An ontology for describing ontology metrics. It contains the underlying information of the NEOntometrics application by connecting database and calculation values with background information and proposed metric frameworks.
The individuals stored in this ontology correspond to metric values that are calculated and stored in the database. They are connected to subclasses from the class Elemental Metrics. These kind of metrics describe atomic measurements for assessing ontologies. The elemental metrics are then connected by mathematical relations to subclasses of "Quality Frameworks". These frameworks represent metric calculations as proposed in the literature.
NEOntometrics Ontology Metrics Ontology.
A formal definiton for the metric given by the framework's authors.
A description for the element given be the metric/frameworks authors.
A guideline by the author of the framework how to interpret a given value.
Connects ontology metrics to quality implications.
Some of the frameworks not only propose ontology metrics, but also connect these metrics to quality dimensions like "Maintainablility" or "Reusability". The implications are mapped using these connections.
states that a metric negatively affects a quality dimension.
states that a metric positively affects a quality dimension.
The relation asserts how a metric is decomositioned into the essential Metrics
States that a metric directly uses the given Elemental Metrics.
An Example for this property is oquals "Maximum Depth" measurement. While it originates from a framework, it does not propose a ratio between two measurements, but directly reuses the Elemental_Metric "maximum depth".
use the following: "numerator only METRIC_A and divisor only METRIC_B" Do not use the division-class directly!
Represents the composition of a ratio-value through the use of its subclasses numerator and divisor.
Points from the elemental metrics to the individuals representing the actual measurements in database and calculation engine.
States that a quality dimension is negatively affected by a metric.
States that a quality dimension is positively affected by a metric.
Defines that two framework metrics measures something similar (But not the same)
Even though this measurement indeed says that two things measure the same element, saying that they are equivalent in description logic has large side effects, so we use this similarTO relation.
Calculates the Standard Deviation of a set of values. Takes a list of values as an input
The relations to handle subtstractions of metrics.
States that two or more metrics are summed up.
An array containing the imported ontologies (with transitive closure).
Often, an ontology imports other ontologies, to facilitate the reusing of knowledge or the seperation of concerns. This item shows all imported ontologies, including such with transitive closure.
It means if A imports B, and B imports C, this for A, this metric shows B and C.
Non logical annotations on a class (e.g., rdfs:comment)
Metrics related to annotation properties.
Annotations provide human centered descriptions and explanations.
Counts the number of annotation domain declarations of the annotation properties.
Annotation Domain restrictions in the settings of the annotation properties limit the classes on where an annotation can be put. If "Class" (1) "hasAnnotation" (2) "Annotation" (3), the class (1) is limited through the domain element.
Counts the number of annotation range declarations of the (custom) annotation properties.
Annotation Range restrictions in the settings of the annotation properties limit the types or classes that can be used as an annotation. If "Class" (1) "hasAnnotation" (2) "Annotation" (3), the annotation (3) is limited through the Range element. Examples are datatypes like "xsd:integer" or other classes (if these other classes are used as annotations for a class)
Annotations can be put on almost all elements of the ontology. This metric counts how many annotation elements are put on classes.
Counts the number of Annotations on Classes.
Counts the number of annotations on data properties.
This metric counts how manny annoations are put on data properties E.g., hasAge -> "How old a thing is"
Counts the number of annotations on datatypes.
Counts the number of annotation on data types (e.g., xsd:Int)
Counts the number of annotations on individuals.
Counts the number of annotation on individuals (or instances). E.g. Individual 'Herbert' which is an instance of the class 'Person' has the Annotation 'rdfs:comment: Nice person"
Counts the number of annotations on object properties.
Measures the annotations set on object properties, thus relations between classes. E.g.: inLoveWith -> The romantical feeling to one another.
Counts the number of annotations on the ontology in general.
Counts the annotations set on the ontology in general. E.g.,: "This is an ontology about family relations"
Calculates the number of human centered class annotations. This can be based on built-in annotation properties like e.g., rdfs:comment, or rdfs:seeAlso, or self-created properties.
Class expressions that are not classes itself (e.g., relations)
Counts the number of object properties that are "asymmetric"
If an object property is asymmetric, and a relation of individual A->B exist, then there can be no relation B->A. E.g., the parentOf would be asymmetric.
Git-Based Information. The name of the person who made the change.
The number of axioms declared in an ontology.
The building blocks of an ontology. Triple that state a fact about the conceptualized reality (e.g.Rat rdfs:subClassOf Animal) is an Axiom.
Every other metric is, at least in a way, derived from the axioms that form the conceptualization we want to analyze.The larger this axioms number is, the larger is the ontology normally. However, an axiom can be anything. Like a class declaration, an annotation or relationship assertions. So a larger number of axioms does not necessarly mean the ontology is more complex, it could also be a a mere taxonomy (is-a statements).
Metrics that measure the very basic constructs every ontology consists of.
Metrics concerned with the width of the Graph
Breath metrics measure aspects regarding the siblings in an ontology graph. Sibblings are classes that are on the same inheritance (e.g., with one sub class distance from the root classes).
Counts the number of assertions from instances to classes.
A declared individual (or instance) can belong to none, one or many classes (as long as they are not disjoint).
Metrics that are calculated per class in the ontology.
Class Metrics give an further insight into the individual classes. They are calculated once for every class in the ontology.
The number of declared classes in the ontology.E.g, through rdfs:subClassOf or owl:Class declarations.
Classes are the objects that the ontology describes further. They are the objects in our conceptualizations, the elements that we want to link with each other. Taking the W3C definition, "A class defines a group of individuals that belong together because they share some properties"
The higher the number of classes, the larger is our universe of discourse. An ontology that defines a large number of classes, thus can be considered "large"
Cycles are subclass relationships like A subClassOf B; B subClassOf C, C subClassOf A. This metrics counts the number of classes in these kind of cycles.
Cycles are ususally bad ontology design. Please note that the occurence of cycles in the ontology prevents a lot of further calculations (e.g., how to measure depth of there are cyclic sub class relationships. Further, most reasoners cannot work with cycles in the ontology, thus detecting (rightfully so) inconsistencies.
The number of classes that use share a relation with another class.
Can be used to determine whether the usage of the various relation properties is rather diverse or homogenous.
The number of Classes that have asserted individuals
Ontologies are often used to structure actual items into abstract concepts (e.g. "Peter" is an individual of the class "Human"). This number shows how many of the abstract concepts actually have a instances (also often named "individuals").
Can be used to find how much of the ontological structure of a knowledge base is used, and how much is e.g., obsolete.
