Mining Cardinalities from Knowledge Bases Emir Muñoz and Matthias Nickles Fujitsu Ireland Ltd. Insight Centre for Data Analytics, NUI Galway DEXA 2017, August 28-31, Lyon, France 

Structured data Dynamic data Schema-less data Resource Description Framework (RDF) is … Good for the Web (data integration, transfer, etc.) Bad for users (reusability, trust, understanding, etc.) Challenges arise due to the Open World Assumption (OWA) and non-Unique Name Assumption (nUNA) in OWL/RDF Motivation (1/4) 

Motivation (2/4) ▷ Open World Assumption: The truth value of an assertion is not necessarily known If an assertion is not in the knowledge base we cannot say it is negative ▷ No Unique Name Assumption: Individuals may have more than one name 

Motivation (3/4) ▷ Domains, ranges, and cardinalities are usually not defined :Ireland 6,378,000 idemo:population dbpedia- owl:Population 6,378,000 igeo:capitale :Dublin dbpedia- owl:Capital :Dublin No central schema! • Hard to write queries [1] • How am I suppose to reuse these data? Cardinalities! :Irlande igeo:capitale :Dublin Many different ontologies [1] Schmidt, M., Meier, M., Lausen, G.: Foundations of SPARQL query optimization. In: ICDT, ACM (2010) 4-33 Same entity 

Motivation (4/4) ▷ Cardinalities indicate us the structure of things (concepts) height width weight legs (2) arms (2) head (1) name address age … capital (1) counties (many) height weight rivers (0 to many) mountains population languages (1 to many) time zone 

Related work (1/2) ▷ Cardinality constraints/bounds Constraint Languages for RDF: ShEx[2], RDD[3], SHACL[4], SPIN[5], OSLC[6] ▷ Consistency in RDF KBs No work has focused on the extraction of cardinalities to detect inconsistencies in KBs. Previous work focused on property values missing, not cardinalities ▷ RDF schema discovery Use of rule mining to infer an ontology Use of SPARQL queries to mine simple cardinalities (issues) [2] https://www.w3.org/2013/ShEx/Primer [3] P. M. Fischer, G. Lausen, A. Schatzle, and M. Schmidt. RDF Constraint Checking. EDBT/ICDT Workshops 2015. [4] https://www.w3.org/TR/shacl/ [5] http://spinrdf.org/ [6] https://www.w3.org/Submission/2014/SUBM-shapes-20140211/ 

Related work (2/2) ▷ The cardinality query problem: how many cities? :Ireland dbpedia-owl:city :Dublin :Irlande dbpedia-owl:city :Galway owl:sameAs SELECT COUNT(?city) WHERE { :Ireland dbpedia-owl:city ?city . } SELECT COUNT(?city) WHERE { :Irlande dbpedia-owl:city ?city . } 1 1 2 

Preliminaries (1/2) ▷ Knowledge bases can be represented using RDF model ▷ RDF does not assume unique names  we need UNA 2.0 RDF model  Set of resource: ℛ e.g.: ex:JonSnow  Set of blank nodes: ℬ e.g.: _:bnode  Set of predicates: e.g.: rdf:type  Set of literals: ℒ e.g.: “Francia@es”  ≡ { , , ∈ ∪ × × ( ∪ ∪ )} 

Preliminaries (2/2) ▷ Knowledge bases can be represented using RDF model ▷ RDF does not assume unique names  we need UNA 2.0 

Cardinality bounds in RDF ▷ A cardinality bound in RDF data restricts the number of properties P related with a resource in a given context ▷ Formally, ≡ , = (, ) ▷ Lower bound ∈ ℕ, and upper bound ∈ ℕ ∪ ∞ 

Mining cardinality patterns (1/6) ▷ In practice, a cardinality bound could be validated using SPARQL 1.1 ▷ (1) But a normalization on equality is required Two implementations: SPARQL rewrite, and Programmatic rewrite 

Mining cardinality patterns (2/6) ▷ owl:sameAs is reflexive, symmetric and transitive owl:sameAs-cliques and data rewriting :Ireland :Irlande owl:sameAs :Irlanda owl:sameAs :Irlandia owl:sameAs :Ireland :Irlande owl:sameAs :Irlanda owl:sameAs :Irlandia owl:sameAs owl:sameAs owl:sameAs 

Mining cardinality patterns (3/6) ▷ (2) After, cardinality can be extracted ▷ (3) However, data are not always clean Outliers detection and filtering is required max min median box Q1 Q3 arms (4)?!? 

Mining cardinality patterns (4/6) 

Mining cardinality patterns (5/6) Representative element equivalence type induced by owl:sameAs-cliques Very expensive query! 

Mining cardinality patterns (6/6) Parallelism  

Evaluation (1/6) ▷ We took different syntactic and real-world knowledge bases Good number of owl:sameAs axioms 

Evaluation (2/6) ▷ Qualitative evaluation: runtime ▷ UOBM with owl:sameAs axioms ▷ Mondial without owl:sameAs axioms SPARQL 253.908 sec Spark 15.634 sec SPARQL 117.739 sec Spark 2.948 sec 16x faster 40x faster 

Evaluation (3/6) ▷ Quantitative evaluation: consistency and completeness ▷ Randomly selected 1 class per dataset and 5 predicates ▷ A property in the context of a type is complete given a cardinality constraint if every entity of type has the ‘right number’ of triples (, , ); and incomplete otherwise ▷ A predicate in the context of a type is consistent if the triples with predicate and subject of type comply with the cardinality bounds; and inconsistent otherwise 

Evaluation (4/6) ▷ For example: ▷ Completeness: All books should have a property author, but not all should have a review property ▷ Consistency A single book should have between x and y authors 

Evaluation (5/6) ▷ Synthetic datasets are more consistent than real-world 

Evaluation (6/6) ▷ Subset of cardinality bounds from the Mondial dataset ▷ card({mondial:hasCity}, mondial:Country) = (1, 31) Not satisfied by China (306), India (99), USA (250), Brazil (210) and Russia (171) 

Thanks! Any questions? Emir Muñoz [email protected] Key points: - KBs lack the description of cardinalities - A data normalization is required to extract accurate cardinalities - An outlier filtering is required to extract robust cardinalities - Cardinality bounds can help us to assess consistency and completeness