Constraint-based Modeling and Ambiguity

Constraint-based modeling has been used in many application areas of Intelligent Tutoring Systems as a powerful means to analyse erroneous student solutions and generate helpful feedback. In contrast to domains where the structure of the problem under consideration allows a constraint to (almost) uniquely determine the possible cause of a particular student error there are other applications, where a multitude of competing error explanations has to be considered. In such cases constraint-based models alone hardly meet the requirements for a student model. Instead a constraint-based model clearly serves the purpose of error diagnosis and needs to be complemented by additional components for diagnosis selection based on general or individually tailored heuristics. By investigating the apparent and strong parallelism between constraint-based modeling and model-based diagnosis, this paper identifies four major sources of ambiguity that need to be considered when using constraint-based modeling and describes options for dealing with situations in which alternative error descriptions are available. Examples are primarily drawn from the area of foreign language learning.