Intensional Concept Graphs as Patterns over Power Context Families

Intension graphs are introduced as an intensional variant of Wille’s concept graphs. Windowed intension graphs are then introduced as formalizations of conjunctive queries. Realizations describe pattern matching over power context families, which have been introduced with concept graphs as representations of relational data using a sequence of formal contexts. Using windowed intension graphs as patterns within pattern structures, we can define concept lattices, where power context families take the role of formal contexts. Relational Context Families, used in Relational Concept Analysis (RCA), correspond to power context families using sorts and only binary relations, and the lattices generated by the RCA algorithm (using wide scaling) can be represented using rooted trees as intents, which are introduced as a subclass of windowed intension graphs. Consequently, projections of the previously introduced pattern structure can be used as an alternative to the RCA algorithm.