Triplifying Equivalence Set Graphs

Abstract

In order to conduct large-scale semantic analyses, it is necessary to calculate the deductive closure of very large hierarchical structures. Unfortunately, contemporary reasoners cannot be applied at this scale, unless they rely on expensive hardware such as a multi-node inmemory cluster. In order to handle large-scale semantic analyses on commodity hardware such as regular laptops we introduced [1] a novel data structure called Equivalence Set Graph (ESG). An ESG allows to specify compact views of large RDF graphs thus easing the accomplishment of statistical observations like the number of concepts de ned in a graph, the shape of ontological hierarchies etc. ESGs are built by a procedure presented in [1] that delivers graphs as a set of maps storing nodes and edges. In this demo paper (i) we show how facts entailed by an ESG and the graph itself can be speci ed in RDF following a novel introduced ontology; and, (ii) we present two datasets resulting from the tripli cation of two ESG graphs (one for classes and one for properties).

Keywords

• Semantic Web Linked Open Data Empirical Semantics

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An Equivalence Set Graph (ESG) is a tuple hV; E ; peq; psub; pe; psi. The nodes V of an ESG are equivalence sets of terms from the universe of discourse. The directed edges E of an ESG are specialization relations between those equivalence sets. peq is an equivalence relation that determines which equivalence sets are formed from the terms in the universe of discourse. psub is a partial order relation that determines the specialization relation between the equivalence sets. In order to handle equivalences and specializations of peq and psub (see below for details and examples), we introduce pe, an equivalence relation over properties (e.g., owl:equivalentProperty) that allows to retrieve all the properties that are equivalent to peq and psub, and ps which is a specialization relation over Copyright c 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

Asprino et al. owl:equivalentProperty :myEquivalentClass :mySubClassOf rdfs:subPropertyOf rdfs:subClassOf

:myEquivalentClass :mySubClassOf dbo:Person foaf:Person org:Agent

owl:equivalentClass owl:equivalentClass dul:Person owl:equivalentClass rdfs:subClassOf dul:Agent

rdfs:subClassOf rdfs:subClassOf dul:SocialAgent dul:PhysicalAgent dul:Agent, org:Agent dbo:Person, dul:Person, foaf:Person dul:PhysicalAgent dul:SocialAgent (a) RDF Knowledge Graph (b) Equivalence Set Graph properties (e.g., rdfs:subPropertyOf) that allows to retrieve all the properties that specialize peq and psub.

The inclusion of the parameters peq, psub, pe, and ps makes the Equivalence Set Graph a very generic concept. By changing the equivalence relation (peq), ESG can be applied to classes (owl:equivalentClass), properties (owl:equivalentProperty), or instances (owl:sameAs). By changing the specialization relation (psub), ESG can be applied to class hierarchies (rdfs:subClassOf), property hierarchies (rdfs:subPropertyOf), or concept hierarchies (skos:broader).

Figure 1 shows an example of an RDF Knowledge Graph (Sub gure 1a). The equivalence predicate (peq) is owl:equivalentClass; the specialization predicate (psub) is rdfs:subClassOf, the property for asserting equivalences among predicates (pe) is owl:equivalentProperty, the property for asserting specializations among predicates (ps) is rdfs:subPropertyOf. The corresponding Equivalence Set Graph (Sub gure 1b) contains four equivalence sets. The top node represents the agent node, which encapsulates entities in DOLCE and W3C's Organization ontology. Three nodes inherit from the agent node. Two nodes contain classes that specialize dul:Agent in the DOLCE ontology (i.e. dul:PhysicalAgent and dul:SocialAgent). The third node represents the person concept, which encapsulates entities in DBpedia, DOLCE, and FOAF. The equivalence of these classes is asserted by owl:equivalentClass and :myEquivalentClass. Since foaf:Person specialises org:Agent (using :mySubClassOf which specialises rdfs:subClassOf) and dul:Person specialises dul:Agent the ESG contains an edge between the person and the agent concept.

