Surmise Systems

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 5 in Learning Spaces, 2011, pp 81-101 from Springer

Abstract: Abstract When a knowledge structure is a quasi ordinal space, it can be faithfully represented by its surmise relation (cf. Theorem 3.8.3). In fact, as illustrated by Example 3.7.4, a fnite ordinal space is completely recoverable from the Hasse diagram of the surmise relation. However, for knowledge structures in general, and even for knowledge spaces, the information provided by the surmise relation may be insufficient. In this chapter, we study the ‘surmise system,’ a concept generalizing that of a surmise relation, and allowing more than one possible learning ‘foundation’1 for an item2. One of the two main results of this chapter is Theorem 5.2.5 which establishes, in the style of Theorem 3.8.3 for quasi ordinal spaces, a one-to-one correspondence between knowledge spaces and surmise systems.

Keywords: Partial Order; Linear Order; Knowledge Structure; Knowledge State; Hasse Diagram (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01039-2_5

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DOI: 10.1007/978-3-642-01039-2_5

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