OntoMetrics - New pages [en]

Annotation Axioms

2016-06-01T11:54:55Z

Adminofwiki:

Annotations can be used to associate information to ontologies, this information could be the version of the ontology or the creator.
The annotation itself consists of an annotation property and an annotation value.

==Annotation axiom==
Count the number of annotation axioms in the given ontology.

==Annotation assertion axiom==
These axioms are used to add additional information to a class, it can be used to describe the class using the natural language description.

For example:
AnnotationAssertion( rdfs:comment :car "Represents the set of all cars." )

==Annotation property domain axiom==

The annotation property domain axiom states that the domain of the annotation property is a specific IRI.

==Annotation property range axiom==

The annotation property range axiom states that the range of the annotation property is a specific IRI.

==Sources==
#''https://www.w3.org/TR/owl2-syntax/#Annotations''
#''https://www.w3.org/TR/owl2-primer/#Annotating_Axioms_and_Entities''

Individual Axioms

2016-06-01T11:54:29Z

Adminofwiki: /* Sources */

These are axioms concerning individuals.

==Class assertion axiom==
The class assertion axiom states that an individual is an instance of an class expression.

==Object property assertion axiom==

It states that the individual 'a1' is connected by the object property 'op' to an individual 'a2'.

==Negative object property assertion axiom==
It states that the individual 'a1' is not connected by the object property 'op' to an individual 'a2'.

==Data property assertion axiom==

With this axiom it is possible to state that an individual 'a' is connected by a data property 'dp' expression to a literal 'l1'.

==Negative data property assertion axiom==

The opposite of the data property assertion, so the individual 'a' is not connected by a data property 'dp' expression to a literal 'l1'.

==Same individuals axiom==

This axiom states that all individuals contained by this axiom are equal to each other.

==Different individuals axiom==
Other than the same individual's axiom, this one states that all contained individuals are not equal to each other.

==Sources==
#''https://www.w3.org/TR/owl2-syntax/#Assertions''
#''https://www.w3.org/TR/owl2-primer/#Equality_and_Inequality_of_Individuals''

Data Property Axioms

2016-06-01T11:53:55Z

Adminofwiki: /* Sources */

Data properties link individuals to data values.

A set of instances connected to the property is called a property extension.

==SubDataPropertyOf axiom==

This axiom says that a property 'p1' is a subproperty 'sp1' of another property 'p2'.
It also means that the instances of the subproperty are subsets to the property extension of the second property.

==Equivalent data properties axiom==

Equivalent property axioms exist when two properties have the same property extension.

==Disjoint data properties axiom==
Two properties are disjoint when they don't have individuals in common.

==Functional data property axiom==
A functional property is a property which can only have one value.

For an individual 'x', there can be only one definite individual 'y' such that 'x' is connected by the data property expression 'DPE' to 'y'.

For example:
FunctionalDataProperty( a:hasAge ) Each object can have at most one age.
DataPropertyAssertion( a:hasAge a:John "21"^^xsd:integer ) John is twenty-one years old.

==Data property domain axiom==
This axiom states that the class expression is the domain of the data property expression.

==Data Property range axiom==
It says that the data range is the range of the data property expression.

==Sources==
#''https://www.w3.org/TR/owl2-syntax/#Data_Property_Axioms''

Object Property Axioms

2016-06-01T11:53:24Z

Adminofwiki:

Object properties link individuals to individuals.

A set of instances connected to the property is called a property extension.

==SubObjectPropertyOf axiom==

This axiom says that a property 'p1' is a subproperty 'sp1' of another property 'p2'.
It also means that the instances of the subproperty are subsets to the property extension of the second property.

==Equivalent object property axiom==

Equivalent property axioms exist, when two properties have the same property extension.

==Inverse object properties axiom==
Properties have a direction defined with domain to range, the 'inverseof' term is used to mirror the direction.

This Axiom can equally be used on object properties and data properties.

==Disjoint object properties axiom==

Two properties are disjoint when they don't have individuals in common.

==Functional object properties axiom==
A functional property is a property which can only have one value.

