Extending Domain Theories: Two Case Studies in Student Modeling |
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Authors: | D. Sleeman Haym Hirsh Ian Ellery In-Yung Kim |
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Affiliation: | (1) Computing Science Department, King's College, The University of Aberdeen, AB9 2UB Aberdeen, Scotland, UK;(2) Knowledge Systems Laboratory, Computer Science Department, Stanford University, 94304 Palo Alto, CA;(3) Present address: Computer Science Department, Rutgers University, Hill Center, Busch Campus, 08903 New Brunswick, NJ;(4) Computing Science Department, King's College, The University of Aberdeen, AB9 2UB Aberdeen, Scotland, UK;(5) Central Engineering Laboratories, FMC AI Center, 1205 Coleman Avenue, 95052 Santa Clara, CA |
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Abstract: | By its very nature, artificial intelligence is concerned with investigating topics that are ill-defined and ill-understood. This paper describes two approaches to expanding a good but incomplete theory of a domain. The first uses the domain theory as far as possible and fills in specific gaps in the reasoning process, generalizing the suggested missing steps and adding them to the domain theory. The second takes existing operators of the domain theory and applies perturbations to form new plausible operators for the theory. The specific domain to which these techniques have been applied is high-school algebra problems. The domain theory is represented as operators corresponding to algebraic manipulations, and the problem of expanding the domain theory becomes one of discovering new algebraic operators. The general framework used is one of generate and test—generating new operators for the domain and using tests to filter out unreasonable ones. The paper compares two algorithms, INFER* and MALGEN, examining their performance on actual data collected in two Scottish schools and concluding with a critical discussion of the two methods. |
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Keywords: | Incomplete domain theories generate and test failure-driven learning explanation-based learning student modeling intelligent tutoring systems |
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