Proofs as Discourse: An Empirical Study

Jon Oberlander, Richard Cox, and Keith Stenning

Computer-based logic proofs are a form of 'unnatural' language discourse, but the structure and process of proof can be observed in considerable detail, and analysis is leading to a number of general insights. We have been studying how students respond to multimodal logic teaching. First, psychological measures indicate that students’ pre-existing cognitive styles have a sigaificant impact on teaching outcome. Secondly, a large corpus of proofs has been gathered via automatic logging of proof development. Frequency analysis and cluster analysis of this corpus indicate that students’ cognitive styles influence the structure of their logical discourse. Our current objective is to apply further statistical methods to the proof development logs, to derive various transition frequencies, and then construct process models which explain the differences in discourse style.

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