The number of classes that have more than one parent.
Depending on the kind of conceptualization, a class often belongs to more than one parent. (E.g., A "human" could be part of "mammal" and "carnivore").
For some kind of conceptualizations, one might want to discourage multi-inheritance relationships.Often, these mutli-inheritance relationships make the ontology harder to understand and also increases the chance of incoonsistencies in combination with the usage of disjoint axioms.
Number of Classes that are connected to other classes using Object Properties
The number of classes that have subclasses (and are, thus, not leaf classes)
Counts the number of classes that have children (Thus, all classes that are not leaf classes)
This metric (in composition with others) can tell much on the structure of the ontology graph. E.g., many leaf classes and just a few "classes with subclasses" indicate a shallow ontology
Average Depth of Inheritance Tree of all Leaf Nodes, ADIT-LN is the sum of depths of all paths divided by the total number of paths. A depth is the total number of nodes. A depth is the total number of nodes starting from the root node to the leaf node in a path. The total number of paths in an ontology is all distinct paths from each root node to each leaf node if there exists an inheritance path from the root node to the leaf node. And root node is the first level in each path.
cohesion metrics ADIT-LN is a direct measure to count the depth of the inheritance tree for all leaf nodes measurement: (classes) in ontologies.
Number of Leaf Classes (NoL) is the number of leaf classes explicitly defined in the ontology Oi . A leaf class in an ontology means the class has no semantic subclass explicitly defined in the ontology Oi.
Number of Root Classes (NoR) is the number of root classes explicitly defined in the ontology Oi . A root class in an ontology means the class has no semantic super class explicitly defined in the ontology Oi.
Count the root nodes (classes) in ontologies
Yao, Haining; Orme, Anthony Mark; Etzkorn, Letha (2005): Cohesion Metrics for Ontology Design and Application. In J. of Computer Science 1 (1), pp. 107–113. DOI: 10.3844/jcssp.2005.107.113.
Git-Based Information. The name of the person who commits the change.
Git-Based Information. A Hex-Information that unambigously identifies a commit in a repository.
Git-Based Information. The (manually provided) git commit message.
Git-Based Information. The date and time when the commit occured.
The E-Mail of the person who accepts the commit.
The average path length of the ontology.
Please note that the number of pathes is understood in this paper as the number of connections of all concepts to the root classes. For our calculation engine, that is equivalent to the number of Superclasses (As it states how many connections there are to the top) plus the number of subclasses of thing. The latter is necessary as these metrics would not otherwise be counted as they have no superclasses. But for the given metric framework, these top level concepts are counted as the first hierachical level
Average Paths Per Concept must be equal to or greater than 1 (each concept must have a parent except for the most general concept). If =1 then the ontology is a tree. Multi relation cocepts multi relation concepts(higher "average relationships per concept ratio ratio) result in gy higher ρ ratio for an ontology Please note that the number of pathes is understood in this paper as the number of connections of all concepts to the root classes. For our calculation engine, that is equivalent to the number of Superclasses (As it states how many connections there are to the top) plus the number of subclasses of thing. The latter is necessary as these metrics would not otherwise be counted as they have no superclasses. But for the given metric framework, these top level concepts are counted as the first hierachical level
The average relations per concept in an ontology
Indicates the average connectivity degree of a concept
MetricInterpretation "Please note that the number of pathes is understood in this paper as the number of connections of all concepts to the root classes. For our calculation engine, that is equivalent to the number of Superclasses (As it states how many connections there are to the top) plus the number of subclasses of thing. The latter is necessary as these metrics would not otherwise be counted as they have no superclasses. But for the given metric framework, these top level concepts are counted as the first hierachical level"
Total Number Of Concepts: The number of concepts in the set.
As ontology consists of concepts and relations, TNOC and TNOR are the two basic attributes of ontology, we can see the change of basic size of an ontology by analyzing these two attributes. As path consists of relations and can reflect the inner structure and hierarchy of ontology,
Total number of Paths: The sum of paths of each concept.
A path is a distinct trace in direct acyclic graph from a specific particular concept to the most general concept in the ontology, which is the concept without any parent or superclass(
TNOP represents an ontology’s hierarchical complexity and its value is proportionate to difficulties in navigating and visualizing the ontology[
Total Number Of Relations: The sum of the number of relations of each concept in an ontology.
- Let P1,P2,.. . ,Pn be the set of n properties defined in an ontology. - Let C1,C2,... ,Cm be the set of m classes defined in an ontology. - Let Fc1,Fc2,... , Fcm be the Fanout of each class Ci (see below for the definition of Fanout). - Let O1 be the ontology of interest. - Let -> be a mapping from set Ci ,to Cj such that Ci -> Cj if class Cj is a subclass of class Ci - Let & be a mapping from set Ci to set Pj such that Ci & Pj if class Ci includes property Pj as part of its definition.
Orme, Anthony Mark; Yao, Haining; Etzkorn, Letha H. (2007): Indicating ontology data quality, stability, and completeness throughout ontology evolution. In Journal of Software Maintenance and Evolution 19 (1), pp. 49–75. DOI: 10.1002/smr.341.
Yang, Zhe; Zhang, Dalu; Ye, Chuan (2006): Ontology Analysis on Complexity and Evolution Based on Conceptual Model. In Ulf Leser (Ed.): Data integration in the life sciences. Third international workshop, DILS 2006, Hinxton, UK, July 20 - 22, 2006 ; proceedings, vol. 4075. Berlin: Springer (Lecture notes in computer science Lecture notes in bioinformatics, 4075), pp. 216–223.
Computational ontologies are build on description logic as their foundation. Description Logic comes in several subsets, depending on their expressivity. This element shows to which subset this ontology belongs.
Metrics that count just a subset of all available metrics (Under a specific conditiion)
Measures the number of independent graphs in an ontology.
At times, an ontology does not only contain one large, interconnected graph, but "islands" that are independent from each other. This metric does measure if the subclasses of root classes are connected with each other (through object properties). If not, it shows how much graphs (graphs that start on root level) are isolated.
Ontologies can get quite large. If there are "islands" within an ontology, it can make sense to seperate these into seperate ontology files, to reduce complexity.
Indicates whether the ontology is consistent. Needs reasoning enabled to be calculated
A reasoner can detect complex inconsistencies in an ontology. An inconsistent ontology contains statements that contradict each other (e.g., an individual is asserted in two disjoint classes).
