For the last decade, set pattern discovery from binary relations has been studied in depth. Today, many complete and efficient algorithms for frequent closed set mining are available. More recently, their extensions towards n-ary relation mining have been considered. In this paper, we consider the recent proposal for closed n-set pattern discovery and we discuss their relevancy. Indeed, starting with experiments on two real-life multidimensional data sets, we discuss the quality of the extracted local patterns thanks to an inside and outside perspective on the discovered closed n-sets. This original analysis enables to support the declarative specification of a priori relevant patterns thanks to the conjunction of primitive constraints (minimal size, minimal area, delta-isolated and fault-tolerance constraints) they have to satisfy. Interestingly, some of these primitive constraints can be exploited within available solvers.