Query Inseparability for ALC Ontologies

Abstract We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable for conjunctive queries (CQs), but 2 ExpTime -complete for unions of CQs (UCQs). The same results hold if (U)CQs are replaced by rooted (U)CQs, where every variable is connected to an answer variable. We also show that inseparability by CQs is still undecidable if one KB is given in the lightweight DL EL and if no restrictions are imposed on the signature of the CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query over any ABox in a given signature and show that, for CQs, this problem is undecidable, too. We then develop model-theoretic criteria for Horn ALC TBoxes and show using tree automata that, in contrast, inseparability becomes decidable and 2 ExpTime -complete, even ExpTime -complete when restricted to (unions of) rooted CQs.

[1]  Ian Horrocks,et al.  Module Extraction in Expressive Ontology Languages via Datalog Reasoning , 2016, J. Artif. Intell. Res..

[2]  Mark A. Musen,et al.  Promptdiff: a fixed-point algorithm for comparing ontology versions , 2002, AAAI/IAAI.

[3]  Boris Motik,et al.  Reasoning in Description Logics by a Reduction to Disjunctive Datalog , 2007, Journal of Automated Reasoning.

[4]  Kewen Wang,et al.  Revising General Knowledge Bases in Description Logics , 2010, KR.

[5]  Carsten Lutz,et al.  Foundations for Uniform Interpolation and Forgetting in Expressive Description Logics , 2011, IJCAI.

[6]  Boris Konev,et al.  Logical Difference Computation with CEX2.5 , 2012, IJCAR.

[7]  Carsten Lutz,et al.  The Complexity of Conjunctive Query Answering in Expressive Description Logics , 2008, IJCAR.

[8]  T. S. E. Maibaum,et al.  Conservative Extensions, Interpretations Between Theories and All That! , 1997, TAPSOFT.

[9]  Magdalena Ortiz,et al.  Ontology-Mediated Query Answering with Data-Tractable Description Logics , 2015, Reasoning Web.

[10]  Diego Calvanese,et al.  The MASTRO system for ontology-based data access , 2011, Semantic Web.

[11]  Carsten Lutz,et al.  Query-Based Entailment and Inseparability for ALC Ontologies , 2016, IJCAI.

[12]  Petros S. Stefaneas,et al.  Logical support for modularisation , 1993 .

[13]  Till Mossakowski,et al.  Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design , 2010, Logica Universalis.

[14]  Carsten Lutz,et al.  Foundations of instance level updates in expressive description logics , 2011, Artif. Intell..

[15]  Wolfgang Rautenberg,et al.  A concise introduction to mathematical logic , 2006 .

[16]  David Pearce,et al.  Infinitary equilibrium logic and strongly equivalent logic programs , 2017, Artif. Intell..

[17]  Boris Konev,et al.  Forgetting and Uniform Interpolation in Large-Scale Description Logic Terminologies , 2009, IJCAI.

[18]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[19]  Ian Horrocks,et al.  Modular Reuse of Ontologies: Theory and Practice , 2008, J. Artif. Intell. Res..

[20]  Riccardo Rosati,et al.  Query-Based Comparison of Mappings in Ontology-Based Data Access , 2016, KR.

[21]  Boris Konev,et al.  Inseparability and Conservative Extensions of Description Logic Ontologies: A Survey , 2016, RW.

[22]  Jean Christoph Jung,et al.  Conservative Extensions in Horn Description Logics with Inverse Roles , 2020, J. Artif. Intell. Res..

[23]  Ian Horrocks,et al.  Supporting concurrent ontology development: Framework, algorithms and tool , 2011, Data Knowl. Eng..

[24]  Luca Pulina,et al.  Minimal Module Extraction from DL-Lite Ontologies Using QBF Solvers , 2009, IJCAI.

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

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

[27]  David Pearce,et al.  Strongly equivalent logic programs , 2001, ACM Trans. Comput. Log..

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

[29]  Stefan Woltran,et al.  Semantical characterizations and complexity of equivalences in answer set programming , 2005, TOCL.

[30]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[31]  Carsten Lutz,et al.  Deciding inseparability and conservative extensions in the description logic EL , 2010, J. Symb. Comput..

[32]  Frank Wolter,et al.  Query Inseparability for Description Logic Knowledge Bases , 2014, KR.

[33]  Wolfgang Thomas,et al.  Languages, Automata, and Logic , 1997, Handbook of Formal Languages.

[34]  Ludwig Staiger,et al.  Ω-languages , 1997 .

[35]  Boris Konev,et al.  The Logical Difference for the Lightweight Description Logic EL , 2012, J. Artif. Intell. Res..

[36]  David E. Muller,et al.  Alternating Automata on Infinite Trees , 1987, Theor. Comput. Sci..

