Intelligent Tutoring Systems have made great strides in recent years. Many of these gains have been achieved for welldefined problems. However, solving ill-defined problems is important because it can enhance the cognitive, metacognitive and argumentation skills of a student. In this paper, we demonstrate how to apply the constraint-based modelling approach to describe the solution space of ill-defined problems in logic programming. This technology has been integrated into a web-based ITS (INCOM) and has been evaluated with student solutions from past examinations. Keywords ill-defined problems, error diagnosis, logic programming, constraint-based modelling, ITS.