Towards Higher-order OWL

A Case for Extensional Non-Wellfounded Metamodeling

“…This is obviously appropriate for a relation that means 'picking out a set' rather than 'being a set.' The difference between L IntM and L M parallels that of the HiLog and injective HiLog semantics discussed in [10]; that paper shows (in the appendix) that the latter is equivalent to the more usual Henkin semantics for extensional metamodeling.…”

“…To treat the classes and relations of the ontology as subjects of the same kind of modeling is 'meta-modeling'. [10] classifies the many applications of metamodeling into two kinds: domain-specific (e.g., in biology, a family may belong to an order), and general issues of the ontology-modeling process (e.g., associating a class with the researcher who added it to the ontology).…”

“…While working with reasoning over aggregate individuals, we realized we could do it elegantly by treating the class of the parts as an individual (see section 6). But this required an 'extensional' notion of metamodeling, whereas most existing approaches are 'intensional', and for good reason (see below for explanation, and [10] for arguments in favor of the intensional; we have found that compelling use cases for the extensional are hard to find in the literature). In this paper, we demonstrate how intensional metamodeling can be simulated in an extensionalmetamodeling language by careful ontology design, and argue that this is better than baking the somewhat mysterious concept of intension into the language semantics.…”