Acyclic Query Answering under Guarded Disjunctive Existential Rules and Consequences to DLs

The complete picture of the complexity of conjunctive query answer-ing under guarded disjunctive existential rules has been recently settled. However, in the case of (unions of) acyclic conjunctive queries ((U)ACQs) there are some fundamental questions which are still open. It is the precise aim of the present paper to close those questions, and to understand whether the acyclicity of the query has a positive impact on the complexity of query answering. Our main re-sult states that acyclic conjunctive query answering under a fixed set of guarded disjunctive existential rules is EXPTIME-hard. This result together with an EXP-TIME upper bound obtained by exploiting classical results on guarded first-order logic, gives us a complete picture of the complexity of our problem. We also show that our results can be used as a generic tool for establishing results on (U)ACQ answering under several central DLs. In fact, restricting the query lan-guage to UACQs improves the complexity to EXPTIME-complete for any DL between DL-Lite bool and ALCHI; this holds even for fixed TBoxes.

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

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

[3]  Alin Deutsch,et al.  Reformulation of XML Queries and Constraints , 2003, ICDT.

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

[5]  Franz Baader.  Least Common Subsumers and Most Specific Concepts in a Description Logic with Existential Restrictions and Terminological Cycles , 2003, IJCAI.

[6]  Erich Grädel,et al.  On the Restraining Power of Guards , 1999, Journal of Symbolic Logic.

[7]  Andrea Calì,et al.  Towards more expressive ontology languages: The query answering problem , 2012, Artif. Intell..

[8]  Mario Alviano,et al.  Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues , 2012, Theory Pract. Log. Program..

[9]  Diego Calvanese,et al.  The DL-Lite Family and Relations , 2009, J. Artif. Intell. Res..

[10]  Anand Rajaraman,et al.  Conjunctive query containment revisited , 1997, Theor. Comput. Sci..

[11]  Georg Gottlob,et al.  Disjunctive datalog , 1997, TODS.

[12]  Giorgio Terracina,et al.  Efficiently Computable Datalog∃ Programs , 2012, KR.

[13]  Diego Calvanese,et al.  Data Complexity of Query Answering in Description Logics , 2006, Description Logics.

[14]  Sebastian Rudolph,et al.  Extending Decidable Existential Rules by Joining Acyclicity and Guardedness , 2011, IJCAI.

[15]  Ian Horrocks,et al.  Consequence-Based Reasoning beyond Horn Ontologies , 2011, IJCAI.

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

[17]  Johan van Benthem,et al.  Modal Languages and Bounded Fragments of Predicate Logic , 1998, J. Philos. Log..

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

[19]  Georg Gottlob,et al.  Querying the Guarded Fragment , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[20]  Andreas Pieris,et al.  The Impact of Disjunction on Query Answering Under Guarded-Based Existential Rules , 2013, Description Logics.

[21]  Andrea Calì,et al.  A general Datalog-based framework for tractable query answering over ontologies , 2012, J. Web Semant..

[22]  Georg Gottlob,et al.  On the Complexity of Ontological Reasoning under Disjunctive Existential Rules , 2012, MFCS.

[23]  Andrea Calì,et al.  A general datalog-based framework for tractable query answering over ontologies , 2009, SEBD.

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

[25]  Sebastian Rudolph,et al.  A Generic Querying Algorithm for Greedy Sets of Existential Rules , 2012, KR.

[26]  Georg Gottlob,et al.  Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width , 2001, PODS '01.