Pattern mining consists in discovering interesting patterns in data. For that, algorithms rely on smart techniques for enumerating the pattern search space and, generally, focus on compressed collections of patterns (e.g. closed patterns), to avoid redundancy. Formal Concept Analysis offers a generic framework, called pattern structures, to formalize many types of patterns, such as closed itemsets, intervals, graph and sequence sets. Additionally, it provides generic algorithms to enumerate all

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... closed patterns and only them. The only condition is that the pattern space is a meet-semilattice, which, unfortunately does not always hold (e.g., for sequential and graph patterns). In this paper, we discuss pattern setups, a tool that models pattern search spaces relying only on posets. Subsequently, we revisit some techniques transforming pattern setups to a pattern structure using set of patterns, namely completions, and we state a necessary and sufficient condition for a pattern setup completion using antichains to be a pattern structure.