Chase Variants & Boundedness

The chase is a family of algorithms designed to infer data with the use of ontological knowledge, which is encoded in existential rules, a sub-language of first-order logic. A considerable literature has been devoted to its analysis, approaching it from a variety of presupposed terminological and notational background. We define a unifying framework for the specification and study of chase algorithms. We utilize it to compare and clarify the properties that discern the different variants of the chase. We particularly focus on studying whether there is a bound to the maximum length of a chain of interdependent rule applications (where interdependency means that the output of a rule application is contributing to triggering the next rule application). This is the problem of boundedness, or k-boundedness, when the bound k is given. By investigating a number of intermediate properties, we find that k-boundedness is decidable for several chase variants. In addition to other secondary results, we define two new chase variants with the aim of reducing redundant rule applications without heavily increasing the computation cost.

[1]  Carsten Lutz,et al.  First Order-Rewritability and Containment of Conjunctive Queries in Horn Description Logics , 2016, Description Logics.

[2]  Harry G. Mairson,et al.  Undecidable optimization problems for database logic programs , 1993, JACM.

[3]  Jia-Huai You,et al.  Beyond Skolem Chase: A Study of Finite Chase under Standard Chase Variant , 2017, Description Logics.

[4]  Boris Motik,et al.  Acyclicity Notions for Existential Rules and Their Application to Query Answering in Ontologies , 2013, J. Artif. Intell. Res..

[5]  Alin Deutsch,et al.  The chase revisited , 2008, PODS.

[6]  Serge Abiteboul,et al.  Foundations of Databases: The Logical Level , 1995 .

[7]  Sebastian Rudolph,et al.  Preserving Constraints with the Stable Chase , 2018, ICDT.

[8]  Alfred V. Aho,et al.  The theory of joins in relational data bases , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[9]  Michaël Thomazo,et al.  Conjunctive Query Answering Under Existential Rules - Decidability, Complexity, and Algorithms , 2013 .

[10]  Sebastian Rudolph,et al.  The Two Views on Ontological Query Answering , 2014, AMW.

[11]  Andrea Calì,et al.  A logical toolbox for ontological reasoning , 2011, SGMD.

[12]  Bruno Marnette,et al.  Generalized schema-mappings: from termination to tractability , 2009, PODS.

[13]  Swan Rocher,et al.  Querying Existential Rule Knowledge Bases: Decidability and Complexity. (Interrogation de Bases de Connaissances avec Règles Existentielles : Décidabilité et Complexité) , 2016 .

[14]  Michaël Thomazo,et al.  A Sound and Complete Backward Chaining Algorithm for Existential Rules , 2012, RR.

[15]  David Maier,et al.  On the foundations of the universal relation model , 1984, TODS.

[16]  Adrian Onet,et al.  The Chase Procedure and its Applications in Data Exchange , 2013, Data Exchange, Information, and Streams.

[17]  Irène Guessarian.  Deciding Boundedness for Uniformly Connected Datalog Programs , 1990, ICDT.

[18]  Catriel Beeri,et al.  The Implication Problem for Data Dependencies , 1981, ICALP.

[19]  Georg Gottlob,et al.  Chase Termination for Guarded Existential Rules , 2015, AMW.

[20]  André Hernich.  Computing universal models under guarded TGDs , 2012, ICDT '12.

[21]  Moshe Y. Vardi.  Decidability and undecidability results for boundedness of linear recursive queries , 1988, PODS.

[22]  Jerzy Marcinkowski,et al.  Achilles, Turtle, and Undecidable Boundedness Problems for Small DATALOG Programs , 1999, SIAM J. Comput..

[23]  Carsten Lutz,et al.  First-Order Rewritability of Frontier-Guarded Ontology-Mediated Queries , 2018, AMW.

[24]  Franz Baader,et al.  Pushing the EL Envelope , 2005, IJCAI.

[25]  Ke Wang.  Some Positive Results for Boundedness of Multiple Recursive Rules , 1995, ICDT.

[26]  Michaël Thomazo,et al.  Sound, Complete, and Minimal Query Rewriting for Existential Rules , 2013, IJCAI.

[27]  Harry G. Mairson,et al.  Undecidable Boundedness Problems for Datalog Programs , 1995, J. Log. Program..

[28]  Diego Calvanese,et al.  DL-Lite: Tractable Description Logics for Ontologies , 2005, AAAI.

[29]  José Luis Ambite,et al.  Optimizing the Chase: Scalable Data Integration under Constraints , 2014, Proc. VLDB Endow..

[30]  Boris Motik,et al.  Benchmarking the Chase , 2017, PODS.

[31]  Andrea Calì,et al.  Taming the Infinite Chase: Query Answering under Expressive Relational Constraints , 2008, Description Logics.

[32]  Michaël Thomazo,et al.  A Single Approach to Decide Chase Termination on Linear Existential Rules , 2018, Description Logics.

[33]  Jean-François Baget,et al.  On rules with existential variables: Walking the decidability line , 2011, Artif. Intell..

[34]  Ronald Fagin,et al.  Data exchange: semantics and query answering , 2003, Theor. Comput. Sci..

[35]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[36]  Jaroslav Nesetril,et al.  The core of a graph , 1992, Discret. Math..

[37]  David Maier,et al.  Testing implications of data dependencies , 1979, SIGMOD '79.

[38]  Jerzy Marcinkowski,et al.  All-Instances Termination of Chase is Undecidable , 2014, ICALP.

[39]  Serge Abiteboul.  Boundedness is Undecidable for Datalog Programs with a Single Recursive Rule , 1989, Inf. Process. Lett..

[40]  Diego Calvanese,et al.  Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family , 2007, Journal of Automated Reasoning.

[41]  Ian Horrocks,et al.  An Introduction to Ontology-Based Query Answering with Existential Rules , 2019 .

[42]  Andrea Calì,et al.  Datalog Extensions for Tractable Query Answering over Ontologies , 2009, Semantic Web Information Management.

[43]  Marie-Laure Mugnier,et al.  On the k-Boundedness for Existential Rules , 2018, RuleML+RR.

[44]  Marie-Laure Mugnier,et al.  Graph-based Knowledge Representation - Computational Foundations of Conceptual Graphs , 2008, Advanced Information and Knowledge Processing.

[45]  Jia-Huai You,et al.  Restricted Chase Termination: A Hierarchical Approach and Experimentation , 2018, RuleML+RR.

[46]  Stavros S. Cosmadakis,et al.  Parallel evaluation of recursive rule queries , 1985, PODS '86.

[47]  Haim Gaifman,et al.  Decidable optimization problems for database logic programs , 1988, STOC '88.

[48]  Jerzy Marcinkowski,et al.  All-Instances Restricted Chase Termination: The Guarded Case , 2019, ArXiv.

[49]  Marie-Laure Mugnier,et al.  On Bounded Positive Existential Rules , 2016, Description Logics.

[50]  Sebastian Rudolph,et al.  Walking the Complexity Lines for Generalized Guarded Existential Rules , 2011, IJCAI.