OntoViBe: An Ontology Visualization Benchmark Florian Haag1 , Steffen Lohmann1 , Stefan Negru2 , and Thomas Ertl1 1 Institute for Visualization and Interactive Systems, University of Stuttgart, Universitätsstraße 38, 70569 Stuttgart, Germany {Florian.Haag,Steffen.Lohmann,Thomas.Ertl}@vis.uni-stuttgart.de 2 Faculty of Computer Science, Alexandru Ioan Cuza University, Strada General Henri Mathias Berthelot 16, 700483 Iasi, Romania stefan.negru@info.uaic.ro Abstract. A variety of ontology visualizations have been presented in the last couple of years. The features of these visualizations often need to be tested during their development or for evaluation purposes. How- ever, in particular for the testing of special concepts and combinations thereof, it can be difficult to find suitable ontologies. We have developed OntoViBe, an ontology covering a wide variety of OWL 2 language con- structs for the purpose of testing ontology visualizations. We describe the design principles underlying OntoViBe and present the supported features in coverage matrices. Finally, we load OntoViBe with ontology visualization tools and point to some noteworthy aspects of the respec- tive visualizations that become apparent and demonstrate how OntoViBe can be used for testing ontology visualizations. Keywords: Ontology, visualization, benchmark, evaluation, OWL. 1 Introduction Developing and working with ontologies can be supported by ontology visu- alizations. Over the past years, a number of visualization approaches geared towards the peculiarities of ontologies have been proposed. Most of the available approaches use node-link diagrams to depict the graph structure of ontologies, while some apply other diagram types like treemaps or nested circles [7,9,11]. During the development of such ontology visualizations, testing with a variety of existing ontologies is required to ensure that the concepts from the underlying ontology language are adequately represented. The same needs to be done to determine the features of an ontology visualization and get an impression of how different ontology language constructs are visually represented. Still, repeatedly loading a set of ontologies that cover a wide variety of language constructs can be a tedious task, even more so as the most common constructs tend to appear over and over in each of the tested ontologies. In order to help that process with respect to ontologies based on the OWL 2 Web Ontology Language, we developed OntoViBe, an Ontology Visualization Benchmark. 14 OntoViBe: An Ontology Visualization Benchmark Basically, OntoViBe is an ontology that has been designed to incorporate a comprehensive set of OWL 2 language constructs and systematic combina- tions thereof. While it is oriented towards OWL 2, it also includes the concepts of OWL 1 due to the complete backwards compatibility of the two ontology languages, i.e., all OWL 1 ontologies are valid OWL 2 ontologies [17]. As opposed to most other benchmarks found in the computing world, On- toViBe is not meant for testing the scalability of visualizations with respect to the number of elements contained in ontologies, but rather aims for the scope of visualizations in terms of supported features. Related to this, it focuses on the representation of what is usually called the TBox of ontologies (i.e., the classes, properties, and datatypes), while it does not support the testing of ABox in- formation (i.e., individuals and data values), which is the focus of most related work. 2 Related Work Several benchmarks for ontology tools have been developed in the past. One well- known benchmark in this area is the Lehigh University Benchmark (LUBM), published by the SWAT research group of Lehigh University [8]. It consist of three components: 1) an ontology of moderate size and complexity describing concepts and relationships from the university domain, 2) a generator for random and repeatable instance data that can be scaled to an arbitrary size, and 3) a set of test queries for the instance data as well as performance metrics. Since the LUBM benchmark is bound to the university domain, the