Structural Subsumption and Least Common Subsumers in a Description Logic with Existential and Number Restrictions

The least common subsumer (lcs) of a set of concept descriptions is the most specific concept description that subsumes all of the concept descriptions in the given set. By computing the lcs, commonalities between concept descriptions can be made explicit. This is an important inference task useful in several applications, including, for instance, the bottom-up construction of description logic knowledge bases.Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an algorithm for computing the lcs in the description logic ALEN which comprises both constructors—number and existential restrictions—as well as concept conjunction, primitive negation, and value restrictions. To prove correctness of our lcs algorithm, we develop a structural characterization of subsumption in ALEN.

[1]  Edith Hemaspaandra The Complexity of Poor Man's Logic , 2001, J. Log. Comput..

[2]  William W. Cohen,et al.  Learning the Classic Description Logic: Theoretical and Experimental Results , 1994, KR.

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

[4]  Francesco M. Donini,et al.  Complexity of Reasoning , 2003, Description Logic Handbook.

[5]  Thomas Mantay Computing Least Common Subsumers in Expressive Description Logics , 1999, Australian Joint Conference on Artificial Intelligence.

[6]  Michael Frazier,et al.  Classic learning , 1994, COLT '94.

[7]  Ulrike Sattler,et al.  Terminological knowledge representation systems in a process engineering application , 1998 .

[8]  Alexander Borgida,et al.  Computing Least Common Subsumers in Description Logics , 1992, AAAI.

[9]  Michael Frazier,et al.  CLASSIC Learning , 1994, COLT.

[10]  Anni-Yasmin Turhan,et al.  Sonic - Non-standard Inferences Go OilEd , 2004, IJCAR.

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

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

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

[14]  M. de Rijke,et al.  JFAK. Essays Dedicated to Johan van Benthem on the occasion of his 50th Birthday , 1999 .

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

[16]  Ralf Küsters,et al.  Computing the Least Common Subsumer and the Most Specific Concept in the Presence of Cyclic ALN-Concept Descriptions , 1998, KI.

[17]  Volker Haarslev,et al.  Description Logic Systems , 2003, Description Logic Handbook.

[18]  Wolfgang Marquardt,et al.  Rome: A repository to support the integration of models over the lifecycle of model-based engineering processes , 2000 .

[19]  Ian Horrocks,et al.  Implementation and Optimization Techniques , 2003, Description Logic Handbook.

[20]  Ralf Möller,et al.  Computing Probabilistic Least Common Subsumers in Description Logics , 1999, KI.

[21]  Franz Baader,et al.  Qualifying Number Restrictions in Concept Languages , 1991, KR.

[22]  Diego Calvanese,et al.  Expressive Description Logics , 2003, Description Logic Handbook.

[23]  Ian Horrocks The FaCT System , 1998, TABLEAUX.

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

[25]  Franz Baader Computing the Least Common Subsumer in the Description Logic EL w.r.t. Terminological Cycles with Descriptive Semantics , 2003, ICCS.

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

[27]  Deborah L. McGuinness,et al.  Matching in Description Logics , 1999, J. Log. Comput..

[28]  Alexander Borgida,et al.  What's in an Attribute? Consequences for the Least Common Subsumer , 2001, J. Artif. Intell. Res..

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

[30]  Volker Haarslev,et al.  SEMANTICS-BASED INFORMATION RETRIEVAL , 1998 .

[31]  Bernhard Nebel,et al.  Terminological Cycles: Semantics and Computational Properties , 1991, Principles of Semantic Networks.

[32]  Franz Baader,et al.  Using automata theory for characterizing the semantics of terminological cycles , 1996, Annals of Mathematics and Artificial Intelligence.

[33]  William W. Cohen,et al.  The learnability of description logics with equality constraints , 1994, Machine Learning.

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