For an individual 'x', there can be only one definite individual 'y' such that 'x' is connected by the object property expression 'OPE' to 'y'.

For example:
FunctionalObjectProperty( a:hasHusband ) Each object can have at most one husband.
ObjectPropertyAssertion( a:hasHusband a:Nicole a:Steve ) Steve is Nicole's husband.

==Inverse functional object properties axiom==
For an individual 'x', there can be at most one individual 'y' such that 'y' is connected by the object property expression 'OPE' with 'x'.

InverseFunctionalObjectProperty( a:hasHusband ) Each object can have at most one husband.
ObjectPropertyAssertion( a:hasHusband a:Steve a:Nicole ) Steve is Nicole's husband.

==Transitive object property axiom==
Transitive means that if a property contains the pair(x,y)and the pair (y,z) then we can conclude that the pair(x,z) is also part of der property.

<math>\begin{align}
&\forall a,b,c \in A\colon\\
&(a,b) \in R \,\land\, (b,c) \in R\\
&\Rightarrow\; (a,c) \in R
\end{align}</math>

==Symmetric object property axiom==

If a property is symmetric it means that if a pair(x,y) exists, then there is also a pair (y,x).

<math>\begin{align}
&\forall a,b \in A\colon\\
&(a,b) \in R \;\Rightarrow\; (b,a) \in R
\end{align}</math>

==Asymmetric object property axiom==

A asymmetric property has a pair(x,y) but never a pair(y,x).

<math>\begin{align}
&\forall a,b \in A\colon\\
& (a,b) \in R \;\Rightarrow\; (b,a) \notin R
\end{align}</math>

==Reflexive object property axiom==

Reflexive means that a property relates to itself.

<math>\forall a \in A\colon\; (a,a) \in R</math>

==Irreflexive object property axiom==
Subsequently irreflexive means that no individual relates to itself.
<math>\forall a \in A\colon\; (a,a) \notin R</math>

==Object property domain axiom==
This axiom states that the domain of the object property expression is the class expression.

==Object property range axiom==
This axiom states that the range of the object property expression is the class expression.

==SubPropertyChainOf axiom==

These axioms are used to create a chain of multiple properties. E.g. two 'hasParents' properties are linked by a chain thus a 'hasGrandparents' property will be identified.

==Sources==
#''https://www.w3.org/TR/owl2-primer/#Object_Properties/''
#''https://www.w3.org/TR/owl2-syntax/#Object_Property_Axioms''

Class Axioms

2016-06-01T11:52:52Z

Adminofwiki:

Class Axioms are used to define classes, e.g. an <owl:class/> defines the existence of a class and is a class axiom, likewise is the ID of the class a class axiom.

The set of individuals linked to the class is called class extension.

==SubClassOf axiom==
It means the class expression is an instance of another class's expression, it is used to display hierarchy. It follows that the set of individuals in the class 1 are a subset of the set of individuals of class 2.
Due to that the first class expression which is the subclass of the other is more specific than the other.

==Equivalent classes axiom==
Equivalent class axioms state that multiple class expressions are equivalent to each other. Thus these class expressions can be used as synonym, when the meaning of the ontology won't be changed.

==Disjoint classes axiom==
These axioms state that class expressions are disjoint, thus they have no instances in common.

==GCI==
Counts the number of the General Concept Inclusion (GCI).

==HiddenGCI==
Counts the number of "hidden" GCIs in an ontology imports closure. A GCI is regarded to be a "hidden" GCI if it is essentially introduce via an equivalent class axiom and a subclass axioms where the LHS of the subclass axiom is nameed. For example, A equivalentTo p some C, A subClassOf B results in a "hidden" GCI.

==Sources==
#''https://www.w3.org/TR/owl2-syntax/#Class_Expression_Axioms''
#''http://owlapi.sourceforge.net/javadoc/org/semanticweb/owlapi/metrics''

Base Metrics

2016-06-01T11:51:53Z

Adminofwiki: /* Annotation Axioms */

Base Metrics comprise of simple metrics, like the counting of classes, axioms, objects etc. These metrics show the quantity of ontology elements.