SWAT research group developed another benchmark that can be tailored to different domains [18]. It uses a probabilistic model to generate an arbitrary number of instances based on representative data from the domain in focus. As an example, the Lehigh BibTeX Benchmark (LBBM) has been created with the probabilistic model and a BibTex ontology. Another extension of LUBM has been proposed with the University Ontology Benchmark (UOBM) [12]. UOBM aims to include the complete set of OWL 1 language constructs and defines two ontologies, one being compliant with OWL Lite and the other with OWL DL. Furthermore, it adds several links to the generated instance data and provides related test cases for reasoners. All these benchmarks focus primarily on performance, efficiency, and scala- bility, but do not address the visual representation of ontologies. Furthermore, they are mainly oriented towards instance data (the ABox), while systematic combinations of classes, properties, and datatypes (the TBox) are not further considered. Even though UOBM provides comparatively complete TBox infor- mation, it has been designed to test OWL reasoners and not ontology visual- izations. This is also the case for JustBench [4], which uses small and clearly defined ontology subsets to evaluate the behavior of OWL reasoners. There are also some benchmarks addressing specific aspects of ontology en- gineering. A number of datasets and test cases emerged, for instance, as part of the Ontology Alignment Evaluation Initiative (OAEI) [1]. A related dataset 15 OntoViBe: An Ontology Visualization Benchmark has been created in the OntoFarm project, which provides a collection of on- tologies for the task of of testing and comparing different ontology alignment methods [16]. An extension of the OntoFarm idea is the MultiFarm project, which offers ontologies translated into different languages with corresponding alignments between them [13]. Overall, the test cases are intended to evaluate and compare the quality and performance of matching algorithms, in the latter case with a special focus on multilingualism. The W3C Web Ontology Working Group has also developed test cases for OWL 1 [6] and OWL 2 [15]. They are meant to provide examples for the norma- tive definition of OWL and can, for instance, be used to perform conformance checks. However, there is not yet any benchmark particularly addressing the visualization of ontologies to the best of our knowledge. To close this gap, we developed OntoViBe, which will be described in the following. 3 Ontology Visualization Benchmark (OntoViBe) The structure and content of OntoViBe is based on the OWL 2 specifications [17], with the following requirements: – A wide variety of OWL 2 language constructs must appear. This includes constructs such as class definitions or different kinds of properties, as well as modifiers for these, such as deprecated markers. – Subgraphs that represent compound concepts must appear. This includes small groups of classes that are coupled by a particular property. Moreover, we tried to keep the overall ontology as small as possible in number of elements. Like this, rather than a mere enumeration of the elements and concepts supported by OWL 2, chances are that the ontology can be completely displayed and grasped “at a single glance” and thereby convey a complete impression of the features supported by the visualization being examined. OntoViBe was assembled by creating an instance of each of the subgraph structures. Where possible, classes were reused to keep the ontology small. For instance, to include the OWL element object property, a subgraph structure consisting of two classes connected by an object property was added. Hence, two classes were inserted into the ontology, and an object property that uses either of the two classes as its domain and range, respectively, was defined. Furthermore, the element datatype property needed to appear in the ontology. A compact subgraph structure to express that element consists of a class linked to a datatype property. As the class does not need to have any specific characteristics of its own, one of the two previously inserted classes could be reused. After that, some of the existing elements were modified to cover all elements and features that we wanted to consider at least once in the ontology. For exam- ple, some properties were declared as functional or deprecated. For any element type that still did not appear in the ontology, a minimal number of extra classes were added (the addition of extra properties and datatypes was not necessary). 