Using congruence relations to extract knowledge from concept lattices

It is well-known inside the Formal Concept Analysis (FCA) community that a concept lattice could have an exponential size with respect to the input data. Hence, the size of concept lattices is a critical issue in large real-life data sets. In this paper, we propose to investigate congruence relations as a tool to get meaningful parts of the whole lattice or its implication basis. This paper presents two main theoretical contributions, namely two context (or lattice) decompositions based on congruence relations and new results about implication computation after decomposition.