The difference between the count metrics and the total count metrics is, that the total count metrics takes account of imports from other ontologies.

For the base metrics we chose:

==Class Axioms==
===Axiom===
Axioms are basic statements of an ontology and also the main component, they state what is true in a domain.
It is possible to have axioms for classes, properties, datatype definitions, assertions and annotations.

===Logical Axiom===
Axioms which affect the logical meaning of an ontology are called Logical Axiom.

===Class===
Classes in ontologies are concepts, these classes can contain other classes or individuals. In other words, a class is a set of individuals.
In OWL exists a thing-class, which is a universal class, so every user defined class is a subclass of the thing-class.
The corresponding metric count the classes, including the thing-class, to create a view on the quantity of classes.

More information on the metric page for [[Class_Axioms|Class Axioms]].

==Property==

In OWL there are two types of properties:

===Object property===
[[Object_Property_Axioms|Object properties]] link individuals to individuals.

===Data property===
Other than the Object properties the [[Data_Property_Axioms|Data properties]] link individuals to data values (literals).

==Individual Axioms==

===Individuals===
Individuals are the instances of the classes, so they represent the actual object of the domain.
There are two types of individuals: named- and anonymous individuals.
Named individuals have an explicit name and can be used in every ontology for the same object, while anonymous individuals are used local, only in one ontology.
This metric counts all instances, one class is able to have a set of instances.

More details on page [[Individual_Axioms|Individual Axioms]].

==Annotation Axioms==
===Annotation===
An OWL ontology contains a set of annotations. These can be used to associate information with an ontology — for example the ontology creator's name.
Each annotation consists of an annotation property and an annotation value, and the latter can be a literal, an IRI, or an anonymous individual.

For more see [[Annotation_Axioms|Annotation Axioms]].

==DL expressivity==
Description logics (DL) is a family of formal knowledge representation languages. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). The Web Ontology Language [OWL] and its profile is based on DLs. The DL expressivity gets the human readable name of this metric.

==Sources==
#''https://www.w3.org/TR/owl2-syntax/#Axioms''
#''http://owlapi.sourceforge.net/javadoc/org/semanticweb/owlapi/model/OWLLogicalAxiom.html''
#''https://www.w3.org/TR/owl-ref/#Class''
#''https://www.w3.org/TR/owl2-syntax/#Classes''
#''https://www.w3.org/TR/owl2-syntax/#Individuals''
#''https://www.w3.org/TR/owl-ref/#Property''
#''https://www.w3.org/TR/owl2-syntax/#Annotations''
#''http://owlapi.sourceforge.net/javadoc/org/semanticweb/owlapi/metrics/DLExpressivity.html''
#''https://en.wikipedia.org/wiki/Description_logic''

Ontology

2016-06-01T09:19:54Z

Adminofwiki:

In information science ontologies are used as a model to describe a domain of knowledge with the help of classes, attributes, relationships and some more components.
With the help of this domain of knowledge, the ontology is used as tool to create a common base of understanding on a topic. It can also be reused and extended.

==Sources==
#''https://www.w3.org/TR/2004/REC-owl-semantics-20040210/syntax.html''

Class Metrics

2016-06-01T08:45:42Z

Adminofwiki:

Class Metrics examine the classes and relationships of ontologies.
==Class Connectivity==

This metric is intended to give an indication of what classes are central in the ontology based on the instance relationship graph (where nodes represent instances and edges represent the relationships between them). This measure works in tandem with the importance metric mentioned next to create a better understanding of how focal some classes function. This measure can be used to understand the nature of the ontology by indicating which classes play a central role compared to other classes.

The '''connectivity of a class <math>(Conn(C_i))</math>''' is defined as the '''total number of relationships instances of the class have with instances of other classes (NIREL)'''.

<math>Conn(C_i)=|NIREL(C_i)|</math>

[[Class_Metrics#Sources | Source 1]]

==Class Fullness==

This metric details the knowledgebase average population metric which are part of the [[Knowledgebase_Metrics | knowledgebase metrics]]. 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.

