We reconsider the nature and formal properties of the class inclusion relation, IS-A, from the point of view of information modeling and engineering of formal ontologies. In particular we review approaches to the elusive notion of intensionality. We then conduct an analysis adopting a metalogic setup where classes and properties are reified. This approach affords choices along the extensionality/intensionality spectrum. Our analysis concludes that the distinction between epistemic modes for distinguishing definitions, norms, hypotheses, and observational evidence is more important the extensionality/intensionality dichotomy in ontological engineering.
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