16 OntoViBe: An Ontology Visualization Benchmark Listing 1.1. Concepts based upon set operators are featured in two variants, a small set with two elements, and a larger one with more elements. 30 this : UnionClass a owl : Class ; 31 owl : unionOf ( this : Class1 this : De pr e ca te dC l as s ) . 32 33 this : La rg e Un io nC l as s a owl : Class ; 34 owl : unionOf ( this : UnionClass other : ImportedClass this : PropertyOwner ) . Listing 1.2. OntoViBe defines custom OWL data ranges. 94 this : D i v i s i b l e B y F i v e E n u m e r a t i o n a rdfs : Datatype ; 95 owl : eq u iv al en t Cl as s [ 96 a rdfs : Datatype ; 97 owl : oneOf ( 5 10 15 20 ) 98 ]. 99 100 this : UnionDatatype a rdfs : Datatype ; 101 owl : unionOf ( this : D i v i s i b l e B y T w o E n u m e r a t i o n this : DivisibleByFiveEnumeration ). Lastly, all elements in the ontology were named in a self-descriptive manner to allow for an easier interpretation and analysis. For instance, a deprecated class is called DeprecatedClass, while the larger of the union classes is called LargeUnionClass. 3.1 Exemplary Parts of OntoViBe Many of the structures could be added in a straightforward way. In some cases, further considerations were required to adequately address the more flexible features of OWL. Concepts defined based upon set operators (unionOf, intersectionOf, comple- mentOf ) come in two variants. One of them uses a set comprising two elements as an example for a small set, while the other features more set elements, usually three (Listing 1.1). OntoViBe also includes OWL data ranges (Listing 1.2). Visualizations may or may not represent the exact definitions of these data ranges, but even if they do not, support for datatype properties with custom data ranges needs to be tested. Therefore, custom data ranges are used by some datatype properties in OntoViBe, while common datatypes are used for most other properties (List- ing 1.3). In order to check how imported ontology elements are treated, OntoViBe consists of two components. The core ontology1 contains most of the definitions, but a few classes, properties, and datatypes are defined in an additional module2 , whose content is imported into the core ontology (Listing 1.4). 1 http://ontovibe.visualdataweb.org/1.0# 2 http://ontovibe.visualdataweb.org/1.0/imported# 17 OntoViBe: An Ontology Visualization Benchmark Listing 1.3. Both custom and common datatypes are used by properties. 114 this : s t a n d a r d T y p e D a t a t y p e P r o p e r t y a owl : D a t a t y p e P r o p e r t y ; 115 rdfs : domain this : PropertyOwner ; 116 rdfs : range xsd : integer . 117 118 this : c u s t o m T y p e D a t a t y p e P r o p e r t y a owl : D a t a t y p e P r o p er t y ; 119 rdfs : domain this : PropertyOwner ; 120 rdfs : range this : D i v i s i b l e B y F i v e E n u m e r a t i o n . Listing 1.4. Some of the definitions are imported from a separate ontology module. 9 < http :// ontovibe . visualdataweb . org /1.0# > a owl : Ontology ; 10 owl : versionIRI < http :// ontovibe . visualdataweb . org /1.0# > ; 11 owl : imports < http :// ontovibe . visualdataweb . org /1.0/ imported # > ; 12 < http :// purl . org / dc / elements /1.1/ title > " Ontology Visualization Benchmark ( OntoViBe ) " . Listing 1.5. Sets of properties connected to the same classes allow for testing whether a visualization positions such properties in a non-overlapping way. This example shows two cyclic properties connected to the same class. 173 this : cy cl i cP ro pe r ty 2 a owl : R e f l e x i v e P r o p e r t y ; 174 rdfs : domain this : M u l t i P r o p e r t y O w n e r ; 175 rdfs : range this : M u l t i P r o p e r t y O w n e r . 