# 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  
Simple ontology metrics can be obtained from ontology-authoring tools (e.g., Protege, etc.) or programmatically (e.g., OntoMetriCalc Java API, [[https://sourceforge.net/projects/ontometricalc/](https://sourceforge.net/projects/ontometricalc/)]([https://sourceforge.net/projects/ontometricalc/](https://sourceforge.net/projects/ontometricalc/)), accessed on 10 January 2022). A collection of simple ontology metrics for the CIDOC CRM, (version 6.2, encoded in OWL, [[https://cidoc-crm.org/sites/default/files/cidoc_crm_v6.2-2018](https://cidoc-crm.org/sites/default/files/cidoc_crm_v6.2-2018) April.pdfs]([https://cidoc-crm.org/sites/default/files/cidoc_crm_v6.2-2018](https://cidoc-crm.org/sites/default/files/cidoc_crm_v6.2-2018) April.pdfs), accessed on 10 January 2022) shows that it contains 2455 axioms, 84 classes, 277 object properties, 8 data properties, and 0 individuals. These simple metrics give only a very general quantitative perception of an ontology. In addition, there is ambiguity in naming across different ontology software. For example, number of levels, maximal depth, and maximal length may all expresses maximal depth in the ontology concepts tree (e.g., in the CIDOC CRM the concept _owl:Ting_ is at level 0, the concept E1_CRM_Entity is at level 1, while the concept E34_Inscription is at the level 9). A more complex metric system is needed for further detailed ontology evaluation and comparison. For our research, complex metrics were created as suggested in the ontology-evaluation framework OQuaRE ([[http://miuras.inf.um.es/oquarewiki/](http://miuras.inf.um.es/oquarewiki/)]([http://miuras.inf.um.es/oquarewiki/](http://miuras.inf.um.es/oquarewiki/)), accessed on 10 January 2022). We studied the OQuaRE metrics and have developed a new evaluation framework, which we used for the evaluation of the CIDOC CRM. The framework includes our Java software based on the Apache Jena Ontology API. During the research, some errors and inconsistencies were detected in the definition and formulas of the original OQuaRE metrics, which were corrected. Corrected and improved definition and formulas for the framework, along with the results of the evaluation of the CIDOC CRM, are presented in Section 3. Interoperability of ontologies can be regarded as an integration (reuse) of a conceptualization subset of an ontology A (external) inside an ontology B (internal). Integration is guaranteed by design because the to-be-integrated ontologies use the same mechanisms (e.g., syntax XSD, RDF, RDFS, OWL) to express axioms. The external conceptualization subset must be semantically aligned with the internal conceptualization set. Such interoperability occurs within complementary domains (e.g., wine and food) and at the level of resources (concepts and properties). External concepts are immutably contextualized within the maintained ontology, and this enables new properties relating internal (base) and external concepts. Imported ontologies (e.g., <owl:imports rdf:resource=\"[[http://xmlns.com/foaf/0.1/index.rdf](http://xmlns.com/foaf/0.1/index.rdf)]([http://xmlns.com/foaf/0.1/index.rdf](http://xmlns.com/foaf/0.1/index.rdf))\"/>) are also considered as external. For a better understanding of the quality and quantity of the interoperability between ontologies, we assume the following:  
* \(O_{\text{b}}\)--Maintained (base) ontology (in evaluation);
* \(O_{\text{k}}\)--External ontology, \(1\leq k\leq K\), \(K\) is number of all external ontologies;
* \(N\)--Number of all resources (internal + external) in the \(O_{\text{b}}\);
* \(N_{\text{c}}\)--Number of all resources from all external ontologies in the \(O_{\text{b}}\);
* \(ENS_{i}\)--Namespace of an (external) ontology;
* \(n\)--Number of base resources from the \(O_{\text{b}}\) (excluding external),
* \(p\)--Percentage of base resources in \(O_{\text{b}}\), \(p=n/N\).