Abstract
First, we briefly introduce some of the fundamental notions of knowledge space theory and how they relate to formal concept analysis. Knowledge space theory has a probabilistic extension which allows it to be utilized in order to assess knowledge states by looking at responses to a variety of test items, which are designed to demand performing different sets of cognitive operations. Second, we introduce an easy extension to lambda calculus in order to incorporate extra-logical operations. Further we define a weight function on term reductions, which is to be used as a model to calculate item response probabilities for test items after task analysis. We use the new model in order to review the probabilistic extension of knowledge space theory.
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References
Berardi, S.: Towards a mathematical analysis of the coquand-huet calculus of constructions and the other systems in barendregt’s cube. Tech. rep., Dept. of Computer Science, Carnegie-Mellon University and Dipartimento Matematico, Universita di Torino (1988)
Doignon, J.P., Falmagne, J.C.: Spaces for the assessment of knowledge. International Journal of Man-Machine Studies 23(2), 175–196 (1985)
Falmagne, J., Doble, C., Albert, D., Eppstein, D., Hu, X.: Knowledge Spaces: Applications in Education. Springer-Verlag New York Incorporated (2013)
Falmagne, J.C., Doignon, J.P.: Learning Spaces. Springer (2010)
Glaser, R.: The integration of instruction and testing. In: Freeman, E. (ed.) The Redesign of Testing in the 21st Century: Proceedings of the 1985 ETS Invitational Conference, pp. 45–58. Educational Testing Service, Princeton (1985)
Hindley, J.R.: Basic simple type theory. Cambridge University Press (1997)
Kamareddine, F., Laan, T., Nederpelt, R.: A Modern Perspective on Type Theory: From its Origins until Today. Applied logic series. Kluwer Academic Publishers (2006)
Korossy, K.: Modeling Knowledge as Competence and Performance. In: Albert, D., Lukas, J. (eds.) Knowledge Spaces: Theories, Empirical Research, and Applications, Mahwah, NJ, pp. 103–132 (1999)
Tatsuoka, K.K.: Item Construction and Psychometric Models Appropriate for Constructed Responses. In: Bennett, R., Ward, W. (eds.) Construction Versus Choice in Cognitive Measurement: Issues in Constructed Response, Performance Testing, and Portfolio Assessment, ch. 6, pp. 107–133. Routledge, New York (2009)
Terlouw, J.: Een nadere bewijstheoretische analyse von gstt’s. Tech. rep., Department of Computer Science, University of Nijmegen (1989)
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Albrecht, I., Körndle, H. (2014). On Knowledge Spaces and Item Testing. In: Glodeanu, C.V., Kaytoue, M., Sacarea, C. (eds) Formal Concept Analysis. ICFCA 2014. Lecture Notes in Computer Science(), vol 8478. Springer, Cham. https://doi.org/10.1007/978-3-319-07248-7_11
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DOI: https://doi.org/10.1007/978-3-319-07248-7_11
Publisher Name: Springer, Cham
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