Joining conceptual systems - three remarks on TJS

The Theory of Joining Systems, abbreviated TJS, is a general theory of representing for example legal and other normative systems as formal structures. It uses algebraic tools and a fundamental idea in this algebraic approach is the representation of a conditional norm as an ordered pair of concepts. Another fundamental idea is that the components in such a pair are concepts of different sorts. Conditional norms are thus links from for example descriptive to normative concepts and the result is the joining of two conceptual systems. However, there are often at least three kinds of concepts involved in many normative systems, viz. descriptive, normative and intermediate concepts. Intermediate concepts such as `being the owner' and `being a citizen' have descriptive grounds and normative consequences and can be said to be located intermediately between the system of grounds and the system of consequences. Intermediate concepts function as bridges (links, joinings) between concepts of different sorts. The aim of this paper is to further develop TJS and widen the range of application of the theory. It will be shown that the idea of norms as ordered pairs is flexible enough to handle nested implications and hypothetical consequences. Minimal joinings, which are important in TJS, are shown to be closely related to formal concepts in Formal Concept Analysis. TJS was developed for concepts of a special kind, namely conditions. In this paper a new model of TJS is developed, where the concepts are attributes and aspects, and the role of intermediate concepts in this model is discussed