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Detecting Chase (Non)Termination for Existential Rules with Disjunctions
2017
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
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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]
2020
arXiv
pre-print
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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]
2017
Lecture Notes in Computer Science
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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
2020
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
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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]
2017
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
2016
Synthesis Lectures on Data Management
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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]
2020
arXiv
pre-print
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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
2019
Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
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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]
2010
Lecture Notes in Computer Science
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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]
2015
arXiv
pre-print
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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
2015
The Journal of Artificial Intelligence Research
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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
2018
Proceedings of the VLDB Endowment
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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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