Please note that not all statements that are inconsistent automatically lead to a fully inconsistent ontologies. The reasoner will first try to exclude the statements of the resolution and mark these classes as "inconsistent"
The number of declared individual data properties
Data properties connnect individuals to literal values (e.g., a person has the literal "age" assigned
Counts the number of used object properties in instances.
An individual (or instance) can be connected to none, one or many data properties. E.g., person "Homer" hasAge "42".
Data properties can be further logically described using predefined attributes (like disjointness, equivalence). These statements are covered by this category.
Counts the number of data property domain declarations.
Imagine the data property statements of the class Domain:"Person" "hasAge". Then we use the domain statement to restrict that the Data Property "hasAge" can only be linked to elements of the class "person.
Counts the number of data property range declarations.
Imagine the data property statements of the class "hasAge" Range:"xsd:integer". Then we use the range statement to restrict that the Data Property "hasAge" can only be linked to the datatype "xsd:integer"
An array containing the imported ontologies.
Often, an ontology imports other ontologies, to facilitate the reusing of knowledge or the seperation of concerns. This item does show which ontologies are directly imported. (without transitive closure)
It means if A imports B, and B imports C, this for A, this metric shows B.
Counts the number of relationships on a class
This metrics counts how many relationships are asserted in the respective class.
Counts how many classes are marked as "Deprecated"
Some ontology developers do not like to delete their obsolete classes, as the knowledge would be lost. Instead, they mark them with the standardized annotation 'deprecated'. This tells other knowledge engineers to not use it further in upcoming versions, without loosing the modeled knowledge.
Counts how many data properties are marked as "Deprecated"
Counts how many data types are marked as "Deprecated"
Counts how many individuals are marked as "Deprecated"
Counts how many object properties are marked as 'Deprecated'
Depth is concerend with the deepness of the graph. Deepness is a measure of the number of following subclass hierachies of a path.
Metrics concerning the Depth of the Metric
Counts the number of different individual assertions (or individual inequality)
The differrent individual axiom states that all of the respective individuals are different from each other. It is not possible to derive that these individual are equal.
In OWL, we can explicitly declare that classes are disjoint from one another. In result, if class A and B are disjoint, no individual that is of type A can at the same time be of type B.This metric counts the number of these statements.
A high level of usage of Disjoints can indicate a more formalized semantic.
Counts the number of disjoint data property axioms.
States that one individual cannot have the same literal for the given disjoint values. E.g., if the value "Zip-Code" and "Age" of a person is disjoint, then an individual cannot have Zip-Code=18057, age=18057
Counts the number of disjoint object property declarations
If two (or more) object properties are disjoint, then no individual can have both relations. (E.g., mother and father are disjoint, there is no person who is mother and father at the same time).
The "Elemental Metrics" are the "building blocks" of all other metrics proposed in the Frameworks. E.g., If a framework proposes an "attribute/class" Ratio, it consists of elemental metrics "Attributes" and "Classes"
Classes that are equivalent to each other are semantically the same. E.g., a "Father" isEquivalentTo "Dad".
Counts the "EquivalentTo" statements in the ontology
Counts the number of equivalence data property axioms.
If two data properties are equivalent, they are semantically the same. E.g., the german word "hatName" and "hasName"
Counts the number of equivalent object property declarations.
Two object properties are semantically the same. (E.g., hasBrother equivalentTo hasMaleSibling.)
States that an individual with a functional data property can have at most one distinct property
An example for a classical functional data property would be "birth day", as one person can have at most one birthday.
Counts the number of object properties that are "functional"
if a relation is functional, for each x, there can be at most one y connected. E.g., if "hasFather" is functional, then a person can have at most one father.
Counts the number of General Concept Inclusions (GCI).
GCIs are a way to encode complex sub class relationships to unnamed entitities. E.g.: (HeartDisease and hasLocation some HeartValve) SubClassOf: CriticalDisease Here, a thing that is the subclass of the heartDisease and located near the heartValve is thus a critical disease, without explicitly naming it.
Fernández, Miriam; Overbeeke, Chwhynny; Sabou, Marta; Motta, Enrico (2009): What Makes a Good Ontology? A Case-Study in Fine-Grained Knowledge Reuse. In Asunción Gómez-Pérez, Yong Yu, Ying Ding (Eds.): The semantic web. Fourth Asian conference, ASWC 2009, Shanghai, China, December 6 - 9, 2009 ; proceedings, vol. 5926. ASWC; Asian Semantic Web Conference. Berlin: Springer (Lecture notes in computer science, 5926), pp. 61–75.
Average size of the levels of the ontology
Average size of the branches of the given ontology
Variance of the size of the levels in the ontology
Variance of the size of the branches in the ontology
Number of ontologies importing a given ontology
Size of the largest level of the ontology
Size of the longest branch in the given ontology
Size of the narrowest level of the ontology
Size of the shortest branch in the given ontology
Number of individuals in a given ontology
Number of properties in a given ontology
Metrics concerning the graph structure of the ontology.
Ontologies are built using triples. A triple connects two items (A and C) through a definition B. (A --B-->C). Ontologies, thus, can be seen as a kind of directed graph. We, thus, can apply measurements that assess the properties of graphs.
Counts the number of implicit, hidden general concept inclusions (GCIs).
A hidden GCI is the combination of a named subClass relationship and an anonymous, complex class in the equivalent section. (e.g., A subClassOf B, A equivalentTo some p)
Counts the subClasses of owl:Nothing. Requires selected reasoner.
If the reasoner detects classes that are unsatisfiable, it makes them a subclass of owl:Nothing. This metric counts all these subclasses that logically inconsistent.
Counts the number of Individuals overall.
Individuals are instantiations of things. In Opposite to e.g., programming languages, they do not need to be connected to a class. This metric counts the number of overall declared individuals.
Counts the number of instance assertions
An instance assertion is an instanciation of an actual object. In the context of ontologies, it is an individual that is from a type of a specific class. This measurement shows the number of instances that a specific class has.
The "instances Metrics" are concerned with the actual instance representation (or also "individuals") of an ontology
Counts the number of inverse object property declarations.
An inverse relation is the opposite directed relationship. If A ---->B, then the inverse of this relation is B--2-->A. An example is the relation "isFatherOf" as the inverse of "hasFather".
Counts the number of object properties that are "inverse functional"
if a relation is inverse functional x->y, then an y can have at most one x. An example is the relation isFatherOf. Then a father can have more than one child, but a child can have not more than one father.
Counts the number of object properties that are "irreflexive".
If an object property is irreflexive, then no property can be connected to itself. Married to is an example, as no one can be married to themselves.
