Reasoning and Query Answering in Description Logics

Description Logics (DLs) play a central role as formalisms for representing ontologies and reasoning about them. This lecture introduces the basics of DLs. We discuss the knowledge modeling capabilities of some of the most prominent DLs, including expressive ones, and present some DL reasoning services. Particular attention is devoted to the query answering problem, and to the increasingly popular framework in which data repositories are queried through DL ontologies. We give an overview of the main challenges that arise in this setting, survey some query answering techniques for both lightweight and expressive DLs, and give an overview of the computational complexity landscape.

[1]  Diego Calvanese,et al.  Dwq : Esprit Long Term Research Project, No 22469 on the Decidability of Query Containment under Constraints on the Decidability of Query Containment under Constraints , 2022 .

[2]  Neil Immerman,et al.  Expressibility and Parallel Complexity , 1989, SIAM J. Comput..

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

[4]  Pierre Wolper,et al.  Automata theoretic techniques for modal logics of programs: (Extended abstract) , 1984, STOC '84.

[5]  Vaughan R. Pratt,et al.  Models of program logics , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[6]  Maurizio Lenzerini,et al.  Rewriting Regular Expressions in Semi-Structured Data To appear in ICDT ’ 99 WS on Query Processing for SSD and Non-standard Data Formats , 1999 .

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

[8]  Erich Grädel,et al.  Why are Modal Logics so Robustly Decidable? , 2001, Bull. EATCS.

[9]  Giuseppe De Giacomo.  Decidability of Class Based Knowledge Representation Formalisms , 2009 .

[10]  Diego Calvanese,et al.  Reasoning on regular path queries , 2003, SGMD.

[11]  Ian Horrocks,et al.  Unions of Conjunctive Queries in SHOQ , 2008, KR.

[12]  Ian Horrocks,et al.  The GRAIL concept modelling language for medical terminology , 1997, Artif. Intell. Medicine.

[13]  Moshe Y. Vardi.  The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[14]  Carsten Lutz,et al.  Conjunctive Query Answering in the Description Logic EL Using a Relational Database System , 2009, IJCAI.

[15]  Thomas Eiter,et al.  Query Answering in Description Logics: The Knots Approach , 2009, WoLLIC.

[16]  Carsten Lutz,et al.  Inverse Roles Make Conjunctive Queries Hard , 2007, Description Logics.

[17]  Ian Horrocks,et al.  A Conjunctive Query Language for Description Logic Aboxes , 2000, AAAI/IAAI.

[18]  Ian Horrocks,et al.  Conjunctive Query Answering for the Description Logic SHIQ , 2007, IJCAI.

[19]  Sebastian Rudolph,et al.  Conjunctive Queries for EL with Composition of Roles , 2007, Description Logics.

[20]  Dan Suciu,et al.  Data on the Web: From Relations to Semistructured Data and XML , 1999 .

[21]  Stefano Spaccapietra.  Journal on Data Semantics X , 2008, Journal on Data Semantics X.

[22]  Ian Horrocks,et al.  A Description Logic Based Schema for the Classification of Medical Data , 1996, KRDB.

[23]  Jeffrey D. Ullman,et al.  Generalizing Conjunctive Query Containment for View Maintenance and Integrity Constraint Verification (Abstract) , 1992, Workshop on Deductive Databases, JICSLP.

[24]  Boris Motik,et al.  A Decomposition Rule for Decision Procedures by Resolution-Based Calculi , 2005, LPAR.

[25]  Nikolaj Bjørner,et al.  Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31 - August 5, 2011. Proceedings , 2011, CADE.

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

[27]  Carsten Lutz,et al.  Two Upper Bounds for Conjunctive Query Answering in SHIQ , 2008, Description Logics.

[28]  Diego Calvanese,et al.  Containment of Conjunctive Regular Path Queries with Inverse , 2000, KR.

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

[30]  Carsten Lutz,et al.  Data Complexity in the EL Family of Description Logics , 2007, LPAR.

[31]  Magdalena Ortiz,et al.  Answering Expressive Path Queries over Lightweight DL Knowledge Bases , 2012, Description Logics.

[32]  Heribert Vollmer,et al.  Introduction to Circuit Complexity: A Uniform Approach , 2010 .

[33]  Yevgeny Kazakov,et al.  Status QIO: An Update , 2011, Description Logics.

[34]  Diego Calvanese,et al.  Logical foundations of peer-to-peer data integration , 2004, PODS '04.

