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.
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Falmagne, JC., Doignon, JP. (2011). Surmise Systems. In: Learning Spaces. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01039-2_5
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DOI: https://doi.org/10.1007/978-3-642-01039-2_5
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