Skill Reduction and Assessment in Formal Context

doi:10.3778/j.issn.1673-9418.2008024

Abstract

Abstract:

Knowledge space theory (KST) provides an effective way to construct knowledge evaluation system. Formal concept analysis (FCA) is a powerful tool for knowledge discovery. The knowledge space theory is closely related to the formal concept analysis. Knowledge space theory is applied to assessing learners’ knowledge and guiding future learning. At present, how to construct accurate knowledge structure is the key research problem of knowledge space theory. Based on the relationship between skills and items, this paper studies the relationship between knowledge space theory and formal concept analysis. Firstly, the concept of skill context is proposed, the one-to-one correspondence relationship between skill map and skill context is established, and the method of mutual conversion between skill map and skill context is obtained. Secondly, based on the skill context, the problem of knowledge structure construction is discussed, and the method of knowledge structure construction based on the concept lattice of skill context is obtained. Then, based on the skill context, the method of finding the knowledge base, the skill reduction method of keeping the knowledge base unchanged, and the method of building the skill context through the knowledge base are introduced. Finally, in the case of known knowledge state of learners, skills are assessed by judging the skills that learners must master, and learning path selection is discussed by selecting skills that can promote the change of knowledge state.

Key words: knowledge space theory (KST), formal concept analysis (FCA), skill context, knowledge base, skill reduction, skill assessment

摘要：

知识空间理论（KST）为构建知识评价体系提供了有效的途径。形式概念分析（FCA）是知识发现的有力工具。知识空间理论与形式概念分析间存在密不可分的联系。知识空间理论被运用于评估学习者的知识和指导未来的学习。目前,如何构建准确的知识结构是知识空间理论的重点研究问题。基于技能与问题间的关系,对知识空间理论与形式概念分析间的联系进行研究。首先,提出技能背景的概念,建立技能映射与技能背景间一一对应的关系,得到技能映射与技能背景互相转换的方法。其次,基于技能背景,讨论知识结构的构建问题,得到由技能背景的概念格来构建知识结构的方法。随后,基于技能背景,介绍寻找知识基的方法和保持知识基不变的技能约简方法,以及通过知识基构建技能背景的方法。最后,在已知学习者知识状态的情形下,通过判断学习者对技能的掌握情况来对其进行技能评估,并通过选择学习能够促使知识状态发生改变的技能来讨论学习路径选择等问题。

关键词: 知识空间理论（KST）, 形式概念分析（FCA）, 技能背景, 知识基, 技能约简, 技能评估

CLC Number:

TP182

ZHOU Yinfeng, LI Jinjin. Skill Reduction and Assessment in Formal Context[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(3): 692-702.

周银凤, 李进金. 形式背景下的技能约简与评估[J]. 计算机科学与探索, 2022, 16(3): 692-702.

Figures/Tables 13

Table 1 Skill context ( S 1 , Q 1 , I 1 )

S₁	a	b	c	d	e
s	1	0	1	1	1
t	0	1	0	0	1
u	0	0	1	0	0
v	1	0	1	1	1

Fig.1 Concept lattice L ( S 1 , Q 1 , I 1 )

Table 2 Skill context ( S 2 , Q 2 , I 2 )

$S 2$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 2$					$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$
$s 6$		$×$	$×$

Table 2 Skill context ( S 2 , Q 2 , I 2 )

$S 2$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 2$					$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$
$s 6$		$×$	$×$

Table 3 Skill context ( X , Q 2 , I X )

$X$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$

Table 3 Skill context ( X , Q 2 , I X )

$X$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$

Table 4 Skill context ( T , Q 1 , I T )

$T$	a	b	c	d	e
s	$×$	$↙$	$×$	$×$	$×$
t	$↙$	$×$	$↙$	$↙$	$×$
u	$↙$		$×$	$↙$	$↙$

Table 4 Skill context ( T , Q 1 , I T )

$T$	a	b	c	d	e
s	$×$	$↙$	$×$	$×$	$×$
t	$↙$	$×$	$↙$	$↙$	$×$
u	$↙$		$×$	$↙$	$↙$

Table 5 Skill context ( S , Q , I )

$S$	1	2	3	4
x	0	1	0	1
y	1	0	1	0
z	1	1	0	0

Table 5 Skill context ( S , Q , I )