This group of metrics are concerned not with the ontology overall, but specific elements within the ontology (e.g., metrics for every class or relation). They are not yet implemented in the calculation engine!
Leaf classes are classes that do not have further subclasses, thus are at the end of the inheritance tree.
Counts all axioms that encapsulate formal meaning in the ontology. This comprises all axioms except for such used for annotative purposes (e.g., Annotation Properties and Annotation Property Assertions) or declaration axioms
The longest Path from root to a leaf class.
The maximum number of siblings on a graph
Counts the maximum number of siblings of the different depth levels.
The maximum number of following sub class statements (without regarding multi inheritance) of a path. Imagine a tree, the leaf that is the farthest away from the root.
The max number of subclasses, that a class in the ontology has.
Shows whether there is an outlier in the ontology regarding declared the declared sub class statements
Shows the maximum number of superclasses a class has.
This element indicates the highest level of multi inheritance of a class in the ontology.
The minimum number of siblings on a graph.
Counts the minimum number of siblings of the different depth levels.
The minimum number of following sub class statements (without regarding multi inheritance) of a path. Imagine a tree, the leaf that is the nearest from the root.
Counts the number of negative data property assertions.
Negative property assertions state that an individual (or instance) does not have a specific value. E.g., Maggie is not 4 years old.
Counts how many object properties are negatively asserted overall.
A negative object property assertion is the statement that two individuals are NOT connected with each other.
The number of cyclic subClass relationships
Cycles are subclass relationships like A subClassOf B; B subClassOf C, C subClassOf A. This metrics counts the number of existing cycles.
The degree to which The ontology can be adapted for different specified environments (languages, expresivity levels) without applying actions or means other than those provided for this purpose for the Ontology considered.
The degree to which The ontology can be diagnosed for deficiencies or causes of failures (inconsistences), or for the parts to be modified to be identified.
The degree to which the Ontology enables users to recognise whether it is appropriate for their needs.
The ability to recognise the appropriateness of the functions from initial impressions of the ontology and/or any associated documentation such as Manuals, guides, comments.
Coupling between Objects: Number of related classes. It is the average number of the direct parents per class minus the relationships of Thing.
The degree to which The Ontology enables a specified modification to be implemented. The ease with which a The ontology can be modified.
Degree in which ontology Instances can be recognized as member of a certain class
Degree in which the annotations of data with respect to ontology terms can be used for clustering such data against the aspects of the ontology.
Clustering can be defined as the process of organizing objects into groups whose members are more similar to each other than to individuals in other groups.
The ability of two or more software components to exchange information and/or to perform their required functions while sharing the same hardware or software environment
Degree of the consistency of the ontology
consistent naming conventions, Logical consistency, structural consistency, consistent distinction class - instance
The degree which the formal model and structure of the ontology provide a semantic context to evaluate which are the data wanted by the users, allowing better querying and searching methods
The degree to which usability in use meets requirements in all the intended contexts of use
The degree of usability in use in contexts beyond those initially intended
Capability of the ontology to avoid heterogeneity of the terms.
The labels of the ontological entities are used to avoid heterogeneity, which would complicate data processing and analysis. Ontologies provide terminology management, unifying the terms used for referring to the included knowledge entities which should have an unambiguous and non-redundant definition. ontological concepts are described with different terminologies, different meanings are assigned to the same word in different contexts and different taxonomies are examples of synonymy, polysemy and structural heterogeneity
The existence of cycles through a particular semantic relation is usually a sign of bad design, since they may lead to inconsistencies.
Depth of subsumption hierarchy: Length of the largest path from Thing to a leaf class.
Decision trees are used to represent the logical structures of classification rules for domain specific empirical data.
Capability of the ontology to be used building Decision trees.
The degree to which the ontology makes it easy for users to operate and control it.
The degree to which specified users expend appropriate amounts of resources in relation to the effectiveness achieved in a specified context of use
The degree to which specified users can achieve specified goals with accuracy and completeness in a specified context of use.
Capability of the ontology to represent relations supported for formal theories different to the formal support for taxonomy
It accounts for the types of formal relations supported by the ontology, different to part-of relations
Capability of the ontology to support reasoning
An ontology should be expressed in a common formal language E.g. for biontologies in agree with the ontology principle FP 002 format : OBO Format, OWL or OWL2 concrete syntax, RDF/XML, OWL2-XML, OWL2-Manchester Syntax, Common Logic concrete syntax, CLIF, Conceptual Graphs, etc
The capability of the ontologies to provide concrete functions.
Capability of the ontology to guide the specification of domain theories.
Ontology by capturing knowledge about a domain and encapsulating constraints about class membership provides guidance in the specification of domain theories and support decision making processes.
The degree to which the Ontology provides help when users need assistance.
The ontology provide clear error messages, manuals and guides for help the users, including help comprehensive, effective and easy to find.
Degree in which the classes defined in the ontology can act as indexes for quick information retrieval
The degree to which The formal model of the ontology can be used by reasoners to make implicit knowledge explicit.
Inference expands the knowledge base with additional information using the existing data, metadata, and rules.
The degree to which the ontology can be cooperatively operable combining its knowledge with one or more other ontologies.
Ontology matching consists of matching a concept from one ontology to another.
The degree to which The ontology knowledge can be used to build other ontologies.
The semantic and conceptual relatedness of classes can be used to measure the separation of responsibilities and independence of components of ontologies.
The degree to which the ontology enables users to learn its application.
Effectiveness of the user documentation and/or help system.
The capability of ontologies to be modified for changes in environments, in requirements or in functional specifications.
Reiz, A. and Sandkuhl, K. (2022). Harmonizing the OQuaRE Quality Framework. In Proceedings of the 24th International Conference on Enterprise Information Systems - Volume 2, ISBN 978-989-758-569-2. ISSN 2184-4992, pages 148-158. Duque-Ramos, Astrid; Fernández-Breis, J. T.; Stevens, R.; Aussenac-Gilles, Nathalie (2011): OQuaRE: A square-based approach for evaluating the quality of ontologies. In Journal of Research and Practice in Information Technology 43 (2), pp. 159–176.
The degree to which The ontology can avoid unexpected effects from modifications of the software or knowledge.
The degree to which the ontology is composed of discrete components such that a change to one component has minimal impact on other components.
Number of Ancestor Classes: Mean number of ancestor classes per leaf class. It is the number of direct superclasses per leaf class.
Number of Children: Mean number of direct subclasses. It is the number of relationships divided by the number of classes minus the relationships of Thing.
Number of properties: Number of properties per class.
Effort needed for use, and on the individual assessment of such use, by a stated or implied set of users.