176 177 this : cy cl i cP ro pe r ty 3 a owl : ObjectP roperty ; 178 rdfs : domain this : M u l t i P r o p e r t y O w n e r ; 179 rdfs : range this : M u l t i P r o p e r t y O w n e r . In ontology visualizations, sets of properties between the same pair of classes (or the same class and literal) pose a particular challenge, as they may lead to overlapping and thus illegible representations. Several of these cases have been considered in OntoViBe. For instance, Listing 1.5 shows two cyclic properties (i.e., properties whose domain and range are identical) connected to the same class. Finally, a few of the ontology elements are provided with labels, to check how visualizations cope with multilingual labels that may also contain non- ASCII characters (Listing 1.6). For all non-ASCII characters, the escaped ASCII representation is used in the ontology file, as that maximizes the chances for a good compatibility with the parser reading the file. 3.2 Verification of Coverage and Omissions To verify that OntoViBe covers most of the features defined by the OWL 2 spec- ifications, we provide two coverage matrices. Table 1 juxtaposes the elements of OntoViBe with systematically listed OWL 2 features as described in the spec- ifications. Table 2 shows which OntoViBe elements use which concrete OWL 2 identifiers, as per the IRIs declared in the OWL 2 Namespace Document [3]. 18 OntoViBe: An Ontology Visualization Benchmark Listing 1.6. Multilingual labels, some of which contain characters from different scripts, exist for a few of the ontology elements. 135 this : i m p o r t e d T y p e D a t a t y p e P r o p e r t y a owl : D a t a t y p e P r o p e r t y ; 136 rdfs : domain this : PropertyOwner ; 137 rdfs : range other : D i v i s i b l e B y T h r e e E n u m e r a t i o n ; 138 rdfs : label " imported type datatype property " @en ; 139 rdfs : label " propri \ u00E9t \ u00E9 d ’ un type de donn \ u00E9es import \ u00E9 " @fr ; 140 rdfs : label "\ u4E00 \ u79CD \ u5BFC \ u5165 \ u7C7B \ u578B \ u7684 \ u6570 \ u636E \ u7C7B \ u578B \ u6027 \ u8D28 " @zh - Hans . The tables also reveal some parts of OWL that are intentionally not included in OntoViBe: Cardinalities: OntoViBe defines only a few cases of cardinality constraints for properties: Structurally, these can be distinguished as no cardinality, car- dinality on one end of a property relation and cardinality on both ends of a property relation. Regarding the concrete cardinality constraints applied, exact cardinality, a minimum cardinality, and a combination of a minimum and a maximum cardinality are included in OntoViBe. Moreover, one of the cardinality constraints is qualified and thus applies only to instances of a specific class. These cases can thus only be used for checking whether cardi- nalities are displayed at all. We have opted against integrating all supported cardinalities in OntoViBe, as the number of possible combinations would be considerable—in particu- lar, when considering that “special values” such as zero and one might be displayed in special ways. The total number of properties in OntoViBe would have to be increased while providing only minor additional insight into the tested visualization. Annotations: Informative metadata has no effect on the conceptual structure of an ontology, which is focused in OntoViBe. For that reason, only the most prevalent metadata attributes, such as labels or the ontology title, have been integrated into OntoViBe. Equivalent constructs: In cases of conceptually equivalent ways to express statements in OWL, only one way was integrated into OntoViBe. For in- stance, deprecation of ontology elements can either be expressed by adding the owl:deprecated attribute or by declaring the element as belonging to one of the classes owl:DeprecatedClass or owl:DeprecatedProperty. Deprecated elements: Deprecated language constructs of OWL itself are not used in OntoViBe. An example is owl:DataRange that has been deprecated as of OWL 2 in favor of rdfs:Datatype [3]. Moreover, statements referring to particular individuals have not been included, as OntoViBe focuses on visualizations of the TBox of ontologies. 