An Approach to Exploring Description Logic Knowledge Bases

This paper is the successor to two previous papers published at the ICFCA conference. In the first paper we have shown that in the Description Logics $\mathcal{EL}$ and $\mathcal{EL}_{\rm gfp}$, the set of general concept inclusions holding in a finite model always has a finite basis. An exploration formalism that can be used to obtain this basis was presented in the second paper. In this paper we show how this formalism can be modified such that counterexamples to GCIs can be provided in the form of ABox-individuals. In a second part of the paper we examine which description logics can be used for this ABox.

[1]  Harry S. Delugach,et al.  Conceptual Structures at Work , 2004, Lecture Notes in Computer Science.

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

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

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

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

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

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

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

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

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

[11]  Franz Baader,et al.  How Pervasive Is the Myerson-Satterthwaite Impossibility? , 2009, IJCAI.

[12]  M. Ashburner,et al.  Gene Ontology: tool for the unification of biology , 2000, Nature Genetics.

[13]  Franz Baader,et al.  Exploring Finite Models in the Description Logic , 2009, ICFCA.

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

[15]  Kent A. Spackman,et al.  SNOMED RT: a reference terminology for health care , 1997, AMIA.