A Survey on how Description Logic Ontologies Benefit from FCA

Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and obtained differ significantly between these two research areas. Despite these differences, there have been several attempts to bridge the gap between these two formalisms, and attempts to apply methods from one field in the other. The present work aims to give an overview on the research done in combining Description Logics and Formal Concept Analysis.

[1]  Bijan Parsia,et al.  Laconic and Precise Justifications in OWL , 2008, SEMWEB.

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

[3]  Gerd Stumme,et al.  The Concept Classification of a Terminology Extended by Conjunction and Disjunction , 1996, PRICAI.

[4]  Bernhard Ganter,et al.  Pseudo-models and propositional Horn inference , 2005, Discret. Appl. Math..

[5]  Stefan Schlobach,et al.  Non-Standard Reasoning Services for the Debugging of Description Logic Terminologies , 2003, IJCAI.

[6]  Sebastian Rudolph,et al.  Exploring Relational Structures Via FLE , 2004, ICCS.

[7]  Holger Knublauch,et al.  The Protégé OWL Plugin: An Open Development Environment for Semantic Web Applications , 2004, SEMWEB.

[8]  Sebastian Rudolph.  An FCA Method for the Extensional Exploration of Relational Data , 2003 .

[9]  Bijan Parsia,et al.  Finding All Justifications of OWL DL Entailments , 2007, ISWC/ASWC.

[10]  Franz Baader,et al.  A Finite Basis for the Set of EL-Implications Holding in a Finite Model , 2008, ICFCA.

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

[12]  Susanne Prediger.  Terminologische Merkmalslogik in der Formalen Begriffsanalyse , 2000 .

[13]  Franz Baader,et al.  CEL - A Polynomial-Time Reasoner for Life Science Ontologies , 2006, IJCAR.

[14]  Ian Horrocks,et al.  FaCT++ Description Logic Reasoner: System Description , 2006, IJCAR.

[15]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

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

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

[18]  B. Sertkaya.  Computing the hierarchy of conjunctions of concept names and their negations in a Description Logic knowledge base using Formal Concept Analysis ? , 2005 .

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

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

[21]  Gerd Stumme,et al.  Theory-driven Logical Scaling: Conceptual Information Systems meet Description Logics , 1999, KRDB.

[22]  Sebastian Rudolph,et al.  Relational exploration: combining description logics and formal concept analysis for knowledge specification , 2006 .

[23]  Richard Holzer.  Knowledge Acquisition under Incomplete Knowledge using Methods from Formal Concept Analysis: Part I , 2004, Fundam. Informaticae.

[24]  Gerd Stumme,et al.  Distributive Concept Exploration - A Knowledge Acquisition Tool in Formal Concept Analysis , 1998, KI.

[25]  Richard Holzer,et al.  Treating Incomplete Knowledge in Formal Concept Analysis , 2005, Formal Concept Analysis.

[26]  Amedeo Napoli,et al.  Ontology Refinement through Role Assertion Analysis: Example in Pharmacogenomics , 2008, Description Logics.

[27]  Amedeo Napoli,et al.  Role Assertion Analysis: a proposed method for ontology refinement through assertion learning , 2008, STAIRS.

[28]  Rudolf Wille,et al.  Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts , 2009, ICFCA.

[29]  Sebastian Rudolph,et al.  Acquiring Generalized Domain-Range Restrictions , 2008, ICFCA.

[30]  Franz Baader,et al.  Computing the Least Common Subsumer w.r.t. a Background Terminology , 2004, Description Logics.

[31]  Bernhard Ganter,et al.  Attribute Exploration with Background Knowledge , 1999, Theor. Comput. Sci..

[32]  Richard Holzer,et al.  On the Treatment of Incomplete Knowledge in Formal Concept Analysis , 2000, ICCS.

[33]  Franz Baader,et al.  Applying Formal Concept Analysis to Description Logics , 2004, ICFCA.

[34]  Sergei A. Obiedkov,et al.  Modal Logic for Evaluating Formulas in Incomplete Contexts , 2002, ICCS.

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

[36]  Felix Distel,et al.  Exploring Finite Models in the Description Logic ELgfp , 2009 .

[37]  Bernhard Ganter,et al.  Two Basic Algorithms in Concept Analysis , 2010, ICFCA.

[38]  Felix Distel.  An Approach to Exploring Description Logic Knowledge Bases , 2010, ICFCA.

[39]  Bijan Parsia,et al.  Pellet: An OWL DL Reasoner , 2004, Description Logics.

[40]  Franz Baader,et al.  Building and Structuring Description Logic Knowledge Bases Using Least Common Subsumers and Concept Analysis , 2000, ICCS.

[41]  Fakultat Informatik,et al.  Formal Concept Analysis Methods for Description Logics , 2008 .

[42]  Rafael Peñaloza,et al.  On the Complexity of Axiom Pinpointing in the EL Family of Description Logics , 2010, KR.

[43]  Rafael Peñaloza,et al.  Axiom Pinpointing in General Tableaux , 2007, TABLEAUX.

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

[45]  Ralf Küsters,et al.  Computing Least Common Subsumers in Description Logics with Existential Restrictions , 1999, IJCAI.

[46]  Franz Baader,et al.  Usability Issues in Description Logic Knowledge Base Completion , 2009, ICFCA.

[47]  Ralf Küsters,et al.  Computing Least Common Subsumers in ALEN , 2001, IJCAI.

[48]  Bernhard Ganter,et al.  Completing Description Logic Knowledge Bases Using Formal Concept Analysis , 2007, IJCAI.

[49]  Amedeo Napoli,et al.  A Proposal for Combining Formal Concept Analysis and Description Logics for Mining Relational Data , 2007, ICFCA.

[50]  Bijan Parsia,et al.  Repairing Unsatisfiable Concepts in OWL Ontologies , 2006, ESWC.

[51]  HolzerRichard.  Knowledge Acquisition under Incomplete Knowledge using Methods from Formal Concept Analysis: Part II , 2004 .

[52]  Olivier Ridoux,et al.  Arbitrary Relations in Formal Concept Analysis and Logical Information Systems , 2005, ICCS.

[53]  Boris Motik,et al.  Hypertableau Reasoning for Description Logics , 2009, J. Artif. Intell. Res..

[54]  F. Baader.  Computing a Minimal Representation of the Subsumption Lattice of All Conjunctions of Concepts De ned in a Terminology ? , 1995 .

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