Well-Graded Knowledge Structures

Jean-Claude Falmagne () and Jean-Paul Doignon ()
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Jean-Claude Falmagne: University of California, Irvine, Department of Cognitive Sciences, Institute of Mathematical Behavioral Sciences
Jean-Paul Doignon: Université Libre de Bruxelles, Département de Mathématique

Chapter 4 in Learning Spaces, 2011, pp 61-79 from Springer

Abstract: Abstract Wellgradedness was introduced in Definition 2.2.2 as a powerful property implied by the two axioms [L1] and [L2] defining learning spaces (cf. Section 2.2). As stated in Theorem 2.2.4, any well-graded knowledge space is in fact a learning space and conversely. In this chapter, we focus on the wellgradedness property per se. We define some new concepts, derive important consequences, and describe a variety of applications to topics quite different from education. The results of this chapter will have applications elsewhere in this book. For example, they will provide the combinatoric skeleton for the learning theories developed in Chapters 9 and 12 and for some of the assessment procedures described in Chapters 13 and 14. To avoid minor technicalities, we restrict consideration to discriminative structures.

Keywords: Knowledge Structure; Maximal Chain; Interval Order; Ordinal Space; Learning Space (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-01039-2_4

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