Attributed Description Logics : Ontologies for Knowledge Graphs ( Extended Technical Report )

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 EL, and we cover SROIQ, the DL underlying OWL 2 DL.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[17]  A. K. Chandra,et al.  Alternation , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

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

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

[20]  Sebastian Rudolph,et al.  Complexities of Horn Description Logics , 2013, TOCL.

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