Assessing the local identifiability of probabilistic knowledge structures
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Updated: May 22, 2026

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Published on: November 2, 2012
Luca Stefanutti1, Jürgen Heller, Pasquale Anselmi
1Dipartimento di Psicologia Applicata, University of Padua, Via Venezia 8, 35313, Padova, Italy. luca.stefanutti@unipd.it
Abstract:
Given a collection Q of problems, in knowledge space theory Doignon & Falmagne, (International Journal of Man-Machine Studies 23:175-196, 1985) the knowledge state of a student is the collection K ⊆ Q of all problems that this student is capable of solving. A knowledge structure is a pair (Q, ), where is a collection of knowledge states that contains at least the empty set and Q. A probabilistic knowledge structure (PKS) is a knowledge structure (Q, , π), where π is a probability distribution on the knowledge states. The PKS that has received the most attention is the basic local independence model BLIM; Falmagne & Doignon, (British Journal of Mathematical and Statistical Psychology 41:1-23, 1988a, Journal of Mathematical Psychology 32:232-258, 1988b). To the best of our knowledge, systematic investigations in the literature concerning the identifiability of the BLIM are totally missing. Based on the theoretical work of Bamber and van Santen (Journal of Mathematical Psychology 29:443-473, 1985), the present article is aimed to present a method and a corresponding computerized procedure for assessing the local identifiability of the BLIM, which is applicable to any finite knowledge structure of moderate size.
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