On alternative representations for knowledge spaces. (English) Zbl 0923.92039
Summary: In the context of knowledge structures, alternative representations have been obtained for the class of knowledge spaces, such as surmise mappings and entail relations. In this paper, various additional conditions on surmise mappings are introduced and their consequences for the corresponding spaces are investigated. In particular, the condition describing well-graded knowledge spaces is detected. These results are related to the mathematical theory of convex geometries. In addition, a direct \(1-1\) correspondence between surmise mappings and entail relations is described and finally an overview of the different representations, together with the corresponding special cases, is presented.
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