$S$	1	2	3	4
x	0	1	0	1
y	1	0	1	0
z	1	1	0	0

Table 6 Skill mastery of knowledge state in K 1

知识状态	需掌握的核心技能
$∅$	$∅$
$b$	$∅$
${a, c, d}$	$t$
${a, b, d, e}$	$u$
${a, b, c, d}$	$t$
$Q 1$	${t, u}$

Table 6 Skill mastery of knowledge state in K 1

知识状态	需掌握的核心技能
$∅$	$∅$
$b$	$∅$
${a, c, d}$	$t$
${a, b, d, e}$	$u$
${a, b, c, d}$	$t$
$Q 1$	${t, u}$

Fig.2 Learning path in K 1

Fig.3 Concept lattice L ( S 2 , Q 2 , I 2 )

Table 7 Skill mastery of knowledge state in K 2

知识状态	需掌握的核心技能
$∅$	$∅$
${1}$	${s 4}$
${2,3}$	${s 3}$
${4,5}$	${s 5}$
${1,2, 3}$	${s 3, s 4}$
${1,2, 4}$	${s 1}$
${1,4, 5}$	${s 4, s 5}$
${1,2, 3,4}$	${s 1, s 3}$
${1,2, 4,5}$	${s 1, s 5}$
${2,3, 4,5}$	${s 3, s 5}$
$Q 2$	${s 1, s 3, s 5}$

Table 7 Skill mastery of knowledge state in K 2

知识状态	需掌握的核心技能
$∅$	$∅$
${1}$	${s 4}$
${2,3}$	${s 3}$
${4,5}$	${s 5}$
${1,2, 3}$	${s 3, s 4}$
${1,2, 4}$	${s 1}$
${1,4, 5}$	${s 4, s 5}$
${1,2, 3,4}$	${s 1, s 3}$
${1,2, 4,5}$	${s 1, s 5}$
${2,3, 4,5}$	${s 3, s 5}$
$Q 2$	${s 1, s 3, s 5}$

Fig.4 Learning path in K 2

Table 8 Skill mastery of knowledge state in L 1

知识状态	必掌握技能
$∅$	$∅$
${c}$	${t}$
${e}$	${u}$
${b, e}$	${s, u, v}$
${a, c, d, e}$	${t, u}$
$Q 1$	$S 1$

Table 8 Skill mastery of knowledge state in L 1

知识状态	必掌握技能
$∅$	$∅$
${c}$	${t}$
${e}$	${u}$
${b, e}$	${s, u, v}$
${a, c, d, e}$	${t, u}$
$Q 1$	$S 1$

