Enhancement and Use of a Mathematical Ontology in a Tutorial Dialog System

Despite empirical evidence that natural language dialog capabilities are necessary for the success of tutorial sessions, only few state-of-the-art tutoring systems use natural-language style interaction. Since domain knowledge, tutoring and pedagogical knowledge, and dialog management are tightly intertwined, the modeling and integration of proper natural language dialog capabilities in a tutoring system turns out to be barely manageable. In the DIALOG project, we aim at a mathematical tutoring dialog system that employs an elaborate natural language dialog component. To tutor naive set theory, we use a formally encoded mathematical theory including definitions and theorems along with their proofs. In this paper we present how we enhance this ontology by making relations explicit and we show how these relations can be used by the socratic tutoring strategy, which we employ, in planning the next system utterance. The decisive characteristic of the socratic strategy is the use of hints in order to achieve self-explanation.