EL++ Implementation Notes

Below is a summary of the Arity/Prolog term form of EL++ that we have implemented (including Prolog operator definitions).

Axioms:

  Role inclusion                     R1 @< R2                              op(700,xfx)

  Role equality                       R1 @= R2                              op(700,xfx) (nonstd op)

  Concept inclusion              C1 < C2                  op(600,xfx)

  Concept equality                C1 = C2                  op(700,xfy)

 

Role operator:

  Composition                        *                                              R1 * R2 (uses std op(400,yfx))

 

Concept operators:

  Conjunction                        list                                           [C1, ... Cn]

  Existential                            e(R,C)                    

  Top                                       '$t'

  Bottom                 '$b'

  Nominal                               n(I)                                          (singleton name for non-unique individual)

  Concrete                             cc(T)                                       Term is for concrete concept (NYI)

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  

ABox assertions:

  Concept                               Nom << Concept  op(550,yfx)

  Role                                      r(Role,Nom1,Nom2)

 

 

References

More information on Ontologies and DLs may be found at the following sites:

The DL Home Page

http://dl.kr.org/

The DAML Home Page

http://www.daml.org/

The Semantic Web Home Page

http://www.semanticweb.org/

The International Conference on Automated Reasoning with Analytic Tableaux and Related Methods

http://i12www.ira.uka.de/TABLEAUX/

The Laboratory for Applied Ontology

http://ontology.ip.rm.cnr.it/Publications.html

 

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Horrocks, I. , Sattler, U. , and Tobies S.  “Reasoning with Individuals for the Description Logic SHIQ.”

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Horrocks, I. , Sattler, U. , and Tobies S.  A Description Logic with Transitive and Converse Roles, Role Hierarchies and Qualifying Number Restrictions. LTCS-Report LTCS-99-08, LuFG Theoretical Computer Science, RWTH Aachen, 1999. Revised version. 

Horrocks, I. and Tessaris, S. Querying the semantic web: a formal approach. In I. Horrocks and J. Hendler, editors, Proc. of the 2002 International Semantic Web Conference (ISWC 2002), number 2342 in Lecture Notes in Computer Science. Springer-Verlag, 2002.

Lutz, C. The Complexity of Reasoning with Concrete Domains. PhD thesis, Teaching and Research Area for Theoretical Computer Science, RWTH Aachen, 2001.