Reasoning in Description Logics: Basics, Extensions, and Relatives

This tutorial covers the very basics of Description Logics (DLs): first, we present the primary DL ALC, namely its syntax, semantics, and reasoning problems, making use of a running example. Next, we discuss a few important extensions and explain DL's relationship with first order logic, with modal logic, with OWL, and with rule-based formalisms, and give a brief sketch of tableau-based reasoning algorithms for DLs.

[1]  Boris Motik,et al.  Bridging the gap between OWL and relational databases , 2007, WWW '07.

[2]  Gernot Salzer,et al.  Automated Deduction in Classical and Non-Classical Logics , 2002, Lecture Notes in Computer Science.

[3]  Franz Baader,et al.  A Formal Definition for the Expressive Power of Terminological Knowledge Representation Languages , 1996, J. Log. Comput..

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

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

[6]  Peter F. Patel-Schneider,et al.  Optimising Propositional Modal Satisfiability for Description Logic Subsumption , 1998, AISC.

[7]  Steffen Staab,et al.  OntoEdit: Guiding Ontology Development by Methodology and Inferencing , 2002, OTM.

[8]  Riccardo Rosati,et al.  Towards expressive KR systems integrating datalog and description logics: preliminary report , 1999, Description Logics.

[9]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[10]  Boris Motik,et al.  A Faithful Integration of Description Logics with Logic Programming , 2007, IJCAI.

[11]  Carlos Areces,et al.  Logic Engineering. The Case of Description and Hybrid Logics , 2000 .

[12]  Ian Horrocks,et al.  A Little Semantic Web Goes a Long Way in Biology , 2005, SEMWEB.

[13]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

[14]  Peter F. Patel-Schneider,et al.  Next Steps for OWL , 2006, OWLED.

[15]  Franz Baader,et al.  An Overview of Tableau Algorithms for Description Logics , 2001, Stud Logica.

[16]  Ian Horrocks,et al.  A Tableaux Decision Procedure for SHOIQ , 2005, IJCAI.

[17]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[18]  Enrico Motta,et al.  The Semantic Web - ISWC 2005, 4th International Semantic Web Conference, ISWC 2005, Galway, Ireland, November 6-10, 2005, Proceedings , 2005, SEMWEB.

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

[20]  Ralf Küsters,et al.  Approximation and Difference in Description Logics , 2002, KR.

[21]  Ralf Küsters.  Non-Standard Inferences in Description Logics , 2001, Lecture Notes in Computer Science.

[22]  Maarten Marx,et al.  A Road-Map on Complexity for Hybrid Logics , 1999, CSL.

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

[24]  Ian Horrocks,et al.  A proposal for an owl rules language , 2004, WWW '04.

[25]  I. Horrocks,et al.  A Tableau Decision Procedure for $\mathcal{SHOIQ}$ , 2007, Journal of Automated Reasoning.

[26]  Thomas R. Gruber,et al.  Toward principles for the design of ontologies used for knowledge sharing? , 1995, Int. J. Hum. Comput. Stud..

[27]  A. Zimmermann,et al.  Entering the 21st century. , 2007 .

[28]  Franz Baader,et al.  Expressive Number Restrictions in Description Logics , 1999, J. Log. Comput..

[29]  Raymond Reiter,et al.  What should a database know? , 1988, PODS '88.

[30]  Enrico Franconi,et al.  A survey of temporal extensions of description logics , 2001, Annals of Mathematics and Artificial Intelligence.

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

[32]  Franz Baader,et al.  On the Problem of Computing Small Representations of Least Common Subsumers , 2002, KI.

[33]  Boris Motik,et al.  Query Answering for OWL-DL with Rules , 2004, International Semantic Web Conference.

[34]  Volker Haarslev,et al.  RACER System Description , 2001, IJCAR.

[35]  Roy Dyckhoff.  Automated Reasoning with Analytic Tableaux and Related Methods , 2000, Lecture Notes in Computer Science.

[36]  James A. Hendler,et al.  Swoop: A Web Ontology Editing Browser , 2006, J. Web Semant..

[37]  James A. Hendler,et al.  Debugging unsatisfiable classes in OWL ontologies , 2005, J. Web Semant..

[38]  Andrei Voronkov,et al.  Current Trends in Theoretical Computer Science , 2001 .

[39]  Moshe Y. Vardi.  Why is Modal Logic So Robustly Decidable? , 1996, Descriptive Complexity and Finite Models.

[40]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[41]  Ian Horrocks,et al.  Practical Reasoning for Expressive Description Logics , 1999, LPAR.

[42]  Hans Tompits,et al.  Combining answer set programming with description logics for the Semantic Web , 2004, Artif. Intell..

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

[44]  Jan L. Top,et al.  Engineering ontologies , 1997, Int. J. Hum. Comput. Stud..

[45]  P. Schönemann.  On artificial intelligence , 1985, Behavioral and Brain Sciences.

[46]  Alexander Borgida,et al.  On the Relative Expressiveness of Description Logics and Predicate Logics , 1996, Artif. Intell..

[47]  Erich Grädel,et al.  Decidability issues for action guarded logics , 2000, Description Logics.