The degree in which an Ontology or one part of the ontology can be transferred from one hardware or software environment to another
The degree to which The ontology can be translated between different formal languages, or how easily the code can be moved to another language
The degree to which The ontology provides the right or specified results with the needed degree of accuracy
Quality in a particular context of use. Quality in use is the degree to which a product used by specific users meets their needs to achieve specific goals
Response for a class: Number of properties that can be directly accessed from the class.
Relationship Richness: Number of properties defined in the ontology divided by the number of relationships and properties
Capability of the ontology to be informative
Some redundancy types are: Inferred information more than once from the relations, classes and instances found in ontology The same/different formal definition of classes, properties or instances referring to different/same classes, properties or instances
Degree in which the ontology can be used as a reference resource for the particular domain the ontology is built for.
Machines can exploit better the reference knowledge offered by an ontology which have a more explicit structure
The degree to which The ontology can be used in place of another specified Ontology for the same purpose in the same environment.
Capability of the ontology to analize complex results such as microarrays experiments
The degree to which an asset (part of) the ontology can be used in more than one ontology, or in building other assets.
Degree in which ontology provide a common data model that can be applied to reconciliation and integration.
Integration is building a new ontology reusing other available ontologies. Different ontologies with subjective features and particular perspective on the world, cannot be compared without reconciliation and integration, which are necessary to interchange, migration and standardization of information and knowledge of such ontologies
Capability of the component of the ontology to be compared for similarity
There exist different similarity measures: Taxonomy similarity, Relation similarity, Attribute similarity, semantic similarity.
This category is the only one in this framework that is not specified as such in SQuaRE, but it is important when evaluating ontologies, since it accounts for ontology quality factors such as consistency, formalisation, redundancy or tangledness
Correctness of taxonomic links, use of upper level with disjoint categories, consideration of "all some rule" in case of existential Restrictions, value restrictions only if disjoint partitions available, domain and range restrictions of object properties, sufficient metadata and annotation properties, free text definitions where necessary
Degree of the correctness of the terms used in the ontology
This measures the distribution of multiple parent categories, so that it is related to the existence of multiple inheritance.
The degree to which the ontology modified can be validated.
Capability of the structure of the ontology to helps detecting associations between words or concepts and classifying word types.
The degree to which the software product can be transferred from one environment to another
Weighted Method Count: Mean number of properties and relationships per class.
The cardinality of the set of anonymous classes divided by the cardinality of the set of (class) nodes.
meaningful only when metric values or lists of values are represented as classes. For metric spaces this is rarely practiced, specially becaue languages like OWL have separate domains for datatypes.
The cardinality of the set of classes represents by nodes in g divided by the cardinality of the set of axioms represented by subgraphs in g.
This principle prospects an ontology that can be easily understood, manipulated, and exploited.
this principle prospects an ontology that is compliant to one or more users.
this principle prospects an ontology that can be easily understood and manipulated for reuse and adaptation.
this principle prospects an ontology that can be successfully/easily processed by a reasoner (inference engine, classifier, etc.).
This principle prospects an ontology that can be easily adapted to multiple views
This principle prospects an ontology that can be easily accessed for effective application.
a complexity scale, e.g. the one used for description logics
The cardinality of the set of classes represents by nodes in g divided by the cardinality of the set of individuals represented by special nodes in g.
Breadth is a property related to the cardinality of levels (generations) in a graph, where the arcs considered here are again only isa arcs. This measure only applies to digraphs.
Depth is a graph property related to the cardinality of paths in a graph, where the arcs considered here are only isa arcs. This measure type only applies to digraphs (directed graphs).
related to the “rationale” behind sibling node sets. The rationale behind a sibling node set can be measured by looking for arcs that do not represent isa relationships, and are shared by all siblings in the set (these arcs represent a common relational property). For a more relevant measure, we exclude from this measure the sibling nodes that represent values from a metric space of just a list
Formal semantics can go beyond first-order, in order to attempt at representing functional adequacy as well. The major example of that attempt is OntoClean [Guarino&Welty 2004]. OntoClean aims to classify the classes of an ontology according to some meta-properties, e.g. rigidity, unity, dependence. OntoClean metaproperties try to reduce some functional measures to the measurement of adequacy w.r.t. series of possible worlds (states of affairs). Possible worlds can be used to check the quality of an ontology only in an ex-post way, e.g. by analyzing the history of a temporal database built according to the ontology that must be evaluated. This is unfit, since an ontology is supposed to be evaluated before its application, not afterwords. For this reason, OntoClean methodology suggests designers or experts to assign metaproperties in advance, and then to use these assignments to check the meta-logical consistency of the taxonomy.
This principle prospects an ontology that respects certain ordering criteria that are assumed as quality indicators
A module is any subgraph sg of a graph g, where the set of graph elements S’ for sg is such that S’ ⊆ S. Two modules sg1 and sg2 are disjoint when only ≥0 isa arcs ai connect sg1 to sg2, and each ai has the same direction. Modularity is related to the asserted modules of a graph, where the arcs considered here are either isa or non-isa arcs. We distinguish the following modularity measures. The set of modules from a graph g is called here M. m = n_m / n_s where n_m is the cardinality of M and n_s is the cardinalty of S( The set of graph elements)
This principle prospects an ontology that can be easily deployed within an organization, and that has a good coverage for that context.
Gangemi, Aldo; Catenacci, Carola; Ciaramita, Massimiliano; Lehmann, Jos; Gil, Rosa; Bolici, Francesco; Strignano Onofrio (2005): Ontology evaluation and validation. An integrated formal model for the quality diagnostic task.
This principle prospects an ontology that can be analyzed in detail, with a rich formalization of conceptual choices and motivations
Measures the number of declared object properties (also such, that are implicit stated). Is different from the object property assertion.
Counts how many object properties are asserted overall.
An object property assertion is the statement that two individuals are connected with each other.
Object properties can be further logically described usiing predefined attributes (like disjointness, equivalence). These statements are covered by this category.
Number of declared Object Properties on Classes
Classes can be connected using object properties in SubClassOf relations. This metric measures, how often that is the case.
Counts the number of object property domain axioms.
The "domain" restriction limits the available classes from where a relation starts. If a relation is A->B, then the domain limits what classes A can be. (E.g., isParent has the domain "Person")
Number of Object Properties on Individuals
Measures how often individuals are connected using object properties.
Counts the number of object property range axioms.