The procedure for computing an Equivalence Set Graph has been presented in [ 1 ]. In the remaining of this document we present how to specify statements entailed by an ESG and the graph itself in RDF. 2

Equivalence Set Graph Ontology

individual of the class esgs:EquivalenceSetGraph and it is connected to its nodes by the object property esgs:hasNode having esgs:Node as range. Nodes are associated with entities composing the equivalence set by the object property esgs:contains. Edges of the graph can be speci ed as triples having esgs:isAdjacentTo (or one of its sub-properties) as predicate. Currently the ontology declares two sub-properties of esgs:isAdjacentTo, namely esgs:specia lizes and its inverse esgs:isSpecializedBy (that have been used for the analysis presented in [ 1 ]), but esgs:isAdjacentTo can be furtherly specialized whenever the framework is extended to allow the analysis of other kinds of relations. Individuals of esgs:EquivalenceSetGraph are also associated with the relations used for building the graph, namely peq, psub, pe and ps, by means of properties esgs:observesEquivalenceProperty, esgs:observesSpecializationProperty, esgs:equivalencePropertyForProperties and esgs:specializationProperty ForProperties. Moreover, the property esgs:computedFrom allows to associate an ESG with the dcat:Dataset from which the graph has been computed. Rules. The ontology also de nes two rules (in SWRL) that allow to materialise statements entailed by an ESG:

Equivalence Closure. If equivalence sets of a graph ?g have been formed using the property ?peq as ground term and two entities ?e1 and ?e2 belong to the same node ?n (i.e. ?e1 and ?e2 belong to the equivalence set) of the graph ?g, then, ?e1 and ?e2 are declared equivalent by means of property ?peq. esgs:hasNode(?g, ?n) ^ esgs:observesEquivalenceProperty(?g, ?peq)^ esgs:contains(?n, ?e1) ^ esgs:contains(?n, ?e2) )

swrlb:add(?e1, ?peq, ?e2) ^ swrlb:add(?e2, ?peq, ?e1)

Specialization. If the following conditions hold: (i) specialization relations (i.e. edges) of an ESG ?g have been computed using a property ?psub as ground term; (ii) nodes ?n1 and ?n2 contain the entities ?e1 and ?e2 respectively; and, (iii) ?n1 specializes ?n2 ; then, we can assert that ?e1 specializes ?e2 by means of property ?psub.

esgs:observesSpecializationProperty(?g, ?psub) ^ esgs:hasNode(?g, ?n1)^ esgs:hasNode(?g, ?n2) ^ esgs:contains(?n1, ?e1) ^ esgs:contains(?n2, ?e2)^ 3

Planned Demonstration

We plan a live demonstration where the audience will be able to compute and query a number of Equivalence Set Graphs speci ed in RDF. Some of Equivalence Set Graphs available for querying will be pre-computed, while others will be computed live during the demo. Pre-computed datasets include the triplication of two (very large) Equivalence Set Graphs computed from LOD-a-lot [ 2 ] and presented in [ 1 ]: one for classes and one for properties.

Moreover, the audience will be able to compute some (small) Equivalence Set Graphs using the framework presented in [ 1 ]. The framework provides a simple command line interface that allows the users to input the parameters needed for computing the ESG, i.e.: an equivalence relation (i.e. peq) and a specialization relation (i.e. psub) they would like observe (pe and ps will be xed to owl:equivalentProperty and rdfs:subPropertyOf, otherwise an ESG for pe and ps would need to be calculated to retrieve properties in the closure of peq and psub). Then, the framework will estimate the time needed for computing the ESG for the input properties so to ensure that the ESG can be computed during the demo session. Once the ESG is computed, it will be uploaded to a triple store and available for querying.

In [ 1 ] we have shown how Equivalence Set Graphs can be used for performing statistical observation on modeling style and semantic structure of very large datasets. In this demonstration our objective is to show that Equivalence Set Graphs are also useful for retrieving data that are not explicitly asserted in an input dataset (that could be very large). By querying the tripli ed ESG a user is able to retrieve all the entities (e.g. classes, properties, individuals) that are implicitly equivalent to or specialized by a given entity. This is can be done even for very large datasets, like LOD-a-lot, without running reasoners or using property paths that may require expensive computational resources.

References

[1] Luigi Asprino , Wouter Beek, Paolo Ciancarini, Frank van Harmelen, and Valentina Presutti. \ Observing LOD using Equivalent Set Graphs: it is mostly at and sparsely linked" . In: Proc of ISWC 2019 .

[2] Javier D. Fernandez , Wouter Beek, Miguel A. Mart nez-Prieto, and Mario Arias. \LOD-a-lot - A Queryable Dump of the LOD Cloud" . In: Proc of ISWC 2017 .