On category theory as a (meta) ontology for information systems research

ABSTRACT

Category theory is a branch of mathematics that is renowned for its semantic power despite its very simple axiom set. The use of category theory as a meta-ontology for abstract algebra via the highly developed field of universal algebra has suggested that it be used as a foundation for research in computing. To date it has been widely used in, inter alia, the definition of abstract data types, the semantics of programming languages, and the design of functional programming languages. This paper illustrates the use of category theory as a meta-ontology for information systems research. It is based on the authors' extensive consultancy work using category theory to solve real problems in industrial applications involving information systems. In addition to discussing the role of category theory as an ontological tool for information systems research, the paper illustrates its use with a number of examples including system specification, the definitions of views and view updates, and system interoperations.

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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.3 LOGICS AND MEANINGS OF PROGRAMS
      F.3.2 Semantics of Programming Languages
          Subjects: Algebraic approaches to semantics

Additional Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.4 Software/Program Verification
          Subjects: Formal methods

  F. Theory of Computation
  F.3 LOGICS AND MEANINGS OF PROGRAMS
      F.3.1 Specifying and Verifying and Reasoning about Programs
          Subjects: Specification techniques

  H. Information Systems
  H.2 DATABASE MANAGEMENT
      H.2.1 Logical Design
          Subjects: Data models

General Terms:
Design, Management, Standardization, Theory

Keywords:
category theory, data modeling, information systems, interoperating systems, ontology, view update