Formally, the '''fullness (F)''' of a '''class <math> C_i</math>''' is defined as the '''actual number of instances''' that belong to the subtree rooted at <math>C_i (C_i (I))</math> compared to the '''expected number of instances''' that belong to the subtree rooted at <math>C_i (C_i'(I))</math>.

<math>F=\frac{|C_i (I)|}{C_i'(I)}</math>

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 knowledgebase where most classes have a low F would require more data extraction. On the other hand, a knowledgebase where most classes are almost full would indicate that it reflects more closely the knowledge encoded in the schema.

[[Class_Metrics#Sources | Source 2]]

==Class Importance==

This metric calculates the percentage of instances that belong to classes at the inheritance subtree rooted at the current class with respect to the total number of instances. This metric is important in that it will help in identifying which areas of the schema are in focus when the instances are added to the knowledgebase. Although this measure doesn’t consider the domain characteristics, it can still be used to give an idea on what parts of the ontology are considered focal and what parts are on the edges.

The '''importance of a class''' <math>(Imp(C_i))</math> is defined as the '''percentage of the number of instances''' that belong to the inheritance subtree rooted at <math>C_i</math> in the knowledgebase <math>(inst(C_i))</math> compared to the '''total number of class instances in the knowledgebase''' <math>KB(CI)</math>.

<math>Imp(Ci)=\frac{|INST(Ci)|}{|KB(CI)|}</math>

[[Class_Metrics#Sources | Source 1]]

==Class Inheritance Richness==

This measure details the schema IR metric mentioned in [[Schema_Metrics | schema metrics]] 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 categories and subcategories under this class.

Formally, the '''inheritance richness (IRc) of class''' <math>C_i</math> is defined as the '''average number of subclasses per class''' in the subtree. The '''number of subclasses for a class''' <math>C_i</math> is defined as <math>|H^C(C_1,C_i)|</math> and the '''number of nodes in the subtree''' is |C'|.

<math>IRc = \frac{\sum_{Cj\in C'} |H^C(C1,Ci)|}{|C'|}</math>

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.

[[Class_Metrics#Sources | Source 2]]

==Class Readability==

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. Formally, the '''readability (Rd)''' of a class <math>C_i</math> is defined as the '''sum of the number of attributes that are comments and the number of attributes that are labels''' the class has.

<math> Rd = |A, A = rdfs:comment| + |A, A=refs:label|</math>

The result of the formula will be an integer representing the availability of human-readable information for the instances of the current class.

[[Class_Metrics#Sources | Source 1]]

==Class Relationship Richness==

This is an important metric reflecting how much of the relationships defined for the class in the schema are actually being used at the instances level. This is another good indication of the utilization of the knowledge modelled in the schema.

The '''relationship richness (RR)''' of a class <math>C_i</math> is defined as the '''percentage of the number of relationships''' that are being used by instances <math>I_i</math> that belong to <math>C_i (P(I_i,I_j))</math> compared to the '''number of relationships''' that are defined for <math>C_i</math> at the schema level <math>(P(C_i,C_j))</math>.

[[Class_Metrics#Sources | Source 2]]

==Class children==
This count-metric measures the number of immediate descendants of the given class, also known as a number of children (NOC).

==Class instances==
Displays the number of instances of a given class. OWL classes provide an abstraction mechanism for grouping resources with similar characteristics. Like RDF classes, every OWL class is associated with a set of individuals, called the class extension. The individuals in the class extension are called the instances of the class. A class has an intensional meaning (the underlying concept) which is related but not equal to its class extension. Thus, two classes may have the same class extension, but still be different classes.

==Class properties==
Summarize the properties of an given class. Properties can be used to state relationships between individuals or from individuals to data values. Examples of properties include hasChild, hasRelative, hasSibling, and hasAge. The first three can be used to relate an instance of a class Person to another instance of the class Person (and are thus occurences of ObjectProperty), and the last (hasAge) can be used to relate an instance of the class Person to an instance of the datatype Integer (and is thus an occurence of DatatypeProperty). Both owl:ObjectProperty and owl:DatatypeProperty are subclasses of the RDF class rdf:Property.

