Extending Domain Theories: Two Case Studies in Student Modeling

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.