Spatio-temporal Reasoning for Vague Regions Zina M. Ibrahim and Ahmed Y. Tawfik University of Windsor, 401 Sunset Avenue, Windsor, Ontario N9B 3P4, Canada {ibrahim,atawfik}@uwindsor.ca Abstract. This paper extends a mereotopological theory of spatiotem- poral reasoning to vague ”egg-yolk” regions. In this extension, the egg and its yolk are allowed to move and change over time. We present a classification of motion classes for vague regions as well as composition tables for reasoning about moving vague regions. We also discuss the formation of scrambled eggs when it becomes impossible to distinguish the yolk from the white and examine how to incorporate temporally and spatially dispersed observations to recover the yolk and white from a scrambled egg. Egg splitting may occur as a result of the recovery process when available information supports multiple egg recovery alternatives. Egg splitting adds another dimension of uncertainty to reasoning with vague regions. 1 Introduction Spatiotemporal knowledge representations proposed so far include qualitative models of kinematics [14] as well as many spatiotemporal logics [9,11]. These logics augment a temporal logic with a spatial one. For example, temporal modal logic and RCC-8 are combined in [17] to represent and reason about spatiotem- poral change. Muller’s theory [11,12,13] describes the relations among spatiotemporal ob- jects via a primitive of connectedness. As humans usually reason with imprecise or incomplete information, the notion of vague regions of space-time has at- tracted some attention [6]. This paper extends Muller’s theory to vague regions using the egg-yolk theory [5] as a base. Due to the importance of space in AI, lot of work has been put into for- mulating representations of space in the past decade. Also, because systems in AI usually deal with imprecise, incorrect or incomplete information, qualitative models have been the preferred choice as opposed to quantitative ones. In partic- ular, Qualitative Spatial Representation (QSR) models have flourished and are accepted as the models that take as ontological primitives extended regions of space as opposed to points. One such theory is the Region Connectedness Cal- culus (RCC), which is a well-known first-order theory that deals with regions in a topological manner [15]. The theory’s original intension has been for regions with precise boundaries, or in other words crisp regions of space. However, it was extended to deal with vague regions in [4,5,10] and formed what is known as the A.Y. Tawfik and S.D. Goodwin (Eds.): Canadian AI 2004, LNAI 3060, pp. 308–321, 2004. c  Springer-Verlag Berlin Heidelberg 2004