Towards Collaborative Conceptual Exploration
In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.
KeywordsFormal concept analysis Implications Attribute exploration Collaborative knowledge acquisition Collaborative interactive learning
The authors would like to thank Daniel Borchmann and Maximilian Marx for various inspiring discussions on the topic of consortia while starting this project. In particular, the former suggested the name consortium and always is the best critic one can imagine. Furthermore, we are grateful for various challenging discussions with Sergei Obiedkov, including ideas for coping with wrongly accepted implications.
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