[48]  Ian Horrocks,et al.  Just the right amount: extracting modules from ontologies , 2007, WWW '07.

[49]  Yarden Katz,et al.  Pellet: A practical OWL-DL reasoner , 2007, J. Web Semant..

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

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

[52]  Ian Horrocks,et al.  Decidability of SHIQ with Complex Role Inclusion Axioms , 2003, IJCAI.

[53]  Jan Hladik.  Implementation and Optimisation of a Tableau Algorithm for the Guarded Fragment , 2002, TABLEAUX.

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

[55]  Ian Horrocks,et al.  Building a bioinformatics ontology using OIL , 2002, IEEE Transactions on Information Technology in Biomedicine.

[56]  Franz Baader,et al.  A Scheme for Integrating Concrete Domains into Concept Languages , 1991, IJCAI.

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

[58]  Ian Horrocks,et al.  From SHIQ and RDF to OWL: the making of a Web Ontology Language , 2003, J. Web Semant..

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

[60]  Ian Horrocks,et al.  OilEd: a Reason-able Ontology Editor for the Semantic Web , 2001, Description Logics.

[61]  Francesco M. Donini,et al.  AL-log: Integrating Datalog and Description Logics , 1998, Journal of Intelligent Information Systems.

[62]  Alan Robinson,et al.  The Inverse Method , 2001, Handbook of Automated Reasoning.

[63]  Ian Horrocks,et al.  Using an Expressive Description Logic: FaCT or Fiction? , 1998, KR.

[64]  Diego Calvanese,et al.  Reasoning in Expressive Description Logics , 2001, Handbook of Automated Reasoning.

[65]  Matthew Horridge,et al.  Supporting Early Adoption of OWL 1.1 with Protege-OWL and FaCT++ , 2006, OWLED.

[66]  Ian Horrocks,et al.  Optimised Reasoning for SHIQ , 2002, ECAI.

[67]  Stuart J. Russell,et al.  Artificial Intelligence , 1999 .

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

[69]  Ian Horrocks,et al.  Optimised Reasoning for {$\mathcal SHIQ$} , 2002 .

[70]  Klaus Schild,et al.  Terminological Cycles and the Propositional µ-Calculus , 1994, KR.

[71]  Volker Haarslev,et al.  Consistency Testing: The RACE Experience , 2000, TABLEAUX.

[72]  Ian Horrocks,et al.  Experience building a Large, Re-usable Medical Ontology using a Description Logic with Transitivity and Concept Inclusions , 1997 .

[73]  Diego Calvanese,et al.  Description Logics for Conceptual Data Modeling , 1998, Logics for Databases and Information Systems.

[74]  Andrea Schaerf.  Reasoning with Individuals in Concept Languages , 1993, AI*IA.

[75]  K. Upton,et al.  A modern approach , 1995 .

[76]  Olivier Bodenreider,et al.  Bio-ontologies: current trends and future directions , 2006, Briefings Bioinform..

[77]  James A. Hendler,et al.  The Semantic Web" in Scientific American , 2001 .

[78]  Carsten Lutz,et al.  Description Logics with Concrete Domains-A Survey , 2002, Advances in Modal Logic.

[79]  Franz Baader,et al.  How to Prefer More Specific Defaults in Terminological Default Logic , 1993, IJCAI.

[80]  Neil Immerman,et al.  Descriptive Complexity and Finite Models , 1997 .

[81]  G Stix,et al.  The mice that warred. , 2001, Scientific American.

[82]  Riccardo Rosati,et al.  DL+log: Tight Integration of Description Logics and Disjunctive Datalog , 2006, KR.

[83]  Michael Uschold,et al.  The Enterprise Ontology , 1998, The Knowledge Engineering Review.

[84]  Gerhard Lakemeyer,et al.  KI 2002: Advances in Artificial Intelligence , 2002, Lecture Notes in Computer Science.

[85]  Ullrich Hustadt,et al.  Issues of Decidability for Description Logics in the Framework of Resolution , 1998, FTP.

[86]  Francesco M. Donini,et al.  Description logics of minimal knowledge and negation as failure , 2002, TOCL.

[87]  Leszek Pacholski,et al.  Complexity Results for First-Order Two-Variable Logic with Counting , 2000, SIAM J. Comput..

[88]  Gunter Saake,et al.  Logics for databases and information systems , 1998 .

[89]  Diego Calvanese,et al.  Epistemic First-order Queries over Description Logic Knowledge Bases , 2006, Description Logics.

[90]  Nicola Guarino,et al.  Formal ontology, conceptual analysis and knowledge representation , 1995, Int. J. Hum. Comput. Stud..

[91]  Phokion G. Kolaitis,et al.  On the Decision Problem for Two-Variable First-Order Logic , 1997, Bulletin of Symbolic Logic.

[92]  Ralf Küsters,et al.  Matching under Side Conditions in Description Logics , 2001, IJCAI.

[93]  Zahir Tari,et al.  On the Move to Meaningful Internet Systems 2002: CoopIS, DOA, and ODBASE , 2002, Lecture Notes in Computer Science.

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

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