In 1972, the Nobel prize-winning physicist Philip Anderson wrote the essay "More Is Different". In it, he argues that quantitative changes can lead to qualitatively different and unexpected phenomena. While he focused on physics, one can find many examples of More is Different in other domains as well, including biology, economics, and computer science. While some of the examples, like uranium, correspond to a sharp transition, others like specialization are more continuous. I'll use emergence to refer to qualitative changes that arise from quantitative increases in scale, and phase transitions for cases where the change is sharp.

Many formalisms discussed in the literature on qualitative spatial reasoning are designed for expressing static spatial constraints only. However, dynamic situations arise in virtually all applications of these formalisms, which makes it necessary to study variants and extensions involving change. This paper presents a study on the computational complexity of qualitative change. More precisely, we discuss the reasoning task of finding a solution to a temporal sequence of static reasoning problems where this sequence is subject to additional transition constraints. Our focus is primarily on smoothness and continuity constraints: we show how such transitions can be defined as relations and expressed within qualitative constraint formalisms. Our results demonstrate that for point-based constraint formalisms the interesting fragments become NP-completein the presence of continuity constraints, even if the satisfiability problem of its static descriptions is tractable.

In this paper some initial work towards a new approach to qualitative reasoning under uncertainty is presented. This method is not only applicable to qualitative probabilistic reasoning, as is the case with other methods, but also allows the qualitative propagation within networks of values based upon possibility theory and Dempster-Shafer evidence theory. The method is applied to two simple networks from which a large class of directed graphs may be constructed. The results of this analysis are used to compare the qualitative behaviour of the three major quantitative uncertainty handling formalisms, and to demonstrate that the qualitative integration of the formalisms is possible under certain assumptions.