The "Range" restriction limits the available classes to where a relation ends. If a relation is A->B, then the domain limits what classes "B" can be. (E.g., isParentOf has the range "Child")
Tartir, Samir; Arpinar, I. Budak (2007): Ontology Evaluation and Ranking using OntoQA. In : International Conference on Semantic Computing, 2007. ICSC 2007 ; 17 - 19 Sept. 2007, Irvine, California ; proceedings ; [held in conjunction with] the First International Workshop on Semantic Computing and Multimedia Systems (IEEE-SCMS 2007). International Conference on Semantic Computing (ICSC 2007). Irvine, CA, USA, 9/17/2007 - 9/19/2007. IEEE Computer Society; IEEE International Conference on Semantic Computing; ICSC; International Workshop on Semantic Computing and Multimedia Systems; IEEE-SCMS. Los Alamitos, Calif.: IEEE Computer Society, pp. 185–192.
Tartir, Samir; Arpinar, I. Budak; Moore, Michael; Sheth, Amit P.; Aleman-Meza, Boanerges (2005): OntoQA: Metric-Based Ontology Quality Analysis. In : IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources. Houston, 11/27/2005.
Formally, the attribute richness (AR) is defined as the average number of attributes (slots) per class. It is computed as the number attributes for all classes (att) divided by the number of classes (C).
The number of attributes (slots) that are defined for each class can indicate both the quality of ontology design and the amount of information pertaining to instance data. In general we assume that the more slots that are defined the more knowledge the ontology conveys.
The result will be a real number representing the average number of attributes per class, which gives insight into how much knowledge about classes is in the schema. An ontology with a high value for the AR indicates that each class has a high number of attributes on the average, while a lower value might indicate that less information is provided about each class.
Formally, the average population (P) of classes in a KB is defined as the number of instances of the KB (I) divided by the number of classes defined in the ontology schema (C). P = I / C
(average distribution of instances across all classes): This measure is an indication of the number of instances compared to the number of classes. It can be useful if the ontology developer is not sure if enough instances were extracted compared to the number of classes.
The result will be a real number that shows how well is the data extraction process that was performed to populate the KB. For example, if the average number of instances per class is low, when read in conjunction with the previous metric, this number would indicate that the instances extracted into the KB might be insufficient to represent all of the knowledge in the schema. Keep in mind that some of the schema classes might have a very low number or a very high number by the nature of what it is representing.
The class instance distribution of an ontology is defined as the standard deviation in the number of instances per class.
This metric is also useful to evaluate the instance extraction process. It provides an indication on how instances are spread across the classes of the schema. It can be used to discover problems in the instance extraction process.
The connectivity of a class (Conn(Ci)) is defined as the total number of relationships instances of the class have with instances of other classes. Conn(Ci) = |NIREL(Ci)|
This metric gives an indication of the centrality of a class. With the importance metric mentioned below, both metrics provide a better understanding of how focal some classes are in the KB, which might be help in cases where a user has two ontologies with the similar classes defined in their schemas, but classes that are be important to the user play a central role in one of them, while being on the boundary in the other.
The result of the formula will be an integer apresenting the popularity of instances of the class. A class with a high Cn plays a central role in the ontology compared to a class with a lower value. This measure can be used to understand the nature of the ontology by indicating which classes play a central role compared to other classes.
Formally, the fullness (F) of a class Ci is defined as the actual number of instances that belong to the subtree rooted at Ci (Ci(I)) compared to the expected number of instances that belong to the subtree rooted at Ci (Ci`(I)). F = Ci(I) / Ci`(I)
This metric details the KB average population metric mentioned above. It would be mainly used by an ontology developer interested in knowing how well the data extraction was with respect to the expected number of instances of each class. This is helpful in directing the extraction process to any resources that will add instances belonging to classes that are not full.
The result of the formula will be a percentage representing the actual coverage of instances compared to the expected coverage. In most cases, this measure is an indication of how well the instance extraction process performed. For example, a KB where most classes have a low F would require more data extraction. On the other hand, a KB where most classes are almost full would indicate that it reflects more closely the knowledge encoded in the schema.
The importance of a class (Imp(Ci)) is defined as the number of instances that belong to the inheritance subtree rooted at Ci in the KB(inst(Ci)) compared to the total number of class instances in the KB (CI). Imp(Ci) = Inst(Ci)/KB(CI)
This metric is important because it helps in identifying which areas of the schema are in focus when the instances are extracted and inform the user of the suitability of his/her intended use. It will also help direct the ontology developer or data extractor to where s/he should focus on getting data if the intention is to get a consistent coverage of all classes in the schema. Although this measure does not consider the real world semantics, where some classes naturally have more instances than others, the class importance can still be used (together with the class connectivity measure mentioned above) to give an indication on what parts of the ontology are considered focal and what parts are on the edges.
Formally, the inheritance richness of class Ci is defined as the average number of subclasses per class in the subtree. The number of subclasses for a class Ci is defined as Hc (Cl,Ci) and the number of nodes in the subtree is C'l.
This measure details the schema IRS metric mentioned above and describes the distribution of information in the current class subtree per class. This measure is a good indication of how well knowledge is grouped into different categoreis and subcategories under this class.
The result of the formula will be a real number representing the average number of classes per schema level. The interpretation of the results of this metric depends highly on the nature of the ontology. Classes in an ontology that represents a very specific domain will have low IRC values, while classes in an ontology that represents a wide domain will usually have higher IRC values.
This group of metrics indicates how each class defined in the ontology schema is being utilized in the KB.
Formally, the readability (Rd) of a class Ci is defined as the sum of the number attributes that are comments and the number of attributes that are labels the class has.
This metric indicates the existence of human readable descriptions in the ontology, such as comments, labels, or captions. This metric can be a good indication if the ontology is going to be queried and the results listed to users.
The result of the formula will be an integer representing the availability of human-readable information for the instances of the current class.
Formally, the relationship richness (RR) of a class Ci is defined as the number of relationships that are being used by instances Ii that belong to Ci (P(Ii,Ij)) compared to the number of relationships that are defined for Ci at the schema level (P(Ci,Cj)) RRc = (P(Ii, Ij), Ii eCi(I))/P(Ci, Cj)
This is an important metric reflecting how much of the properties in each class in the schema is actually being used at the instances level. It is a good indication of the how well the extraction process performed in the utilization of information defined at the schema level.
The result of the formula will be a percentage representing how well the KB utilizes the knowledge defined in the schema regarding the class in focus. For example, if most classes have low RRC values, this would mean that instances are using only a few number of the class relationships in the schema in contrast to another ontology where instances have relationships that span most of the relationships available at the class level in the schema.
