Information Modeling and Higher-order Types

While some information modeling approaches (e.g. the Relational Model, and Object-Role Modeling) are typically formalized using first-order logic, other approaches to information modeling include support for higher-order types. There appear to be three main reasons for requiring higher-order types: (1) to permit instances of categorization types to be types themselves (e.g. the Unified Modeling Language introduced power types for this purpose); (2) to directly support quantification over sets and general concepts; (3) to specify business rules that cross levels/metalevels (or ignore level distinctions) in the same model. As the move to higher-order logic may add considerable complexity to the task of formalizing and implementing a modeling approach, it is worth investigating whether the same practical modeling objectives can be met while staying within a first-order framework. This paper examines some key issues involved, suggests techniques for retaining a first-order formalization, and also makes some suggestions for adopting a higher-order semantics.