Fig.5 Learning path in L 1

References 23

[1]	DOIGNON J P, FALMAGNE J C. Spaces for the assessment of knowledge[J]. International Journal of Man-Machine Studies, 1985, 23(2): 175-196. DOI URL
[2]	周弦, 谢深泉. 基于知识空间理论的自适应测试过程[J]. 计算机应用, 2007, 27(S1): 68-69.
	ZHOU X, XIE S Q. Adaptive testing process based on knowledge space theory[J]. Journal of Computer Applications, 2007, 27(S1): 68-69.
[3]	刘艳花. 基于知识空间的自适应测试方法研究及实现[D]. 长沙: 湖南大学, 2010.
	LIU Y H. Research and implementation of adaptive testing method based on knowledge space theory[D]. Changsha: Hunan University, 2010.
[4]	郭维威, 刘锋. 基于扩展知识空间的计算机自适应测试方法的研究与实施[J]. 计算机产品与流通, 2017(8): 6.
	GUO W W, LIU F. Computer adaptive test method based on extended knowledge space in the research and implementation[J]. Computer Products and Circulation, 2017(8): 6.
[5]	DOBLE C, MATAYOSHI J, COSYN E, et al. A data-based simulation study of reliability for an adaptive assessment based on knowledge space theory[J]. International Journal of Artificial Intelligence in Education, 2019, 29(2): 258-282. DOI URL
[6]	HOCKEMEYER C, HELD T, ALBERT D. RATH—a relat-ional adaptive tutoring hypertext WWW-environment based on knowledge space theory[C]// Proceedings of the 4th Internat- ional Conference on Computer Aided Learning in Science and Engineering, Sweden, Jun 15-17, 1998. New York: ACM, 1998: 417-423.
[7]	COSYN E, DOBLE C, FALMAGNE J C, et al. Assessing mathematical knowledge in a learning space[M]// FALMAGNE J C, ALBERT D, DOBLE C, eds. Knowledge Spaces, Applicat-ions in Education. Berlin, Heidelberg: Springer, 2013.
[8]	张治, 刘小龙, 余明华, 等. 研究型课程自适应学习系统: 理念、策略与实践[J]. 中国电化教育, 2018(4): 119-130.
	ZHANG Z, LIU X L, YU M H, et al. Adaptive learning system of research curriculum: concept, strategy and practice[J]. China’s Audio-Visual Education, 2018(4): 119-130.
[9]	WILLE R. Restructuring lattice theory:an approach based on hierarchies of concepts[C]// LNCS 5548: Proceedings of the 7th International Conference on Formal Concept Analysis, Darmstadt, May 21-24, 2009. Berlin, Heidelberg: Springer, 2009: 314-339.
[10]	ZUPA B, BOHANCE M, DEMSAR J. Learning by discovering concept hierarchies[J]. Artificial Intelligence, 1999, 109(1/2): 211-242. DOI URL
[11]	DEKEL U. Revealing Java class structure with concept lattices[C]// Proceedings of the 10th Working Conference on Reverse Engineering, Victoria, Nov 13-16, 2003. Piscataway: IEEE, 2003: 353.
[12]	VALTCHEV P, MISSAOUI R, GODIN R, et al. Generating frequent itemsets incrementally: two novel approaches based on Galois lattice theory[J]. Journal of Experimental and Theoretical Artificial Intelligence, 2002, 14(2/3): 115-142. DOI URL
[13]	RUSCH A, WILLE R. Knowledge spaces and formal concept analysis[C]// Proceedings of the 19th Annual Conference of the Gesellschaft für Klassifikation e.V. University of Basel, Mar 8-10, 1995. Berlin, Heidelberg: Springer, 1996: 427-436.
[14]	SPOTO A, STEFANUTTI L, VIDOTTO G. Knowledge space theory, formal concept analysis, and computerized psychological assessment[J]. Behavior Research Methods, 2010, 42(1): 342-350. DOI URL
[15]	李进金, 孙文. 知识空间、形式背景和知识基[J]. 西北大学学报(自然科学版), 2019, 49(4): 517-526.
	LI J J, SUN W. Knowledge space, formal context and knowledge base[J]. Journal of Northwest University (Natural Science Edition), 2019, 49(4): 517-526.
[16]	FALMAGNE J C, DOIGNON J P. Learning spaces: inter-disciplinary applied mathematics[M]. Berlin, Heidelberg: Springer, 2011.
[17]	SPOTO A, STEFANUTTI L, VIDOTTO G. An iterative procedure for extracting skill maps from data[J]. Behavior Research Methods, 2016, 48(2): 729-741. DOI URL
[18]	李金海, 闫梦宇, 徐伟华, 等. 概念认知学习的若干问题与思考[J]. 西北大学学报(自然科学版), 2020, 50(4): 501-515.
	LI J H, YAN M Y, XU W H, et al. Some problems and thoughts on concept-cognitive learning[J]. Journal of Northwest University (Natural Science Edition), 2020, 50(4): 501-515.
[19]	DOIGNON J P. Knowledge spaces and skill assignments[M]// FISCHER G H, LAMING D. Contributions to Mathematical Psychology, Psychometrics, and Methodology. Berlin, Heidelberg: Springer, 1994.
[20]	高纯, 王睿智. 知识空间理论析取模型下最小技能集的生成[J]. 计算机科学与探索, 2010, 4(12): 1109-1114.
	GAO C, WANG R Z. The formation of minimal skill set in disjunctive model of knowledge space theory[J]. Journal of Frontiers of Computer Science and Technology, 2010, 4(12): 1109-1114.
[21]	XU F F, MIAO D Q, YAO Y Y, et al. Analyzing skill sets with or-relation tables in knowledge spaces[C]// Proceedings of the 8th IEEE International Conference on Cognitive Informatics, Hong Kong, China, Jun 15-17, 2009. Washington: IEEE Computer Society, 2009: 174-180.
[22]	李金海, 米允龙, 刘文奇. 概念的渐进式认知理论与方法[J]. 计算机学报, 2019, 42(10): 2233-2250.
	LI J H, MI Y L, LIU W Q. Incremental cognition of concepts: theories and methods[J]. Chinese Journal of Computers, 2019, 42(10): 2233-2250.
[23]	张涛, 任宏雷. 形式背景的属性拓扑表示[J]. 小型微型计算机系统, 2014, 35(3): 590-593.
	ZHANG T, REN H L. Attribute topology of formal context[J]. Journal of Chinese Computer Systems, 2014, 35(3): 590-593.