19 OntoViBe: An Ontology Visualization Benchmark 4 Examples of Application In the following, we demonstrate the usefulness of OntoViBe by applying four ontology visualizations to it: SOVA, VOWL, OWLViz, and OntoGraf. The latter two come with the default installation of the popular ontology editor Protégé [2] (desktop version 5.0), while the first two are comparatively well-specified with regard to the visual elements they are based on. Moreover, we analyze the ontol- ogy documentation generated for OntoViBe by the Live OWL Documentation Environment (LODE). We present screenshots of all these ontology visualizations that give an im- pression of the supported features. We point out peculiarities of the visualiza- tion approaches and their implementations that become apparent based on On- toViBe. By this, we would like to provide some examples of how to use OntoViBe for the qualitative analysis of ontology representations, and to confirm that such an analysis is feasible by using OntoViBe. It should be noted that a comprehensive analysis of ontology visualizations requires additional methods, such as a checklist comprising further evaluation criteria. These methods are typically not generic but tailored to the type of visualization. For instance, measures for graph visualizations of ontologies could include the total number of edges and edge crossings. However, such additional measures are outside the scope of this work. 4.1 SOVA Fig. 1. OntoViBe visualized with SOVA. 20 OntoViBe: An Ontology Visualization Benchmark SOVA is a plugin for Protégé that provides graph visualizations of ontolo- gies [5]. When displaying OntoViBe in SOVA 0.8.4 (Figure 1), the distinction of classes, object and datatype properties is instantly visible—though relying purely on colors. Based on OntoViBe, support for functional, inverse functional, and symmetric properties can be seen, as they are marked by little brown circles with short abbreviations for the property characteristics. Furthermore, some of the limitations of the SOVA implementation can be identified. PropertyOwner and MultiPropertyOwner are classes, but at the same time, they are instances of the class PropertyOwnerType. SOVA displays them twice, once as classes and once as individuals, rather than as a single concept. Cardinality constraints are displayed as small colored circles, which are easy to spot—for a combined minimum and maximum cardinality constraint, however, only the lower bound (the number 5 in the green circle) is shown. Overall, the visualization contains many edges and edge crossings, which significantly reduce its readability. A large number of these edges result from the fact that all implicit subclass relations to owl:Thing are depicted in the SOVA visualization, and that every piece of information is shown in a separate node. 4.2 VOWL Literal Thing complemenkkk PlainClass equivalentkkk AlsoEquivalenkkk [dummyProperty] [SubclassBmEquivalekkk] Thing hexBinary subproperty PropertyOwnekkk Subclassmof functionalkkk 1functionalA disjunktemKlasse Subclassmof MultiSubclass Literal FunctionalAnchor ImportedClass 1externalA Intersekkk inverseFunkkk Subclassmof 1disjointA oppositekkk realProperty 1inversemfunctionalA [equivalentDatkkk] functionalkkk UnionDkkk DivisibleByTwkkk intersectikkk disjointPropkkk 1functionalA DeprecatedClass functionalPkkk 1deprecatedA 1functionalA integer unionTypekkk DeprecatedImpkkk 1deprecatedBmexternalA standardTkkk Divisikkk 一种导kkk EquivalentToPkkk [PropertyOwner] deprecatekkk 1disjointA 1disjointA untypedClkkk 1disjointA classToClkkk cyclicProperty classToUnkkk Thing 1symmetricA rationalProkkk Class- 1disjointA customTykkk classToClkkk 1disjointA classToClkkk untypedDatkkk cyclicPropkkk rational deprecatekkk 1disjointA 1disjointA Divisikkk Literal DivisibleByFivkkk multiLpropertymkkk date cyclicPropkkk cyclicPropkkk Fig. 2. OntoViBe visualized with VOWL. VOWL, the Visual Notation for OWL Ontologies, was developed as a means to both obtain a structural overview of OWL ontologies and