[37]  Carsten Lutz,et al.  Non-Uniform Data Complexity of Query Answering in Description Logics , 2012, Description Logics.

[38]  Patrick Koopmann,et al.  Forgetting and Uniform Interpolation for ALC-Ontologies with ABoxes , 2014, Description Logics.

[39]  Tania Tudorache,et al.  Managing Change: An Ontology Version Control System , 2008, OWLED.

[40]  Maurizio Lenzerini,et al.  On Instance-level Update and Erasure in Description Logic Ontologies , 2009, J. Log. Comput..

[41]  Jeff Z. Pan,et al.  ELIMINATING CONCEPTS AND ROLES FROM ONTOLOGIES IN EXPRESSIVE DESCRIPTIVE LOGICS , 2014, Comput. Intell..

[42]  Giorgos Stoilos,et al.  Optimising Resolution-Based Rewriting Algorithms for DL Ontologies , 2013, Description Logics.

[43]  Michael Zakharyaschev,et al.  Ontology-Based Data Access: Ontop of Databases , 2013, SEMWEB.

[44]  Carsten Lutz,et al.  Did I Damage My Ontology? A Case for Conservative Extensions in Description Logics , 2006, KR.

[45]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[46]  E. Muller David,et al.  Alternating automata on infinite trees , 1987 .

[47]  Frank Wolter,et al.  Logic-based ontology comparison and module extraction, with an application to DL-Lite , 2010, Artif. Intell..

[48]  Diego Calvanese,et al.  Exchanging OWL 2 QL Knowledge Bases , 2013, IJCAI.

[49]  Diego Calvanese,et al.  Answering Regular Path Queries in Expressive Description Logics: An Automata-Theoretic Approach , 2007, AAAI.

[50]  Yevgeny Kazakov,et al.  Consequence-Driven Reasoning for Horn SHIQ Ontologies , 2009, IJCAI.

[51]  Thomas Eiter,et al.  Query Rewriting for Horn-SHIQ Plus Rules , 2012, AAAI.

[52]  Stefan Woltran.  Equivalence between Extended Datalog Programs - A Brief Survey , 2010, Datalog.

[53]  Kewen Wang,et al.  DL-Lite Ontology Revision Based on An Alternative Semantic Characterization , 2015, ACM Trans. Comput. Log..

[54]  Sebastian Rudolph,et al.  (Non-)Succinctness of uniform interpolants of general terminologies in the description logic EL , 2014, Artif. Intell..

[55]  Yavor Nenov,et al.  Pay-as-you-go Ontology Query Answering Using a Datalog Reasoner , 2015, Description Logics.

[56]  Andrea Schaerf.  Query Answering in Concept-Based Knowledge Representation Systems: Algorithms, Complexity, and Seman , 1994 .

[57]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.

[58]  Jérôme Euzenat,et al.  Ontology Matching: State of the Art and Future Challenges , 2013, IEEE Transactions on Knowledge and Data Engineering.

[60]  Carsten Lutz,et al.  First-Order Rewritability of Atomic Queries in Horn Description Logics , 2013, IJCAI.

[61]  Michael Zakharyaschev,et al.  Ontology-Based Data Access with Databases: A Short Course , 2013, Reasoning Web.

[62]  Diego Calvanese,et al.  Knowledge Base Exchange , 2016, Description Logics.

[63]  Frank Wolter,et al.  Games for query inseparability of description logic knowledge bases , 2016, Artif. Intell..

[64]  Franz Baader,et al.  Query and Predicate Emptiness in Ontology-Based Data Access , 2016, J. Artif. Intell. Res..

[65]  M. Rabin.  Automata on Infinite Objects and Church's Problem , 1972 .

[66]  P. van Emde Boas.  The convenience of tiling , 1996 .

[67]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

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

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

[70]  Jeff Z. Pan,et al.  Forgetting for knowledge bases in DL-Lite , 2010, Annals of Mathematics and Artificial Intelligence.

[71]  Moshe Y. Vardi.  Reasoning about The Past with Two-Way Automata , 1998, ICALP.

[72]  Jean Christoph Jung,et al.  Conservative Extensions in Guarded and Two-Variable Fragments , 2017, ICALP.

[73]  Patrick Koopmann,et al.  Uniform Interpolation and Forgetting for ALC Ontologies with ABoxes , 2014, AAAI.

[74]  Michel C. A. Klein,et al.  Ontology Versioning and Change Detection on the Web , 2002, EKAW.

[75]  Carsten Lutz,et al.  Query Containment in Description Logics Reconsidered , 2012, KR.

[76]  Birte Glimm,et al.  Optimizing SPARQL Query Answering over OWL Ontologies , 2013, J. Artif. Intell. Res..

[77]  Diego Calvanese,et al.  Linking Data to Ontologies , 2008, J. Data Semant..