasoning over knowledge graphs [7] and Description Logics (DL) ontologies [5, 6] , to data integration [4] and social  ...  We implement a slightly different version of the restricted chase which leads to termination in more cases [3] , by prioritising the exhaustive application of Datalog rules (rules without existentially  ...  Acknowledgements This work was supported by the DFG within the cfaed Cluster of Excellence, CRC 912 (HAEC), and Emmy Noether grant KR 4381/1-1.  ... 
doi:10.1007/978-3-319-94205-6_44 fatcat:ceirdsuqkne2beituhy4eyyhq4

A Practical Acyclicity Notion for Query Answering Over Horn- $$\mathcal {SRIQ}$$ Ontologies [chapter]

David Carral, Cristina Feier, Pascal Hitzler
2016 Lecture Notes in Computer Science  
In this paper, we define a novel acyclicity notion which provides a sufficient condition for termination of the restricted chase over Horn-SRIQ TBoxes.  ...  Conjunctive query answering over expressive Horn Description Logic ontologies is a relevant and challenging problem which, in some cases, can be addressed by application of the chase algorithm.  ...  Unfortunately, this is not possible: The restricted chase of any set of existential rules always terminates with respect to the critical instance.  ... 
doi:10.1007/978-3-319-46523-4_5 fatcat:kgxxkq4wffai7g5kdo755bakty

Pushing the Boundaries of Tractable Ontology Reasoning [chapter]

David Carral, Cristina Feier, Bernardo Cuenca Grau, Pascal Hitzler, Ian Horrocks
2014 Lecture Notes in Computer Science  
We identify a class of Horn ontologies for which standard reasoning tasks such as instance checking and classification are tractable.  ...  We show empirically that the class includes many real-world ontologies that are not included in any OWL 2 profile, and thus that polynomial time reasoning is possible for these ontologies.  ...  ., every ontology with a functional role used in an existential restriction is not universally RSA. It is well-known that the Skolem chase often does not terminate in the presence of equality [?,?]  ... 
doi:10.1007/978-3-319-11915-1_10 fatcat:kmfxv3jfnje23fb3cw5l6vpboa

Tractable Query Answering for Expressive Ontologies and Existential Rules [chapter]

David Carral, Irina Dragoste, Markus Krötzsch
2017 Lecture Notes in Computer Science  
As shown in [5, 6] , acyclicity notions can be used to determine that the chase will indeed terminate over a large subset of real-world ontologies.  ...  Nevertheless, even if a KB is characterised as acyclic, CQ answering still remains a problem of high theoretical complexity: CQ answering over acyclic programs with disjunctive existential rules is coN2E  ...  Acknowledgements This work was supported by the DFG within the cfaed Cluster of Excellence, CRC 912 (HAEC), and Emmy Noether grant KR 4381/1-1.  ... 
doi:10.1007/978-3-319-68288-4_10 fatcat:sdt47xjoq5hoflronjsmmt4kgi

Acyclicity Notions for Existential Rules and Their Application to Query Answering in Ontologies

B. Cuenca Grau, I. Horrocks, M. Krötzsch, C. Kupke, D. Magka, B. Motik, Z. Wang
2013 The Journal of Artificial Intelligence Research  
Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases.  ...  The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable.  ...  Acknowledgments This work was supported by the Royal Society, the Seventh Framework Program (FP7) of the European Commission under Grant Agreement 318338, 'Optique', and the EPSRC projects ExODA, Score  ... 
doi:10.1613/jair.3949 fatcat:rclovclppfetrloce64n5i37ru

Existential Rule Languages with Finite Chase: Complexity and Expressiveness [article]

Heng Zhang, Yan Zhang, Jia-Huai You
2015 arXiv   pre-print
Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages.  ...  In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase.  ...  Through a chase procedure, fresh nulls have to be introduced for each application of the existential rules, and hence, potential cyclic applications of these rules may lead the chase procedure not to terminate  ... 
arXiv:1411.5220v3 fatcat:aenn7e4f5jbxpj47kjt6irouyq

