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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.  ...  Conclusion To the best of our knowledge, this is the first systematic study of termination of the restricted chase on existential rules (with disjunctions) and the first ever approach to restricted chase  ... 
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.  ...  It is known that the restricted chase variant is a more powerful tool in termination analysis provided a database is given.  ...  These rules are also called non-disjunctive rules as compared to studies on disjunctive rules (see, e.g., (Bourhis et al. 2016; Carral et al. 2017) ).  ... 
arXiv:2005.05423v1 fatcat:3xebbndxknbfzb7uz4cmcx7nq4

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

David Carral, Irina Dragoste, Markus Krötzsch
2017 Lecture Notes in Computer Science  
Answering conjunctive queries (CQs) over knowledge bases (KBs) containing disjunctive existential rules is a relevant reasoning task which can be addressed using the disjunctive chase algorithm-a sound  ...  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  ...  To do so, we transform the DL ontologies in these corpora into KBs with disjunctive existential rules, and then check how many of them satisfy (a-p).  ... 
doi:10.1007/978-3-319-68288-4_10 fatcat:sdt47xjoq5hoflronjsmmt4kgi

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.  ...  In this paper, we propose JAADL, a modal logic for joint abilities under strategy commitments, which is an extension of ATL.  ...  Acknowledgements We thank Sebastian Rudolph for his helpful comments.  ... 
doi:10.24963/ijcai.2020/246 dblp:conf/ijcai/CarralK20 fatcat:biobkota7fgr7ccnediiu2e45a

Constructive completeness and non-discrete languages [article]

Henrik Forssell, Christian Espíndola
2017 arXiv   pre-print
that it is available, with various completeness theorems in terms of presheaf and sheaf semantics (and thus with Kripke and Beth semantics).  ...  languages of arbitrary size and languages for which equality between the elements of the signature is not decidable.  ...  Lumsdaine, and, especially, Erik Palmgren, for discussions, pertinent observations, and feedback.  ... 
arXiv:1709.05817v1 fatcat:dmrt3ayr5bblziezzr3yc276l4

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
Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering.  ...  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.  ...  Acknowledgements This work is partly supported by DFG in project number 389792660 (TRR 248, Center for Perspicuous Systems), by BMBF in the Center for Scalable Data Analytics and Artificial Intelligence  ... 
arXiv:2107.07811v1 fatcat:vh7quzegdrhojjuxv6fkcd7aaa

The Impact of Disjunction on Reasoning under Existential Rules: Research Summary [article]

Michael Morak
2014 arXiv   pre-print
Datalog+/- is a Datalog-based language family enhanced with existential quantification in rule heads, equalities and negative constraints.  ...  For guarded theories with disjunction, we obtain a strong 2EXP lower bound in the combined complexity, even for very restricted formalisms like fixed sets of (disjunctive) inclusion dependencies.  ...  After exhaustively applying such chase steps, we obtain D m , also denoted chase(D, Σ). The chase can have three different outcomes: Failure, non-terminating success or terminating success.  ... 
arXiv:1405.5109v1 fatcat:4al4oxnkenb7pe3q64zqgtfet4

Decision Procedures for Guarded Logics [article]

Kevin Kappelmann
2021 arXiv   pre-print
Moreover, we show a novel normalisation procedure for the widely used chase procedure in case of (disjunctive) GTGDs, which could be useful for future studies.  ...  In this work, we connect the tree-like model property of the guarded fragment with the resolution-based approach.  ...  ∧ ( 1 , 2 , 2 ) )︀ , as this restriction is needed for termination purposes.  ... 
arXiv:1911.03679v2 fatcat:hvheoc3nn5bxrptdrt52tncp5q

Generating Plans from Proofs: The Interpolation-based Approach to Query Reformulation

Michael Benedikt, Julien Leblay, Balder ten Cate, Efthymia Tsamoura
2016 Synthesis Lectures on Data Management  
Query reformulation refers to a process of translating a source query-a request for information in some high-level logic-based language-into a target plan that abides by certain interface restrictions.  ...  We will review the theory of interpolation, and explain its close connection with query reformulation.  ...  We are also thankful to Carsten Lutz, Jan Van den Bussche, and Victor Vianu for their detailed feedback on the first official draft of the book.  ... 
doi:10.2200/s00703ed1v01y201602dtm043 fatcat:pjmzooijszezfaedsqgrpidt6m

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 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  ...  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.  ...  The existential depth of terms in o-chase(I, {σ}) is unbounded, which is in line with the non-termination of the o-chase on (I, {σ}).  ... 
arXiv:2006.08467v1 fatcat:jn7ms57t2rh47f3rmgzqmxchn4

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 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  ...  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.  ...  The existential depth of terms in o-chase(I, {σ}) is unbounded, which is in line with the non-termination of the o-chase on (I, {σ}).  ... 
doi:10.24963/ijcai.2019/219 dblp:conf/ijcai/BourhisLMTUG19 fatcat:hltwg27ahfbo7a7n5mqrvxde4i

On the Termination of the Chase Algorithm [chapter]

Michael Meier
2010 Lecture Notes in Computer Science  
The problem with this result, though, is that the extension of the constraint set by Σ ¬ often leads to non-terminating chase sequences, even if the chase with S terminates. Example 134.  ...  To show that the chase with α terminates, we need weaker termination conditions than inductive restriction.  ... 
doi:10.1007/978-3-642-15918-3_23 fatcat:wsougypcmrhmxm3s6choxxfssm

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.  ...  A novel approach for classifying the existential rule languages with finite Skolem chase is proposed by restricting the use of existential variables in the Skolem chase.  ... 
arXiv:1411.5220v3 fatcat:aenn7e4f5jbxpj47kjt6irouyq

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  
allowing for existential quantification and disjunction in the head; our only assumption is the availability of a datalog reasoner and a fully-fledged reasoner for the language of interest, both of which  ...  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  ...  rules with ⊥ in the head, then str(K) logically entails K: splitting amounts to turning disjunctions in the head of rules into conjunctions, while c-Skolemisation restricts the possible values of existentially  ... 
doi:10.1613/jair.4757 fatcat:spe5shdunzhnlnkncsgvfvahvm

The Vadalog system

Luigi Bellomarini, Emanuel Sallinger, Georg Gottlob
2018 Proceedings of the VLDB Endowment  
as existential quantification.  ...  The Vadalog System: Datalog-based Reasoning for Knowledge Graphs. PVLDB, 11(9): 975-987, 2018.  ...  It covers disjunctive Datalog under the answer sets semantics (with two forms of negation). In the version considered by [11] , existentials have been simulated by Skolemization.  ... 
doi:10.14778/3213880.3213888 fatcat:cbkkhqm2mfhihht76fo6bq5mne
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