==Sources==
#''Samir Tartir, I. Budak Arpinar, Amit P. Sheth: Ontological Evaluation and Validation In: Theory and Applications of Ontology: Computer Applications 2010, pp 115-130. http://link.springer.com/chapter/10.1007%2F978-90-481-8847-5_5
#''Samir Tartir, I. Budak Arpinar, Michael Moore, Amit P. Sheth, and Boanerges Aleman-meza: Ontoqa: Metric-based ontology quality analysis. In: IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources, 2005, pp 4-6. http://cobweb.cs.uga.edu/~budak/papers/ontoqa.pdf
#''http://gromit.iiar.pwr.wroc.pl/p_inf/ckjm/metric.html''
#''http://www.infowebml.ws/rdf-owl/Class-owl.htm''
#''https://www.w3.org/TR/2004/REC-owl-features-20040210/#property''

Knowledgebase Metrics

2016-06-01T08:44:19Z

Adminofwiki:

The way data is placed within an ontology is also a very important measure of ontology quality because it can indicate the effectiveness of the ontology design and the amount of real-world knowledge represented by the ontology. Instance metrics include metrics that describe the knowledgebase as a whole, and metrics that describe the way each schema class is being utilized in the knowledgebase.

==Average Population==

(The 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.

Formally, the '''average population (AP)''' of classes in a knowledgebase is defined as the '''number of instances of the knowledgebase (I)''' divided by the '''number of classes defined in the ontology schema (C)'''.
<math>AP=\frac{|I|}{|C|}</math>

The result will be a real number that shows how well is the data extraction process that was performed to populate the knowledgebase. 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 knowledgebase 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.

[[Knowledgebase_Metrics#Sources | Source 1]]

==Class Richness==

This metric is related to how instances are distributed across classes. The number of classes that have instances in the knowledgebase is compared with the total number of classes, giving a general idea of how well the knowledgebase utilizes the knowledge modelled by the schema classes. Thus, if the knowledgebase has a very low Class Richness, then the knowledgebase does not have data that exemplifies all the class knowledge that exists in the schema. On the other hand, a knowledgebase that has a very high class richness would indicate that the data in the knowledgebase represents most of the knowledge in the schema.

The '''class richness (CR)''' of a knowledgebase is defined as the percentage of the '''number of non-empty classes (classes with instances) (C')''' divided by the '''total number of classes (C)''' defined in the ontology schema.

<math>CR= \frac{|C'|}{|C|}</math>

[[Knowledgebase_Metrics#Sources | Source 1]]

==Cohesion==

'''This metric is not implemented in the ontometrics project yet.'''

The cohesion shows the degree of relatedness between the different entities. When the entities of an ontology are highly related there is a strong cohesion value.

To be able to measure the cohesion three different metrics will be used:

===Number of root classes (NoR)===
''Same as Absolute Root Cardinality in Graph Metrics!''

Displays the number of root classes of an ontology, a root class is a class which is not a sub class of any other class in the ontology. <math> C_j</math> is the jth root class.
<math>NoR= \sum _{1}^n C_j</math>

===Number of leaf classes (NoL)===
''Same as Absolute Leaf Cardinality in Graph Metrics!''

Displays the number of leaf classes of an ontology, a leaf class doesn't have any sub classes. <math> L_j</math> is the jth leaf class.

<math>NoL= \sum_{1}^n L_j </math>

===Average depth of inheritance tree of leaf nodes (ADIT-LN)===
''Same as Average Depth in Graph Metrics!''

It is the sum of the depth of all paths divided by the total number of paths (n). The total number of paths is the number of paths from each root node to each leaf node. while the depth is the total number of nodes starting with the root node, ending with the leaf node of one path. <math> D_j</math> is the total number of nodes on the path j.
<math>ADIT-LN= \frac{\sum_{1}^n D_j} {n} </math>

[[Knowledgebase_Metrics#Sources | Source 2]]

==Sources==
#''Samir Tartir, I. Budak Arpinar, Michael Moore, Amit P. Sheth, and Boanerges Aleman-meza: Ontoqa: Metric-based ontology quality analysis. In: IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources, 2005, p 4. http://cobweb.cs.uga.edu/~budak/papers/ontoqa.pdf
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005 , pp 44-45. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf''

Schema Metrics

2016-06-01T08:43:46Z

Adminofwiki:

Schema metrics address the design of the ontology. Although we cannot definitely know if the ontology design correctly models the domain knowledge, metrics in this category indicate the richness, width, depth, and inheritance of an ontology schema design. The most significant metrics in this category are described next.

