Towards Collaborative Conceptual Exploration

TL;DR

This paper introduces a mathematical framework for collaborative learning groups using formal concept analysis, enabling better understanding and management of distributed knowledge and interactive ontology development.

Contribution

It presents a novel formalization of collaborative groups with local experts and explores their query-answering capabilities and decidability in knowledge exploration.

Findings

Defined a consortium model based on closure systems and attribute exploration.

Analyzed the ability of experts to answer queries and handle false implications.

Provided initial results on the decidability of domain exploration by a consortium.

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.