[35]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[36]  Maurizio Lenzerini,et al.  Boosting the Correspondence between Description Logics and Propositional Dynamic Logics , 1994, AAAI.

[37]  Stephan Tobies,et al.  The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics , 2011, ArXiv.

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

[39]  Diego Calvanese,et al.  Characterizing Data Complexity for Conjunctive Query Answering in Expressive Description Logics , 2006, AAAI.

[40]  Aniello Murano,et al.  The Complexity of Enriched µ-Calculi , 2006, ICALP.

[41]  Ian Pratt-Hartmann,et al.  Complexity of the Two-Variable Fragment with Counting Quantifiers , 2005, J. Log. Lang. Inf..

[42]  Thomas Eiter,et al.  Query Answering in the Description Logic S , 2010, Description Logics.

[43]  Diego Calvanese,et al.  Regular Path Queries in Expressive Description Logics with Nominals , 2009, IJCAI.

[44]  Thomas Eiter,et al.  Worst-case Optimal Conjunctive Query Answering for an Expressive Description Logic without Inverses , 2008, AAAI.

[45]  Alon Y. Halevy,et al.  Combining Horn Rules and Description Logics in CARIN , 1998, Artif. Intell..

[46]  Sebastian Rudolph,et al.  Nominals, Inverses, Counting, and Conjunctive Queries or: Why Infinity is your Friend! , 2010, J. Artif. Intell. Res..

[47]  Thomas Schwentick,et al.  Rewriting Ontological Queries into Small Nonrecursive Datalog Programs , 2011, Description Logics.

[48]  Giorgio Orsi,et al.  Ontological queries: Rewriting and optimization , 2011, 2011 IEEE 27th International Conference on Data Engineering.

[49]  Giorgio Orsi,et al.  Datalog and Its Extensions for Semantic Web Databases , 2012, Reasoning Web.

[50]  Ulrike Sattler,et al.  The Hybrid µ-Calculus , 2001, IJCAR.

[51]  Jan Hladik.  A Tableau System for the Description Logic SHIO , 2004, IJCAR Doctoral Programme.

[52]  Ian Horrocks,et al.  The Irresistible SRIQ , 2005, OWLED.

[53]  Riccardo Rosati,et al.  On Conjunctive Query Answering in EL , 2007, Description Logics.

[54]  Stephan Tobies,et al.  Complexity results and practical algorithms for logics in knowledge representation , 2001, ArXiv.

[55]  Carsten Lutz,et al.  Complexity of Terminological Reasoning Revisited , 1999, LPAR.

[56]  Georg Gottlob,et al.  Query Answering in the Description Logic Horn- , 2008, JELIA.

[57]  Boris Motik,et al.  OWL 2: The next step for OWL , 2008, J. Web Semant..

[58]  Markus Krötzsch,et al.  OWL 2 Profiles: An Introduction to Lightweight Ontology Languages , 2012, Reasoning Web.

[59]  Jeffrey D. Ullman,et al.  Information integration using logical views , 1997, Theor. Comput. Sci..

[60]  Boris Motik,et al.  Data Complexity of Reasoning in Very Expressive Description Logics , 2005, IJCAI.

[61]  Natalya F. Noy,et al.  Semantic integration: a survey of ontology-based approaches , 2004, SGMD.

[62]  Ian Horrocks,et al.  Reasoning with Individuals for the Description Logic SHIQ , 2000, CADE.

[63]  Yevgeny Kazakov,et al.  Role Conjunctions in Expressive Description Logics , 2008, LPAR.

[64]  Syed S. Ali,et al.  Knowledge representation for natural language processing in implemented systems , 1997, Nat. Lang. Eng..

[65]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[66]  Franz Baader.  Augmenting Concept Languages by Transitive Closure of Roles: An Alternative to Terminological Cycles , 1991, IJCAI.

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

[68]  Franz Baader,et al.  From Tableaux to Automata for Description Logics , 2003, Fundam. Informaticae.

[69]  Ian Horrocks,et al.  The Even More Irresistible SROIQ , 2006, KR.

[70]  Andrea Schaerf,et al.  On the complexity of the instance checking problem in concept languages with existential quantification , 1993, Journal of Intelligent Information Systems.

[71]  Riccardo Rosati,et al.  Improving Query Answering over DL-Lite Ontologies , 2010, KR.

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

[73]  Thomas Eiter,et al.  Query answering in description logics with transitive roles , 2009, IJCAI 2009.