Detecting Chase (Non)Termination for Existential Rules with Disjunctions

David Carral, Irina Dragoste, Markus Krötzsch
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
The restricted chase is a sound and complete algorithm for conjunctive query answering over ontologies of disjunctive existential rules. We develop acyclicity conditions to ensure its termination.  ...  Our criteria cannot always detect termination (the problem is undecidable), and we develop the first cyclicity criteria to show non-termination of the restricted chase.  ...  It allows us to show that a majority of practical ontologies is such that the chase will either terminate over all possible sets of input facts, or will necessarily be infinite over at least some inputs  ... 
doi:10.24963/ijcai.2017/128 dblp:conf/ijcai/CarralDK17 fatcat:42ngbxpmdrfoli4on7m3g4cyjy

Restricted Chase Termination for Existential Rules: a Hierarchical Approach and Experimentation [article]

Arash Karimi, Heng Zhang, Jia-Huai You
2020 arXiv   pre-print
The chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks.  ...  This approach applies to any class of finite skolem chase identified with a condition of acyclicity.  ...  categories of up to 5 and 5-200 existential variables with equal probability (350 from each).  ... 
arXiv:2005.05423v1 fatcat:3xebbndxknbfzb7uz4cmcx7nq4

A Modal Logic for Joint Abilities under Strategy Commitments

Zhaoshuai Liu, Liping Xiong, Yongmei Liu, Yves Lespérance, Ronghai Xu, Hongyi Shi
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Firstly, we introduce an operator of elimination of (strictly) dominated strategies, with which we can represent joint abilities of coalitions.  ...  We analyze valid formulas in JAADL, give sufficient/necessary conditions for joint abilities, and show that model checking memoryless JAADL is in EXPTIME.  ...  Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2020/246 dblp:conf/ijcai/CarralK20 fatcat:biobkota7fgr7ccnediiu2e45a

Ontologies for Knowledge Graphs: Breaking the Rules [chapter]

Markus Krötzsch, Veronika Thost
2016 Lecture Notes in Computer Science  
We study this issue for several classes of existential rules and derive new syntactic criteria to recognise well-behaved rule-based ontologies over KGs.  ...  If P is KG frontier guarded and Algorithm 1 terminates on P, then the denormalised rule set Result P is frontier guarded.  ...  In practice, it is more realistic to assume that ontologies are constructed over KGs directly.  ... 
doi:10.1007/978-3-319-46523-4_23 fatcat:i3jgivfb75hdbdohmocj34svfa

A Single Approach to Decide Chase Termination on Linear Existential Rules [article]

Michel Leclere, Marie-Laure Mugnier, Michael Thomazo, Federico Ulliana
2018 arXiv   pre-print
on linear existential rules is decidable for both versions of the problem: Does every fair chase sequence terminate?  ...  of ontology-based query answering.  ...  Chase termination for guarded existential rules.  ... 
arXiv:1810.02132v1 fatcat:gf2xpr6cznaulaamvhailpb2vm

PAGOdA: Pay-As-You-Go Ontology Query Answering Using a Datalog Reasoner

Yujiao Zhou, Bernardo Cuenca Grau, Yavor Nenov, Mark Kaminski, Ian Horrocks
2015 The Journal of Artificial Intelligence Research  
languages that can be captured by rules allowing for existential quantification and disjunction in the head; our only assumption is the availability of a datalog reasoner and a fully-fledged reasoner  ...  In this paper, we describe a hybrid approach to query answering over OWL 2 ontologies that combines a datalog reasoner with a fully-fledged OWL 2 reasoner in order to provide scalable 'pay-as-you-go' performance  ...  Acknowledgments This is an extended version of the papers 'Pay-As-You-Go OWL Query Answering Using a Triple Store' published at AAAI 2014, and 'Complete Query Answering over Horn Ontologies Using a Triple  ... 
doi:10.1613/jair.4757 fatcat:spe5shdunzhnlnkncsgvfvahvm

The Vadalog system

Luigi Bellomarini, Emanuel Sallinger, Georg Gottlob
2018 Proceedings of the VLDB Endowment  
In this context, it has been recognized that to handle the complex knowledge-based scenarios encountered today, such as reasoning over large knowledge graphs, Datalog has to be extended with features such  ...  Over the past years, there has been a resurgence of Datalog-based systems in the database community as well as in industry.  ...  The Vadalog system as presented here is IP of the University of Oxford.  ... 
doi:10.14778/3213880.3213888 fatcat:cbkkhqm2mfhihht76fo6bq5mne
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