The formal analysis of normative systems as initiated by Alchourrón and Bulygin can be complemented by the analysis of normative positions as pursued by Kanger, Lindahl, Sergot and Jones. The paper is a step towards integrating the two approaches within an algebraic theory of so-called Boolean quasi-orderings (Bqo's). In the general Bqo theory presented, a number of theoretical tools are introduced and elucidated by theorems, in particular those of fragment, connection, coupling and pair coupling. Condition implication structures (cis's) are models of the Bqo theory used for the representation of normative systems. A system of normative positions is introduced as a special kind of cis. The final section is devoted to an example exhibiting a legal mini-system where a cis of normative positions (np-cis) is joined to a descriptive cis.

An abstract architecture for idealized multi-agent systems whose behaviour is regulated by normative systems is developed and discussed. Agent choices are determined partially by the preference ordering of possible states and partially by normative considerations: The agent chooses that act which leads to the best outcome of all permissible actions. If an action is non-permissible depends on if the result of performing that action leads to a state satisfying a condition which is forbidden, according to the norms regulating the multi-agent system. This idea is formalized by defining set-theoretic predicates characterizing multi-agent systems. The definition of the predicate uses decision theory, the Kanger-Lindahl theory of normative positions, and an algebraic representation of normative systems.

 The paper discusses normative systems and their revision within an algebraic framework. If a system is logically well-formed, certain norms, called connecting norms, determine the system as a whole. It is maintained that, if the system is well-formed, a relation at least as low as determines a lattice or quasi-lattice of its connecting norms. The ideas are presented mainly in the form of comments on a legal example concerning acquisition of movable property by extinction of another person's previous rights.

Many concepts in legal texts are “intermediaries”, in the sense that they serve as links between statements of legal grounds, on one hand, and of legal consequences, on the other. In our paper, an algebraic representation of normative systems is used for distinguishing between different kinds of intermediaries and making the idea of a joining between grounds and consequences more precise. In Section 1, the idea of intermediaries is presented and earlier discussions of the subjects are outlined. In Section 2, we introduce the algebraic framework and develop the formal theory. After introducing our approach to the representation of a normative system, we here present a theory of “intervenients”, seen as a tool for analysing intermediaries. In Section 3, dealing with applications, after presenting a model of the formal theory, suited for the analysis of concepts in normative systems, we apply the theory to a number of examples, introduced in the first part. Finally, in Section 4, we make some remarks on the methodology of intermediate concepts.

Writing a contract of a specific content is a ground for purchase, purchase is a ground for ownership, ownership is a ground for power to dispose. Also power to dispose is a consequence of ownership, ownership is a consequence of purchase. etc. The paper presents a continuation of the authors’ previous algebraic representation on ground - consequence chains in normative systems.The paper analyzes different kinds of “implicative closeness” between grounds and consequences in chains of legal concepts, in particular combinations of “weakest ground”, “strongest consequence” and “minimal joining”. The idea of a concept’s being intermediate between concepts of two different sorts is captured by the technical notion of “intervenient”, defined in terms of weakest ground and strongest consequence. A legal example concerning grounds and consequences of “ownership” and “trust” is used to illustrate the application of the formal theory.