An algebraic approach to Kauppi's concept theory II: functional representation of concept operations and concept associations

摘要

For concept management and analysis of concept structures, exact formulations of relations and operations that associate concepts are needed. In this paper, we present a covering set of such association relations and concept operations on the basis of Kauppi's concept theory. This theory is appealing, since it emphasises the intensional aspect of conceptual modelling, is most compact and can be applied to many fields of knowledge representation, namely the analysis of the is-a relationship, the has component relationship and the relationships between processes. To appreciate the differences of these fields, we have designed the functions to be more general than in Kauppi's original theory, i.e. the functions are effective also in concept systems that do not follow Kauppi's axiomatisation. We use set theory as the meta-language for concept theory, since set theory is an established and a well-known method of formal representation in computer science. By using this approach we also create a system for an explicit representation of Kauppi's theory. This system can be easily implemented in a programming language, and its usability and computability can be estimated.