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Surmise Systems

In: Learning Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jean-Claude Falmagne & Jean-Paul Doignon, 2011. "Surmise Systems," Springer Books, in: Learning Spaces, chapter 5, pages 81-101, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01039-2_5
    DOI: 10.1007/978-3-642-01039-2_5
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