# A Framework for the Evaluation of the Cultural Heritage Information Ontology
## 3 Evaluation Framework for the Cultural Heritage Information Ontology
#### New Ontology Metrics for Interoperability
If \(1\leq i\leq K\) (\(K\) is number of all external ontologies):
* \(n_{i}\)--Number of resources from external ontology \(O_{i}\) used in the \(O_{\text{b}}\);
* \(p_{i}\)--Percentage of resources from \(O_{i}\) used in the \(O_{\text{b}}\), \(p_{i}=n_{i}/N_{i}\). \(N\) is the number of all resources in \(O_{\text{b}}\):  
\[N=n+\sum_{i=1}^{K}n_{i}, \tag{1}\]\(P_{i}\) is the percentage of resources from the \(O_{i}\) in the \(O_{\text{b}}\):  
\[P_{i}=\frac{n_{i}}{N}=\frac{p_{i}N_{i}}{N}, \tag{2}\]  
Based on this assumption, the following new metrics are proposed:  
1. [leftmargin=*]
2. Externes (_EXOnto_)  
The metric expresses the number of external ontologies used in the maintained ontology. The ontology is considered external if it contributes at least one resource from its external domain conceptualization (concepts, properties). Externality is always considered positive because the usage of external ontologies increases the value of the maintained ontology more than it costs to create (reinvent) its own conceptualization. \[ \begin{array}{c}EXOnto=\sum_{i=1}^{K}ENS_{i},\\ ENS_{i}\
eq[\text{ }XSD,\text{ }RDF,\text{ }RDFS,\text{ }OWL],\\ EXOnto\in[0,\infty]\end{array}  \tag{3}\]  
Extreme values are:  
Minimum value \(EXOnto=0\) means that there are no external ontologies used in the maintained ontology. 3. Composability (_CPOnto_)  
The metric measures the composability of the maintained ontology by exploiting the quality of the composure when external ontologies are used through the name-spacing mechanism. It expresses a percentage of the resources from external ontologies in the maintained ontology not considering the standard namespaces (XSD, RDF, RDFS, OWL). _CPOnto_ is the coverage of the maintained ontology with external ontologies:  
\[ \begin{array}{c}CPOnto=\sum\limits_{i=1}^{K}P_{i}=\frac{\sum_{i=1}^{n}n_{i} }{N}=\frac{N-n}{N}=1-p,\\ K=EXOnto\\ CPOnto\in[0,1]\end{array}  \tag{4}\]  
Extreme values are:  
* Monolithic ontology, no coverage from external ontologies: \(CPOnto=0\), if \(p=1\) or \(n=N\),
* Total coverage from external ontologies: \(CPOnto=1\), if \(p=0\) or \(n=0\). Ontology is monolithic when the composability equals to \(0\) (no external ontologies). If composability is high, then external ontologies are well embedded and are well contextualizing the maintained ontology. Typically, fundamental ontologies have low composability, core ontologies ideally have medium composability, and domain ontologies ideally have higher composability. Initially, the metric was tested with the ontology of bioscientific data analysis and data management (EDAM, version 1.20, [[http://edamontology.org/](http://edamontology.org/)]([http://edamontology.org/](http://edamontology.org/)), accessed on 10 January 2022), as well as the Description of a Project ([[http://usefulinc.com/ns/doap](http://usefulinc.com/ns/doap)]([http://usefulinc.com/ns/doap](http://usefulinc.com/ns/doap)), accessed on 10 January 2022). EDAM (an ontology for bioinformatics and computational biology) uses the following external namespaces:  
* _dc = [[http://purl.org/dc/elements/1.1/_](http://purl.org/dc/elements/1.1/_)]([http://purl.org/dc/elements/1.1/_](http://purl.org/dc/elements/1.1/_));_
* _edam = [[http://purl.obolibrary.org/obo/edam#_](http://purl.obolibrary.org/obo/edam#_)]([http://purl.obolibrary.org/obo/edam#_](http://purl.obolibrary.org/obo/edam#_));_
* _faf = [[http://xmlnns.com/faf/0.1/_](http://xmlnns.com/faf/0.1/_)]([http://xmlnns.com/faf/0.1/_](http://xmlnns.com/faf/0.1/_));_
* _oboInOwl = [[http://www.geneontology.org/formats/oboInOwl_](http://www.geneontology.org/formats/oboInOwl_)]([http://www.geneontology.org/formats/oboInOwl_](http://www.geneontology.org/formats/oboInOwl_));_
* _oboOther = [[http://purl.obolibrary.org/obo/](http://purl.obolibrary.org/obo/)]([http://purl.obolibrary.org/obo/](http://purl.obolibrary.org/obo/));_
* _doap = [[http://usefulinc.com/ns/doap_](http://usefulinc.com/ns/doap_)]([http://usefulinc.com/ns/doap_](http://usefulinc.com/ns/doap_)). The _CPOnto_ value for the EDAM ontology is 0.38.