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In the Hand of the Beholder: Comparing Interactive Proof Visualizations

Christian Alrabbaa; Stefan Borgwardt; Nina Knieriemen; Alisa Kovtunova; Anna Milena Rothermel; Frederik Wiehr
In: Martin Homola; Vladislav Ryzhikov; Renate A. Schmidt (Hrsg.). Proceedings of the 34th International Workshop on Description Logics (DL 2021) part of Bratislava Knowledge September (BAKS 2021), Bratislava, Slovakia, September 19th to 22nd, 2021. International Workshop on Description Logics (DL-2021), CEUR Workshop Proceedings, Vol. 2954,, 2021.


Although logical inferences are interpretable, actually explaining them to a user is still a challenging task. While sometimes it may be enough to point out the axioms from the ontology that lead to the consequence of interest, more complex inferences require proofs with intermediate steps that the user can follow. Our main hypothesis is that different users need different representations of proofs for optimal understanding. To this end, we undertook some user experiments related to logical proofs. We explored how a user’s cognitive abilities influence the performance in and preference for certain proof representations. In particular, we compared tree-shaped representations with linear, textbased ones, and for each we offered an interactive and a static version. After each proof, participants had to solve some tasks measuring their level of understanding and rated each proof according to the perceived comprehensibility. At the end of the questionnaire, subjects ranked the proofs by comprehensibility. We found no differences between the general performance or the subjective ratings of the proof representations. However, in the final ranking participants preferred the conditions with tree-shaped proofs over the textual ones, with significant differences in the rankings of the higher cognitive ability group and across both groups but not in the low cognitive ability group.

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