  Despite the popularity of Formal Concept Analysis (FCA) as a mathematical
framework for data analysis, some of its extensions are still considered
arcane. Polyadic Concept Analysis (PCA) is one of the most promising yet
understudied of these extensions. This formalism offers many interesting open
questions but is hindered in its dissemination by complex notations and a lack
of agreed-upon basic definitions. In this paper, we discuss in a mostly
informal way the fundamental differences between FCA and PCA in the relation
between contexts, conceptual structures, and rules. We identify open questions,
present partial results on the maximal size of concept n-lattices and suggest
new research directions.