==Attribute Richness==
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 '''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)'''.

<math>AR = \dfrac{|ATT|}{|C|}</math>

Note: Usually, only the functional attributes are counted to calculate this metric, as stated in the OWL definition. In our metric calculation, we omit this restriction and use all declared attributes to calculate, because not many modellers use the possibility of defining functional attributes. Also, the datatype are being handled as attributes as well.

==Inheritance Richness==

'''Inheritance Richness (IR)''' measure describes the distribution of information across different levels of the ontology’s 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 (where classes have a large number of direct subclasses) from a vertical ontology (where classes have a small number of direct subclasses). An ontology with a low inheritance richness would be of a deep (or vertical) ontology, which indicates that the ontology covers a specific domain in a detailed manner, while an ontology with a high IR would be a shallow (or horizontal) ontology, which indicates that the ontology represents a wide range of general knowledge with a low level of detail.

The inheritance richness of the schema (IR) is defined as the average number of subclasses per class.
The number of subclasses of a class is defined as <math> |H^C(C_1,C_i)|</math>. '''H''' is the '''number of inheritance relationships'''.

<math>IR = \frac{\sum_{C_i \in C}|H^C(C_1,C_i)|}{|C|}</math>

==Relationship Richness==

This metric reflects the diversity of the types of relations in the ontology. An ontology that contains only inheritance relationships usually conveys less information than an ontology that contains a diverse set of relationships. The relationship richness is represented as the percentage of the (non-inheritance) relationships between classes compared to all of the possible connections that can include inheritance and non-inheritance relationships.

The '''relationship richness (RR)''' of a schema is defined as the ratio of the '''number of (non-inheritance) relationships (P)''', divided by the '''total number of relationships''' defined in the schema (the sum of the '''number of inheritance relationships (H)''' and '''non-inheritance relationships (P)''').

<math>RR = \frac{|P|}{|H|+|P|}</math>

Note: The following relationships are being counted as non-inherited relationships: Object Properties, Equivalent Classes, Disjoint Classes.

The subclasses (Subclasses of) are being handled as inheritance relationships.

==Attribute-Class Ratio==

This metric represents the relation between the classes containing attributes and all classes. The difference to attribute richness is that not the amount of attributes is counted. It is only counted whether a class has attributes or not.

<math>AttributeClass Ratio=\frac{Classes With Attributes}{Number Of Classes}</math>

==Equivalence Ratio==

This metric calculates the ratio between similar classes and all classes in the ontology.

It is being calculated as follows:
<math>Equivalence Ratio =\frac{Same Classes}{Number Of All Classes}</math>

==Axiom Class Ratio==

This metric describes the ratio between axioms and classes. It is calculated as the average amount of axioms per class.
<math>Axiom class ratio=\frac{Axioms}{Classes}</math>

==Inverse Relations Ratio==

This metric describes the ratio between the inverse relations and all relations.
It is calculated as follows:
<math>Inverse Relations Ratio = \frac{Inverse Object Properties + Inverse Functional Data Properties}{All Object Properties + All Functional Data Properties}</math>

==Class Relation Ratio==

This metric describes the ratio between the classes and the relations in the ontology.
<math>Class Relation Ratio =\frac{Classes}{Relationships}</math>

Note: The following ontology components are counted as relationships: Object Properties, Equivalent Classes, Disjoint Classes, Subclasses(Subclass of).

==Sources==

#''Samir Tartir, I. Budak Arpinar, Amit P. Sheth: Ontological Evaluation and Validation In: Theory and Applications of Ontology: Computer Applications 2010, pp 115-130. http://link.springer.com/chapter/10.1007%2F978-90-481-8847-5_5''
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005, pp 19-20. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf