In this paper the framework DESIRE for the design of compositional reasoning systems and multi-agent systems was applied to build a generic nonmonotonic reasoning system. The outcome is a general reasoning system that can be used to model different nonmonotonic reasoning formalisms and that can be executed by a generic execution mechanism. The main advantages of using DESIRE (for example, compared to a direct implementation in a programming language such as PROLOG) are that the design is generic and has a transparent compositional structure, and the explicit declarative specification of both the static and dynamic aspects of the nonmonotonic reasoning processes, including their control. © 2003 Wiley Periodicals, Inc.

In this paper constructions leading to the formation of belief sets by agents are studied. The focus is on the situation when possible belief sets are built incrementally in stages. An infinite sequence of theories that represents such a process is called a reasoning trace. A set of reasoning traces describing all possible reasoning scenarios for the agent is called a reasoning frame. Default logic by Reiter is not powerful enough to represent reasoning frames. In the paper a generalization of default logic of Reiter is introduced by allowing infinite sets of justifications. This formalism is called infinitary default logic. In the main result of the paper it is shown that every reasoning frame can be represented by an infinitary default theory. A similar representability result for antichains of theories (belief frames) is also presented.

A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machines.

Many abstract studies of non-monotonic consequence relations (such as the one by Kraus, Lehmann and Magidor) have focused on logics which, in addition to satisfying some other properties, are cumulative. A number of concrete non-monotonic logics that have been proposed in the literature, however, are not cumulative. Furthermore, the restriction of smoothness that has to be imposed on preferential models to ensure that their consequence relation satisfies Cautious Monotonicity is a strange condition from an ontological point of view. We argue that cumulativity is not a necessary property for non-monotonic logics, and we will give a number of representation results for non-cumulative consequence relations. This paper thus complements the results of Kraus, Lehmann and Magidor for the non-cumulative case.

An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be safely added to the premises without destroying any of the consequences: we say they respect monotonicity. Also, there may be formulae that, when they are a consequence, can not be invalidated when adding any formula to the premises: we call them conservative. We study these two classes of formulae for preferential logics, and show that they are closely linked to the formulae whose truth-value is preserved along the (preferential) ordering. We will consider some preferential logics for illustration, and prove syntactic characterization results for them. The results in this paper may improve the efficiency of theorem provers for preferential logics.