Higher-Order Types and Information Modeling

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 higherorder types. There appear to be three main reasons for requiring higherorder 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/meta levels (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 firstorder framework. This chapter examines some key issues involved, suggests techniques for retaining a first-order formalization, and makes some suggestions for adopting a higher-order semantics. INTRODUCTION This chapter evaluates the advisability of using higher-order types in information models. In case the reader is untutored in logic, we first clarify the notion of higher-order type. First-order logic quantifies over individuals only, not predicates. For example, the constraint “Each Person was born on at most one Date” may be formalized in first-order typed logic thus: IDEA GROUP PUBLISHING This chapter appears in the book, Advanced Topics in Database Research, vol. 4 edited by Keng Siau © 2005, Idea Group Inc. 701 E. Chocolate Avenue, Suite 200, Hershey PA 17033-1240, USA Tel: 717/533-8845; Fax 717/533-8661; URL-http://www.idea-group.com ITB11288