recognize vari- ous attributes of ontology elements at a glance [11]. It has been implemented 21 OntoViBe: An Ontology Visualization Benchmark in two different tools, a plugin for Protégé and a responsive web application. Figure 2 has been created with version 0.2.15 of the web application (called WebVOWL [10]) that is available at http://vowl.visualdataweb.org. Applying VOWL to OntoViBe shows some typical characteristics of VOWL visualizations, such as equivalent classes being represented as one class with a double border, other special elements being multiplied in the visualization (e.g., owl:Thing), or text in brackets below the labels indicating attributes such as functional or symmetric. Like in SOVA, custom data ranges are not (yet) com- pletely shown, as is seen by the respective nodes that simply display the names of the data ranges (e.g., “Divisib...” for “DivisibleByFiveEnumeration”) but no more information on how they are defined. Moreover, it becomes apparent that the WebVOWL implementation tends to route edges between the same pairs of nodes in a way so as to avoid overlapping labels. As the implicit subclass rela- tions to owl:Thing are not shown in VOWL, the nodes of the graph visualization are less connected than in SOVA. 4.3 OWLViz Fig. 3. OntoViBe visualized with OWLViz. The OWLViz visualization is aimed at visualizing exclusively the hierarchical class structure of ontologies. When used to visualize OntoViBe (Figure 3), the fact that only inheritance (“is-a”) relationships are shown by OWLViz 4.1.2, gets apparent. Also, it gets clear that equivalence relationships between classes are expressed as bidirectional inheritance. Other property relations are not visualized in OWLViz, and also further class or property characteristics are not included, making OWLViz an ontology visualization with very limited expressiveness. 4.4 OntoGraf OntoGraf (Figure 4) depicts property relations between classes with colored lines. Given that OntoViBe includes properties of different types and with different characteristics, it is notable that these are not displayed by OntoGraf 1.0.1 in an inherently distinct way. Again, the graph is highly connected, as the implicit subclass relations to owl:Thing are explicitly shown. Like in OWLViz (Section 4.3), equivalence between classes is displayed by two opposite inheritance arrows. Additionally, classes that are equivalent to others 22 OntoViBe: An Ontology Visualization Benchmark Fig. 4. OntoViBe visualized with OntoGraf. are highlighted by an equivalence symbol. Other than that, the test shows that OntoGraf copes well with several cyclic properties applied to the same class. 4.5 LODE LODE is a documentation generator for ontologies [14]. While LODE is not a visualization approach, the output of version 1.2 after processing OntoViBe can be examined in a similar fashion. Features that get apparent in the excerpt shown in Figure 5 include the transformation of the camel-cased element names into separate words (e.g., DeprecatedClass becomes deprecated class), and the lists of superclasses, subclasses, and connected properties per class. 5 Conclusion and Future Work Based on the OWL 2 specifications, we have defined OntoViBe, a benchmark ontology for testing ontology visualizations. We did not focus on scalability or other common benchmark goals, such as execution speed, but rather on feature completeness and flexibility in terms of combination of elements with regard to the OWL 2 specifications. Since OWL may further evolve in the future, On- toViBe needs to keep being updated accordingly. Features not included in OntoViBe may be considered for future adjuncts of the ontology. For instance, these could be separate modules that focus on 23 OntoViBe: An Ontology Visualization Benchmark Fig. 5. Excerpt of the HTML documentation for OntoViBe generated by LODE. testing specific aspects, such as combinations of cardinality constraints or the population of OntoViBe with individuals and other ABox information. Generally, we hope that our experiences from the development of OntoViBe can benefit other projects, including benchmark data models beyond the task of ontology visualization. References 1. Ontology alignment evaluation initiative. http://oaei.ontologymatching.org 2. Protégé ontology editor. http://protege.stanford.edu 3. The OWL 2 schema vocabulary (OWL 2). http://www.w3.org/2002/07/owl.rdf (2009) 4. 