A meta-model is an explicit model of the constructs and rules needed to build specific models within a domain of interest. A valid meta-model is an ontology, but not all ontologies are modeled explicitly as meta-models. A meta-model can be viewed from three different perspectives:
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as a set of building blocks and rules used to build models
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as a model of a domain of interest, and
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as an instance of another model.
When comparing meta-models to ontologies, we are talking about meta-models as models (perspective 2). Note: Meta-modeling as a domain of interest can have its own ontology. For example, the CDIF Family of Standards, which contains the CDIF Meta-meta-model along with rules for modeling and extensibility and transfer format, is such an ontology. When modelers use a modeling tool to construct models, they are making a commitment to use the ontology implemented in the modeling tool. This model making ontology is usually called a meta-model, with 'model making' as its domain of interest.
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There is a very close relationship between a meta-model and an ontology, but it is not necessarily equivalence.
IF: you create an ontology, which is a set of terms naming concepts (classes) and relations, and you use that vocabulary to create a set of data (instances of the classes, and assertions that the instances are related to each other according to the specific relations in the vocabulary), and you think of the set of data you create as the model of your domain,
THEN: the ontology is the meta-model and the set of data created is the model.
In this case, there is little if any useful distinction to be drawn between an ontology and a meta-model. However, meta-models aren't always used in this way to connect to specific models, which is one of the primary uses of ontologies.