Normative Systems Represented by Boolean Quasi-orderings

By a normative system jurists often mean the law of a country, like Swedish law, or part of the law of a country, such as the Swedish law of contracts. With regard to the issue how a logical reconstruction of a normative system should be made, a central question is what kind of entities a normative system is composed of and how it should be represented. The aim of the present paper is to contribute to the study of this field. More specifically, our contribution aims at presenting a framework for analysing different kinds of joinings of conceptual structures in a normative system. A case in view is where one of these structures is descriptive and the other normative. In a previous paper, we presented a working model where conceptual structures were represented by lattices.1 This was the first step in developing the theory, having the limitation that the role of negation for concept formation was not dealt with. This limitation is eliminated in the present paper, which is different in several respects. The framework to be developed is based on the theory of Boolean algebra instead of lattice theory. The basic kind of relations dealt with are quasi-orderings rather than partial orderings, as was the case in our previous paper, where partial orderings were introduced by a transition to equivalence classes. The framework of what we will call ‘‘Boolean quasi-orderings’’ is general in the sense that the main results are not tied to a specific interpretation in terms of conditions as was the case in the earlier paper. Thus, the case where the domains of the orderings have conditions as their members, so-called condition implication structures, only plays the part of one of several models of the theory. Also, the new framework is more flexible in the sense that it is not confined to the joining of two subsystems within a background system. In the new framework it is possible to generate a background system when subsystems are given. The paper is intended as an overview of some central ideas and results pertaining to the theory as it is now developed. For this reason we do not