Note on two necessary and sufficient axioms for a well-graded knowledge space

Cosyn, Eric; Uzun, Hasan

doi:10.1016/j.jmp.2008.09.005

Cited by 33 publications

(10 citation statements)

References 9 publications

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“…Learning spaces (characterized through well-gradedness and stability under union as in Proposition 1) are the ∪-stable antimatroids of Korte, Lovász and Schrader (1991) (except for the missing requirement Q ∈ Knotice that by Proposition 1 any of our learning space has a maximum state containing all the other states, but this state may differ from Q). As a matter of fact, Proposition 1 can be found in Chapter III of the latter reference (see also Cosyn and Uzun, 2009). Notice that the duals of learning spaces are '∩-stable antimatroids' in the sense of Edelman and Jamison (1985) (we give a definition which is different from, but equivalent to, the original one except that we admit the omission of ∅ from C).…”

Section: Definitionmentioning

confidence: 96%

Learning Spaces, and How to Build Them

Doignon

2014

Lecture Notes in Computer Science

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Abstract. In Knowledge Space Theory (KST), a knowledge structure encodes a body of information as a domain, consisting of all the relevant pieces of information, together with the collection of all possible states of knowledge, identified with specific subsets of the domain. Knowledge spaces and learning spaces are defined through pedagogically natural requirements on the collection of all states. We explain here several ways of building in practice such structures on a given domain. In passing we point out some connections linking KST with Formal Concept Analysis (FCA).

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Section: Definitionmentioning

confidence: 96%

Learning Spaces, and How to Build Them

Doignon

2014

Lecture Notes in Computer Science

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“…If H ′ ⊆ H implies H ′ ∈ H , then the knowledge structure H is called a knowledge space. Moreover, a special knowledge structure H is called learning space if H satisfies learning smoothness and learning consistency, see [6,14]. Moreover, each learning space must be finite.…”

Section: Introductionmentioning

confidence: 99%

The language of pre-topology in knowledge spaces

Lin¹,

Xiyan²,

Li³

2021

Preprint

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We systematically study some basic properties of the theory of pre-topological spaces, such as, pre-base, subspace, axioms of separation, connectedness, etc. Pre-topology is also known as knowledge space in the theory of knowledge structures. We discuss the language of axioms of separation of pre-topology in the theory of knowledge spaces, the relation of Alexandroff spaces and quasi ordinal spaces, and the applications of the density of pre-topological spaces in primary items for knowledge spaces. In particular, we give a characterization of a skill multimap such that the delineate knowledge structure is a knowledge space, which gives an answer to a problem in [14] or [18] whenever each item with finitely many competencies; moreover, we give an algorithm to find the set of atom primary items for any finite knowledge spaces.

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“…Well‐graded competence spaces are particularly interesting from a pedagogical point of view because they allow smooth learning: whatever the competence state of a student might be, the student can learn new skills one at a time (Cosyn & Uzun, ). In what follows, the model for independent skills will be denoted by GaLoM, while the model for dependent skills will be denoted by GaLoM‐DS.…”

Section: Introductionmentioning

confidence: 99%

The assessment of knowledge and learning in competence spaces: The gain–loss model for dependent skills

Anselmi

Stefanutti

Chiusole

et al. 2017

Brit J Math & Statis

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The gain-loss model (GaLoM) is a formal model for assessing knowledge and learning. In its original formulation, the GaLoM assumes independence among the skills. Such an assumption is not reasonable in several domains, in which some preliminary knowledge is the foundation for other knowledge. This paper presents an extension of the GaLoM to the case in which the skills are not independent, and the dependence relation among them is described by a well-graded competence space. The probability of mastering skill s at the pretest is conditional on the presence of all skills on which s depends. The probabilities of gaining or losing skill s when moving from pretest to posttest are conditional on the mastery of s at the pretest, and on the presence at the posttest of all skills on which s depends. Two formulations of the model are presented, in which the learning path is allowed to change from pretest to posttest or not. A simulation study shows that models based on the true competence space obtain a better fit than models based on false competence spaces, and are also characterized by a higher assessment accuracy. An empirical application shows that models based on pedagogically sound assumptions about the dependencies among the skills obtain a better fit than models assuming independence among the skills.

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Note on two necessary and sufficient axioms for a well-graded knowledge space

Cited by 33 publications

References 9 publications

Learning Spaces, and How to Build Them

Learning Spaces, and How to Build Them

The language of pre-topology in knowledge spaces

The assessment of knowledge and learning in competence spaces: The gain–loss model for dependent skills

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