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

[75]  G. Gottlob,et al.  Query Answering in the Description Logic Horn-SHIQ ⋆ , 2008 .

[76]  Stanislav Kikot,et al.  On (In)Tractability of OBDA with OWL 2 QL , 2011, Description Logics.

[77]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..

[78]  Yevgeny Kazakov,et al.  RIQ and SROIQ Are Harder than SHOIQ , 2008, KR.

[79]  Thomas Eiter,et al.  Conjunctive query answering in the description logic SH using knots , 2012, J. Comput. Syst. Sci..

[80]  Sebastian Rudolph,et al.  Worst-Case Optimal Reasoning for the Horn-DL Fragments of OWL 1 and 2 , 2010, KR.

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

[82]  Ian Horrocks.  OWL: A Description Logic Based Ontology Language , 2005, ICLP.

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

[84]  K. Selçuk Candan,et al.  Query caching and optimization in distributed mediator systems , 1996, SIGMOD '96.

[85]  Sebastian Rudolph,et al.  Complexity Boundaries for Horn Description Logics , 2007, AAAI.

[86]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[87]  Diego Calvanese,et al.  Conjunctive query containment and answering under description logic constraints , 2008, TOCL.

[88]  Diego Calvanese,et al.  Decidable Containment of Recursive Queries , 2003, ICDT.

[89]  Diego Calvanese,et al.  Data Complexity of Query Answering in Expressive Description Logics via Tableaux , 2008, Journal of Automated Reasoning.

[90]  Moshe Y. Vardi,et al.  The Hybrid mu-Calculus , 2001 .

[91]  Ian Horrocks,et al.  Practical Reasoning for Very Expressive Description Logics , 2000, Log. J. IGPL.

[92]  Robert Demolombe,et al.  An Extended Relational Algebra on Abstract Objects for Summarizing Answers to Queries , 2003, Fundam. Informaticae.

[93]  Enrico Franconi,et al.  Description Logics for Natural Language Processing , 1994 .

[94]  Giorgos B. Stamou,et al.  Optimized Query Rewriting for OWL 2 QL , 2011, CADE.

[95]  Boris Motik,et al.  Tractable query answering and rewriting under description logic constraints , 2010, J. Appl. Log..

[96]  Sebastian Rudolph,et al.  A NSWERING IS UNDECIDABLE IN DL S WITH REGULAR EXPRESSIONS , INVERSES , NOMINALS , AND COUNTING , 2010 .

[97]  Diego Calvanese,et al.  2ATAs make DLs easy , 2002, Description Logics.

[98]  Boris Motik,et al.  A Comparison of Query Rewriting Techniques for DL-lite , 2009, Description Logics.

[99]  Frank Pfenning,et al.  Logic Programming and Automated Reasoning , 1994, Lecture Notes in Computer Science.

[100]  Diego Calvanese,et al.  The Description Logic Handbook , 2007 .

[101]  Alan Bundy,et al.  Towards Ontology Evolution in Physics , 2008, WoLLIC.

[102]  Sebastian Rudolph,et al.  Query Answering in the Horn Fragments of the Description Logics SHOIQ and SROIQ , 2011, IJCAI.

[103]  Peter Buneman,et al.  Semistructured data , 1997, PODS.

[104]  Frank Wolter,et al.  Semi-qualitative Reasoning about Distances: A Preliminary Report , 2000, JELIA.

[105]  Aniello Murano,et al.  The Complexity of Enriched Mu-Calculi , 2008, Log. Methods Comput. Sci..

[106]  Franz Baader.  Description Logics , 2009, Reasoning Web.

[107]  Maurizio Lenzerini,et al.  Data integration: a theoretical perspective , 2002, PODS.

[108]  Ian Horrocks,et al.  The Even More Irresistible $\mathcal{SROIQ}$ , 2006 .

[109]  Reiko Heckel,et al.  Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets , 2007, Log. Methods Comput. Sci..

[110]  Boris Motik,et al.  Reasoning in description logics using resolution and deductive databases , 2006 .

[111]  Klaus Schild,et al.  A Correspondence Theory for Terminological Logics: Preliminary Report , 1991, IJCAI.

[112]  Bernhard Nebel,et al.  Terminological Reasoning is Inherently Intractable , 1990, Artif. Intell..

[113]  David A. McAllester,et al.  Automated Deduction - CADE-17 , 2000, Lecture Notes in Computer Science.