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Titlebook: Knowledge Spaces; Jean-Paul Doignon,Jean-Claude Falmagne Book 1999 Springer-Verlag Berlin Heidelberg 1999 Graph.Sim.Text.algorithms.classi

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书目名称Knowledge Spaces
编辑Jean-Paul Doignon,Jean-Claude Falmagne
视频video
概述Interdisciplinary representation of the theory of Knowledge Spaces..Application oriented introduction based on real and simulated data.
图书封面Titlebook: Knowledge Spaces;  Jean-Paul Doignon,Jean-Claude Falmagne Book 1999 Springer-Verlag Berlin Heidelberg 1999 Graph.Sim.Text.algorithms.classi
描述Knowledge spaces offer a rigorous mathematical foundation for various practical systems of knowledge assessment. An example is offered by the ALEKS system (Assessment and LEarning in Knowledge Spaces), a software for the assessment of mathematical knowledge. From a mathematical standpoint, knowledge spaces generalize partially ordered sets. They are investigated both from a combinatorial and a stochastic viewpoint. The results are applied to real and simulated data. The book gives a systematic presentation of research and extends the results to new situations. It is of interest to mathematically oriented readers in education, computer science and combinatorics at research and graduate levels. The text contains numerous examples and exercises and an extensive bibliography.
出版日期Book 1999
关键词Graph; Sim; Text; algorithms; classification; knowledge; learning; organization; simulation; theory of knowle
版次1
doihttps://doi.org/10.1007/978-3-642-58625-5
isbn_softcover978-3-540-64501-6
isbn_ebook978-3-642-58625-5
copyrightSpringer-Verlag Berlin Heidelberg 1999
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Surmise Systems,ted by Example 1.46, an 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 incomplete. In this chapter, we introduce the ‘surmise
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Skill Maps, Labels and Filters,ning path’ or ‘gradation.’ This makes sense since, as suggested by our Examples in 0.9, 0.10 and 0.11, many of our results are potentially applicable to widely different fields. It must be realized, however, that our basic concepts are consistent with traditional explanatory features of psychometric
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Entailments and the Maximal Mesh,real-life applications, we will typically assume this domain to be finite. The second step is then to construct a list of all the subsets of . that are knowledge states. To secure such a list, we could in principle rely on one or more experts in the particular body of information. However, if no ass
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Galois Connections,ance, Birkhoff’s Theorem 1.49 asserts the existence of a one-to-one correspondence between the collection of all quasi ordinal spaces on a domain ., and the collection of all quasi orders on .. All these correspondences will be shown to derive from natural constructions. Each derivation will be obta
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Stochastic Learning Paths,mplete and takes place in real time, rather than in a sequence of discrete trials. This theory also contains a provision for individual differences. Nevertheless, its basic intuition is similar, in that that any student progresses through some learning path. As time passes, the student successively
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