The relationship richness (RU) of a class Ci is defined as the number of relationships that are being used by instances Ii that belong to Ci (P(Ii,Ij)) compared to the number of relationships that are defined for Ci at the schema level (P(Ci,Cj)). RU(Ci) = IREL(Ci) / CREL(Ci)
This metric reflects how the relationships defined for each class in the schema are being used at the instances level. It is a good indication of the how well the extraction process performed in the utilization of information defined at the schema level. This metric can be used to distinguish between two ontologies having similar schemas but one of them utilizes only a few of the available relationships while other utilizes more.
The class utilization (CU) of an ontology is defined as the ratio of the number of populated classes (C`) divided by the total number of classes defined in the ontology schema (C).
This metric reflects how classes defined in the schema are being utilized in the KB. This metric can be used to differentiate between two ontologies having the same classes defined in their schemas but one of them populates more classes than the other one, indicating a richer KB.
The result will be a percentage indicating how the KB utilizes classes defined in the schema. Thus, if the KB has a very low CU, then the KB does not have data that exemplifies all the knowledge that exists in the schema. This metric will be very useful in situations where instances are being extracted into an ontology and it is needed to evaluate the results of the extraction process.
The cohesion (Coh) of an ontology is defined as the number of connected components (CC) of the graph representing the KB.
This metric represents the number of connected components in the KB. This metric can particularly help if 'islands' form in the KB as a result of extracting data from separate sources that do not have common knowledge, giving insight into what areas need more instances in order to enable the different connected components to connect to each other. Having less connected components (ideally 1) can be helpful, for example, in finding more useful semantic-associations [3] in the ontology.
The result will be an integer representing the number of connected components in the ontology.
Formally, the inheritance richness of the schema (IRs) is defined as the average number of subclasses per class.
This measure describes the distribution of information across different levels of the ontology inheritance tree or the fan-out of parent classes. This is a good indication of how well knowledge is grouped into different categories and subcategories in the ontology. This measure can distinguish a horizontal ontology from a vertical ontology or an ontology with different levels of specialization. A horizontal (or flat) ontology is an ontology that has a small number of inheritance levels, and each class has a relatively large number of subclasses. In contrast, a vertical ontology contains a large number of inheritance levels where classes have a small number of subclasses. This metric can be measured for the whole schema or for a subtree of the schema.
The result of the formula will be a real number representing the average number of subclasses per class. An ontology with a low IRS would be or a vertical nature, which might reflect a very detailed type of knowledge that the ontology represents. while an ontology with a high IRS would be of a horizontal nature, which means that ontology represents a wide range of general knowledge.
The way instances are placed within an ontology is also a very important aspect of ontology evaluation. The placement of instance data and distribution of the data can indicate the effectiveness of the ontology design and the amount of knowledge represented by the ontology. Instance metrics can divided on three main sub-dimensions: Overall KB (knowledgebase) metrics that evaluates the overall placement of instances with regard to the schema, class-specific metrics that evaluate the instances of a specific class and compare it to instances of other classes, and relationship-specific metrics that evaluate the instances of a specific relationship and compare it to instances of other relationships.
This group of metrics gives an overall view on how instances are represented in the KB.
The relationship diversity (RD) of a schema is defined as the ratio of the number of noninheritance relationships (P), divided by the total number of relationships defined in the schema (the sum of the number of inheritance relationships (H) and noninheritance relationships (P)). RD = P / (H +P)
This metric reflects the diversity of relationships in the ontology. An ontology that contains mostly inheritance relationships (taxonomy) usually conveys less information than an ontology that contains a diverse set of relationships. However, in some applications, users might be interestedin ontologies with mostly inheritance relationships (e.g. species classification), and OntoQA gives the user the option to specify whether she prefers a taxonomy or an ontology with diverse relationships.
For example, if an ontology has an RD value close to 0 that would indicate that most of the relationships are inheritance relationships. In contrast, an ontology with a value close to 1 would indicate that most of the relationships are non-inheritance.
The importance of a relationship (Imp(Ri)) is defined as the number of instances of relationship Ri in the KB (inst(Ri)) compared to the total number of property instances in the KB (RI) Imp(Ri) = Inst(Ri) / KB (RI)
Relationship Importance: This metric measures the percentage of instances of a relationship with respect to the total number of relationship instances in the KB. This metric is important in that it will help in identifying which schema relationships were in focus when the instances were extracted and inform the user of the suitability of his/her intended use. This metric can also help in directing the instance extraction process to include a more diverse set of relationships the KB does not include the required diversity.
The result of the formula will be a percentage representing the importance of the current class.
This group or metrics indicates how each relationship defined in the ontology schema is being utilized in the KB.
Formally, the relationship Diversity (RR) of a schema is defined as the ratio of the number of relationships (P) defined in the schema, divided by the sum of the number of subclasses (SC) (which is the same as the number of inheritance relationships). RR = P / (SC + P)
This metric reflects the diversity of relations and placement of relations in the ontology. An ontology that contains many relations other than class-subclass relations is richer than a taxonomy with only class-subclass relationships.
The result of the formula will be a percentage representing how much of the connections between classes are rich relationships compared to all of the possible connections that can include rich relationships and inheritance relationships. For example, if an ontology has an RR close to zero, that would indicate that most of the relationships are class-subclass (i.e. ISA) relationships. In contrast, an ontology with a RR close to one would indicate that most of the relationships are other than class-subclass.
The schema depth of the schema (SD) is defined as the average number of subclasses per class. SD = H/C
This measure describes the distribution of classes across different levels of the ontology inheritance tree. This measure can distinguish a shallow ontology from a deep ontology. A shallow ontology is an ontology that has a small number of inheritance levels, and each class has a relatively large number of subclasses. In contrast, a deep ontology contains a large number of inheritance levels where classes have a small number of subclasses
An ontology with a low SD would be deep, which indicates that the ontology covers a specific domain in a detailed manner (e.g. ProPreO [27]), while an ontology with a high SD would be a shallow (or horizontal) ontology (e.g. TAP), which indicates that the ontology represents a wide range of general knowledge with a low level of detail.
The schema metrics address the design of the ontology schema. Although it is difficult to know if the ontology design correctly models the knowledge of the domain it is trying to represent, we provide some metrics that indicate different features of an ontology schema.
The summed up length of the pathes from root to the leaf classes.
Measurements that are concerned with the various paths in a graph (A path is the structure from the root class to the elements or leafes.)
Number of distinct paths from leaf classes to the root classes
Metrics that are concerned with properties than can be assigned to classes. That includes data-, annotation-, or object property metrics.
