A generalization of Allen's interval-based approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semi-intervals rather than intervals are used as the basic units of knowledge. Semi-intervals correspond to temporal beginnings or endings of events. We demonstrate the advantages of reasoning on the basis of semi-intervals: 1) semi-intervals are rather natural entities both from a cognitive and from a computational point of view; 2) coarse knowledge can be processed directly; computational effort is saved; 3) incomplete knowledge about events can be fully exploited; 4) incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps; 5) there is no trade-off in computational strength for the added flexibility and efficiency; 6) for a natural subset of Allen's algebra, global consistency can be guaranteed in polynomial time; 7) knowledge about relations between events can be represented much more compactly.

Abstract. This paper gives the SNAP and SPAN ontologies relating to recognizing variable vista spatial environments, namely, SNAPVis and SPANVis. It proposes that recognizing spatial environments is a judgment process of whether the perceived environment is compatible with the remembered one. Their compatibility is based on both their spatial changes and the commonsense knowledge of objects ’ stabilities. The recognition result is determined by whether such changes are due to possible movements of related objects or not. This paper presents six SNAPVis ontologies: fiat boundary, near region, fiat parts (the three are fiat regions), classic topologic relations, qualitative orientations, and qualitative distances (the three are spatial relations) and one SPANVis ontology: the commonsense knowledge of stability of spatial objects. The paper briefly presents a cognitive map of vista spatial environments and the process of recognition.

In processing knowledge about spatial situations, spatial concepts are employed for representing objects, properties, and relations in the world. This article presents some fundamental difficulties encountered in representing and processing knowledge about the real geographic world and motivates the need for sophisticated conceptual structures for dealing with spatial knowledge. Consequently, semantic and structural aspects of spatial concepts are discussed. Specific attention is paid to relations among different concepts on one hand and to the relation between conceptual structures and structures in the real world on the other hand. Issues like discrete vs. continuous, crisp vs. fuzzy, fine vs. coarse, and top-down vs. bottom-up concept formation are discussed in the context of spatial representations. The article derives suggestions for task-specific concept formation for the use in future Geographic Information Systems. It concludes with a discussion about fuzzy boundaries of geographic objects.