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Assessing the local identifiability of probabilistic knowledge structures
Authors:Luca Stefanutti  Jürgen Heller  Pasquale Anselmi  Egidio Robusto
Affiliation:1. Dipartimento di Psicologia Applicata, University of Padua, Via Venezia 8, 35313, Padova, Italy
2. Fachbereich Psychologie, Eberhard-Karls-Universit?t Tübingen, Schleichstr. 4, 72076, Tübingen, Germany
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, ></img>                              </span>), where <span class= ></img>                              </span> is a collection of knowledge states that contains at least the empty set and <em>Q</em>. A probabilistic knowledge structure (PKS) is a knowledge structure (<em>Q</em>, <span class= ></img>                              </span>, <em>π</em>), where <em>π</em> is a probability distribution on the knowledge states. The PKS that has received the most attention is the <em>basic local independence model</em> BLIM; Falmagne & Doignon, (British Journal of Mathematical and Statistical Psychology 41:1–23, <span class=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.
Keywords:
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