Towards Collaborative Conceptual Exploration

Abstract

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.

Interactive Collaborative Exploration using Incomplete Contexts

“…Recently Hanika and Zumbrägel suggested an approach for collaborative exploration based on experts for attribute sets [7]. They employ the notion of a consortium of experts and discuss its ability, i.e., how much of the domain can be explored given certain experts for attribute sets, and the value of being able to combine examples.…”

“…We generalize the information order to work on different object sets to be able to compare and combine the knowledge of experts. We then adapt the idea of a consortium [7] to a group of experts, formulate a notion of collaboration, give a few examples and proceed to discuss methods to compare different collaboration strategies.…”

“…The expert, a key component of every attribute exploration, is often only described as an entity that correctly answers the posed questions, especially in many of the earlier works on the subject. Later works, e.g, [4,7], make an effort to also model the expert in a formal way, usually as a mapping from the set of attribute implications into the target domain represented as closure system over M . In the following we suggest a model for experts in an incomplete knowledge setting where we encode the knowledge of an expert by both an incomplete context of examples and a set of valid implications.…”

Triadic Exploration and Exploration with Multiple Experts

“…However, most of the extensions and variants of attribute exploration that have been studied are based on the idea of a single expert answering the questions. As far as we know, there exist only a few papers that mention exploration with multiple experts, notably: Paper [16] deals with how to perform exploration in parallel and potentially offers a way to speed up the exploration with multiple experts; [10] addresses collaborative conceptual exploration based on the notions of local experts for subdomains of a given knowledge domain; and [2] studies attribute exploration in a collaborative exploration setting with multiple experts who share the same view on the domain but only have partial knowledge thereof.…”

“…If we take a closer look at the publications mentioned before, we see that all three avoid this issue in their own way. In [16] the experts all have the same complete knowledge about the domain; in [10] the local experts have partial knowledge about the same consistent domain knowledge; and, in [2] the problem was also avoided by defining expert knowledge as partial knowledge of some consistent domain knowledge.…”