Quality Dimensions. Currently not part of NEOntometrics. Some frameworks propose metrics that are connected to quality measurements. These informations are captured in this class.
Data on the Ontology Frameworks. These frameworks utilize the metrics named in the "Elemental Metric" Section.
At times, the calculation does not function properly. In these cases, the error message is shown in this field.
States whether the reasoner was active while calculating this ontology.
Counts the number of object properties that are "reflexive".
If an object property is reflexive, then all object properties are connected to themselfes through this property.
Counts how much a relation is used in instances.
individuals can be set in relation to each other using object properties. This metric counts how often a specific object property is used to connect individuals.
These metrics are concerned with the individual object property relations. They are calculated per object property.
Counts the number of relationship assertions on a class.
Classes can be connected to other classes using object properties. This measurement counts how many classes are connected to a specific class using object properties in the subClassOf Signature.
Attributes (mostly textual) that originate from the repository.
Counts the number of equal individual axioms.
Equal individuals are equivalent to each other. They can be used synonym to one another, all that is derived for one of the individuals will also be derived for the other.
Burton-Jones, Andrew; Storey, Veda C.; Sugumaran, Vijayan; Ahluwalia, Punit (2005): A semiotic metrics suite for assessing the quality of ontologies. In Data & Knowledge Engineering 55 (1), pp. 84–102. DOI: 10.1016/j.datak.2004.11.010.
Let an ontology in the library be OA. Let the set of other ontologies in the library be L. Let the total number of links from ontologies in L to OA be K. Let the average value for K across ontology library be V. Then OT = K/V
Let Ci = name of class or property in ontology. "Ci, count Ai, (the number of word senses for that term in WordNet). Then EA = A/C
Let C be the total number of classes and properties in ontology. Let V be the average value for C across entire library. Then PO = C/V
Let I= 0. Let C be the number of classes and properties in ontology. "Ci, if meaning in ontology is inconsistent, I+ 1. Therefore, I= number of terms with inconsistent meaning. EC = I/C
Let the total number of accesses to an ontology be A. Let the average value for A across ontology library be H. Then OH = A/H
Let C be the total number of terms used to define classes and properties in ontology. Let Wbe the number of terms that have a sense listed in WordNet. Then EI =W/C
Let X be total syntactical rules. Let Xb be total breached rules. Let NS be the number of statements in the ontology. Then SL = Xb/NS
Let NS be the number of statements in the ontology. Let S be the type of syntax relevant to agent. Let R be the number of statements within NS that use S.PR = R/NS
Let Y be the total syntactical features available in ontology language. Let Z be the total syntactical features used in this ontology. Then SR = Z/Y
This category collects metrics that cannot be accounted to the other categories.
The number of rdfs:SubClassOf Declarations
Sub classes allow the construction of more detailed, complex hierachies.
A high number of subclass statements indicate a rich ontology taxonomy.
Counts the number of subObjectProperty axioms.
Properties can be aligned in hierachical order. All individuals that are part of the bottom entity are then also part of the top entity (E.g., isFather subPropertyOf isParent).
The number of chained sub object properties
A specialized cyclic relationship that does not lead to decidability problems. E.g.: "The sibling of someones child is his child".
Counts all classes that do not have parent classes. Note, that the classes do not necessarily need the statement "rdfs:subClassOf owl:Thing" to be counted.
All the classes at the top of an ontology. It tells us how many "entrypoints" in the inheritance tree exist .
A super class is the direct parent of a class. Through multiple inheritance, one class can have more than one superclass.
Counts the number of parents of the leaf classes
Allows to interpret how the level above the last level is structured. E.g., are there much more "super classes of leaf classes" than "leaf classes"? Then the leafes have a high multi inheritance ratio.
Counts how many parents the classes with multiple inheritance have
In combination with the number of classes with mutlple inheritance, it shows how far spread out the multi iinheritance relationships are. E.g., Do they, on average, have just one 2,1 classes? Then most of the multiple inheritance classes have just two parents.
Superclasses of Classes with Multiple Inheritance
Counts the number of object properties that are "symmetric".
If an object property is symmetric, and a relation of individual A->B exist, then there is the same relation B-A. E.g., A isFriendOf B, then B isFriendOf A
Counts all siblings on all depth levels of the ontology.
The summed up depth of all paths in an ontology. E.g., path a from ROOT to leaf class A has 3 levels, path b has 2, etc.
Counts the number of object properties that are "transitive".
If an object property is transitive, and the individuals are connected as A->B->C, then follows A->C. E.g., If Peter is an ancestorOf Paul, and Paul is an ancestorOf Brian, then Peter is also an ancestorOf Brian.
Calculates the maximum number of siblings of the leaf classes.
This metric measures the maximum amount of leafclasses on a parent class.
Counts the number of subclasses per class iteratively. Also refered to as fan-outness per some papers, though the definition is differently for the papers.
If b subClassOf a, c subClassOf a and b subClassOf b, then the metric would calculate to a 4, as it first recursivly checks all subClasses of a, then of b, and so on.
The Average Fanout of Non-LeafClasses (AF-NL) is defined as the Number of Fanouts (NoF) divided by Number of Non-leaf Classes explicitly defined in the ontology Oi .
The Average Fanout of Root Classes (AF-R) is defined to be the Number of Fanouts (NoF) divided by the Number of Root Classes in the ontology Oi .
The Average Fanout per Class (AF-C) is the Number of Fanouts (NoF) divided by Number of Classes (NoC) explicitly defined in the ontology Oi
The Average Properties per Class (AP-C) is the number of properties explicitly defined in the ontology Oi divided by the number of classes explicitly defined in the ontology Oi .
The Maximum Depth of Inheritance Tree (MaxDIT) of the ontology Oi is defined as follows. A depth is the total number of nodes in a path. A path starts from the root node to the leaf node. All distinct paths in the ontology Oi include every path from each root node to each leaf node if there exists an inheritance path from the root node to the leaf node. The root node is the first level in each path.
Number of Properties (NoP) is the number of properties explicitly defined in the ontology Oi .
Example. Each class can possess properties (but is not required to). Class 1 has one property, class 2 has two properties, class 3 has no properties, class 4 has three properties, and class 5 has one property. Thus, NoP = 7.
Capability of the Ontology to represent the knowledge acquired.
Knowledge acquisition is the gathering, storage, and encoding of existing information.
Highly dependent on the formalization. E.g., Turtle (.ttl) is more space-efficient than xml.
NEOntometrics internal information. The primary key that identifies a repository in the database.