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Springer (2005) 25 b:deprecatedImportedDatatypeProperty b:importedObjectPropertyWithDomain “ˆ” indicates that the re- spective OntoViBe element represents the feature in question, while “ž” signifies that the OntoViBe element is linked to something that Namespace prefix a: de- notes elements of the core ontology, while elements from the additional module b:importedObjectPropertyWithRange b:deprecatedImportedObjectProperty a:complementTypeDatatypeProperty a:intersectionTypeDatatypeProperty OWL 2 features. a:importedTypeDatatypeProperty a:anotherEquivalentDataProperty a:standardTypeDatatypeProperty b:DivisibleByThreeEnumeration a:customTypeDatatypeProperty a:untypedClassToClassProperty a:classToUntypedClassProperty a:deprecatedDatatypeProperty a:unionTypeDatatypeProperty a:DivisibleByTwoEnumeration a:DivisibleByFiveEnumeration a:EquivalentToPropertyOwner a:functionalPropertyAsInverse represents the feature. a:functionalDatatypeProperty b:importedDatatypeProperty a:deprecatedObjectProperty a:inverseFunctionalProperty a:untypedDatatypeProperty a:AlsoEquivalentToSubclass b:DeprecatedImportedClass a:equivalentObjectProperty are marked with b:. a:oppositeDummyProperty a:LargeDisjointUnionClass a:equivalentDataProperty :DisjointPropertyGroup a:LargeIntersectionClass a:classToClassProperty1 a:classToClassProperty2 a:ComplementDatatype a:EquivalentToSubclass a:classToClassProperty a:IntersectionDatatype a:MultiPropertyOwner a:PropertyOwnerType a:DisjointUnionClass :DisjointClassGroup a:functionalProperty :HasSelfRestriction a:FunctionalAnchor a:ComplementClass a:IntersectionClass a:LargeUnionClass a:rationalProperty a:DeprecatedClass a:disjointProperty a:dummyProperty a:cyclicProperty1 a:cyclicProperty2 a:cyclicProperty3 a:PropertyOwner a:UnionDatatype b:ImportedClass a:cyclicProperty a:MultiSubclass a:DisjointClass a:realProperty a:subproperty a:UnionClass a:PlainClass a:Subclass a:Class1 features. b a classes ˆ ˆ ˆ ˆ ˆ ˆ ˆ ž ž ž ž ž ž ž ž ž ž ˆ ˆ ˆ ž ž ž ž ž ž ž ž ž ž ž ž ž ž ž ž ˆ ž ž ž ž ž ˆ ž ž ž ž ž to OWL 2 to plain class deprecated class ˆ ˆ imported class ˆ ˆ ž ž ž ž ž ˆ respect deprecated, imported class complement class ˆ union class ž ž ˆ ˆ ž intersection class ž ž ž ˆ ˆ ž disjoint union class ž ž ž ž ˆ ˆ owl:Thing ž ž ž ž ž ž owl:Nothing datatypes respect enumeration type ˆ ˆ ž ˆ union type ž ž ˆ with intersection type ž ž ˆ complement type ž ˆ by existential quantifiers elements with by universal quantifiers imported type ž ˆ literals elements OntoViBe: An Ontology Visualization Benchmark untyped ž typed, as standard type ž ž ž ž ž typed, as owl:rational ˆ ˆ ˆ ˆ ELEMENTS typed, as owl:real typed, as custom type ˆ ž typed, as union type ˆ ž typed, as intersection type ˆ ž typed, as complement type ˆ ž table of OntoViBe 26 typed, as imported type ž properties ž of OntoViBe subproperty property without domain or range ž ˆ ˆ ˆ ˆ ˆ datatype property ž ž ž ž ž ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ object property ž ž ž ž ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ subclass ž ž ž subproperty ž ž type property ž ž ž disjoint property ž ž ž ž ž ž label property ž ž deprecated property ž ˆ ˆ ˆ ˆ imported property ˆ ˆ ˆ ˆ ˆ 1. Coverage deprecated, imported property class equivalence ž ž ž ž ž property equivalence ž ž ž ž ž inverse property ž functional property ž ˆ ˆ ˆ table inverse functional property ž ˆ reflexive property ž ˆ irreflexive property ž ž ˆ symmetric property ž ˆ ž ˆ Table asymmetric property transitive property ˆ ž ˆ ž Table 1. Coverage property with hasSelf restriction connections class to class ž ž ž ž ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ class to literal ž ž ž ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ equivalent classes ˆ ˆ ˆ ˆ ˆ more than two equivalent