Attributed Description Logics: Ontologies for Knowledge Graphs

In modelling real-world knowledge, there often arises a need to represent and reason with meta-knowledge. To equip description logics (DLs) for dealing with such ontologies, we enrich DL concepts and roles with finite sets of attribute–value pairs, called annotations, and allow concept inclusions to express constraints on annotations. We show that this may lead to increased complexity or even undecidability, and we identify cases where this increased expressivity can be achieved without incurring increased complexity of reasoning. In particular, we describe a tractable fragment based on the lightweight description logic \(\mathcal {EL}\), and we cover \(\mathcal {SROIQ}\), the DL underlying OWL 2 DL.

[1]  Ian Pratt-Hartmann.  Complexity of the Two-Variable Fragment with Counting Quantifiers , 2005, J. Log. Lang. Inf..

[2]  Nicole Tourigny,et al.  Bio2RDF: Towards a mashup to build bioinformatics knowledge systems , 2008, J. Biomed. Informatics.

[3]  Johann A. Makowsky,et al.  Embedded implicational dependencies and their inference problem , 1981, STOC '81.

[4]  Umberto Straccia,et al.  A General Framework for Representing and Reasoning with Annotated Semantic Web Data , 2010, AAAI.

[5]  Markus Krötzsch,et al.  Wikidata , 2014, Commun. ACM.

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

[7]  Diego Calvanese,et al.  Linking Data to Ontologies: The Description Logic DL-Lite_A , 2006, OWLED.

[8]  Jens Lehmann,et al.  DBpedia - A crystallization point for the Web of Data , 2009, J. Web Semant..

[9]  Markus Krötzsch,et al.  Logic on MARS: Ontologies for Generalised Property Graphs , 2017, IJCAI.

[10]  Michael Günther,et al.  Introducing Wikidata to the Linked Data Web , 2014, SEMWEB.

[11]  Catriel Beeri,et al.  The Implication Problem for Data Dependencies , 1981, ICALP.

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

[13]  Val Tannen,et al.  Provenance semirings , 2007, PODS.

[14]  Pascal Hitzler,et al.  A better uncle for OWL: nominal schemas for integrating rules and ontologies , 2011, WWW.

[15]  Marko A. Rodriguez,et al.  Constructions from Dots and Lines , 2010, ArXiv.

[16]  Sebastian Rudolph,et al.  Nominal Schemas in Description Logics: Complexities Clarified , 2014, KR.

[17]  Markus Krötzsch,et al.  Attributed Description Logics : Ontologies for Knowledge Graphs ( Extended Technical Report ) , 2017 .

[18]  Yevgeny Kazakov,et al.  RIQ and SROIQ Are Harder than SHOIQ , 2008, KR.

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

[20]  Diego Reforgiato Recupero,et al.  Annotated RDF , 2006, ESWC.

[21]  Franz Baader,et al.  Pushing the EL Envelope , 2005, IJCAI.