classes ˆ ˆ ˆ equivalent properties ž ˆ ˆ ˆ ˆ ˆ more than two equivalent properties ˆ ˆ ˆ ž ž ˆ ˆ ˆ ˆ STRUCTURES link from one class to itself several links from one class to itself ž ˆ ˆ ˆ several links between pair of classes ž ž ˆ ˆ ˆ ˆ ˆ inverse links between pair of classes ž ž ˆ ˆ ˆ ˆ ˆ cardinality on one side of property ž ž ž ž ž cardinality on both sides of property ž ž ž qualified cardinality on property ž ž disjoint relationship between two classes ž ž disjoint relationship between n classes ž ž ž ˆ disjoint relationship between two properties ˆ ˆ disjoint relationship between n properties ž ž ž ž ž ˆ metainformation several language-tagged labels ž ontology title ˆ ontology IRI ˆ ˆ ontology version ˆ ˆ OntoViBe: An Ontology Visualization Benchmark Table 2. Coverage table Table of OntoViBe 2. Coverage elements table of OntoViBe with elements with respect respect to OWL 2 to OWL 2 identifiers. identifiers. ˆ versionIRI ˆ unionOf ˆ propertyDisjointWith ˆ onProperty ˆ oneOf ˆ onClass ˆ minQualifiedCardinality ˆ minCardinality ˆ members ˆ maxCardinality ˆ inverseOf ˆ intersectionOf ˆ imports ˆ hasSelf ˆ equivalentProperty ˆ equivalentClass ˆ disjointWith ˆ disjointUnionOf ˆ deprecated ˆ complementOf ˆ cardinality ˆ TransitiveProperty ˆ Thing ˆ SymmetricProperty ˆ Restriction ˆ ReflexiveProperty ˆ Ontology ˆ ObjectProperty ˆ IrreflexiveProperty ˆ InverseFunctionalProperty ˆ FunctionalProperty ˆ DatatypeProperty ˆ Class ˆ AsymmetricProperty ˆ AllDisjointProperties ˆ AllDisjointClasses Namespace prefix a: de- withRestrictions versionInfo topObjectProperty topDataProperty targetValue targetIndividual sourceIndividual someValuesFrom sameAs qualifiedCardinality propertyChainAxiom priorVersion onProperties onDatatype onDataRange maxQualifiedCardinality incompatibleWith hasValue hasKey distinctMembers differentFrom datatypeComplementOf bottomObjectProperty bottomDataProperty backwardCompatibleWith assertionProperty annotatedTarget annotatedSource annotatedProperty allValuesFrom OntologyProperty Nothing NegativePropertyAssertion NamedIndividual DeprecatedProperty DeprecatedClass DataRange Axiom AnnotationProperty Annotation notes elements of the core ontology, while elements from the additional module are marked with b:. a ˆ ˆ ˆ a:PlainClass ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ a:DeprecatedClass a:Class1 ˆ ˆ a:ComplementClass ˆ a:UnionClass ˆ ˆ a:LargeUnionClass a:IntersectionClass ˆ ˆ a:LargeIntersectionClass a:DisjointUnionClass ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ a:LargeDisjointUnionClass a:PropertyOwnerType a:PropertyOwner ˆ ˆ ˆ ˆ a:MultiPropertyOwner a:DisjointClass ˆ ˆ ˆ ˆ :DisjointClassGroup ˆ ˆ a:Subclass ˆ ˆ a:MultiSubclass a:DivisibleByTwoEnumeration ˆ ˆ ˆ ˆ a:DivisibleByFiveEnumeration a:UnionDatatype ˆ a:IntersectionDatatype ˆ a:ComplementDatatype ˆ a:standardTypeDatatypeProperty ˆ ˆ ˆ ˆ ˆ ˆ ˆ a:untypedDatatypeProperty a:customTypeDatatypeProperty a:unionTypeDatatypeProperty a:intersectionTypeDatatypeProperty a:complementTypeDatatypeProperty a:importedTypeDatatypeProperty a:classToClassProperty ˆ a:classToUntypedClassProperty ˆ a:untypedClassToClassProperty ˆ a:EquivalentToPropertyOwner ˆ ˆ ˆ ˆ ˆ ˆ a:EquivalentToSubclass a:AlsoEquivalentToSubclass a:cyclicProperty ˆ ˆ a:cyclicProperty1 :HasSelfRestriction ˆ ˆ ˆ a:cyclicProperty2 ˆ a:cyclicProperty3 ˆ ˆ a:classToClassProperty1 a:classToClassProperty2 ˆ a:deprecatedDatatypeProperty ˆ ˆ ˆ a:deprecatedObjectProperty ˆ ˆ ˆ ˆ ˆ ˆ a:dummyProperty a:oppositeDummyProperty a:equivalentObjectProperty ˆ a:subproperty a:realProperty ˆ ˆ ˆ ˆ a:equivalentDataProperty ˆ ˆ a:anotherEquivalentDataProperty a:rationalProperty a:FunctionalAnchor ˆ a:functionalProperty ˆ ˆ a:inverseFunctionalProperty ˆ a:functionalPropertyAsInverse ˆ ˆ ˆ a:functionalDatatypeProperty ˆ a:disjointProperty ˆ ˆ :DisjointPropertyGroup ˆ ˆ b ˆ ˆ b:ImportedClass ˆ ˆ b:DeprecatedImportedClass ˆ b:DivisibleByThreeEnumeration ˆ ˆ b:importedObjectPropertyWithRange ˆ b:importedObjectPropertyWithDomain ˆ b:importedDatatypeProperty ˆ b:deprecatedImportedObjectProperty ˆ ˆ b:deprecatedImportedDatatypeProperty ˆ ˆ 27