  Modern order and lattice theory provides convenient mathematical tools for
pattern mining, in particular for condensed irredundant representations of
pattern spaces and their efficient generation. Formal Concept Analysis (FCA)
offers a generic framework , called pattern structures, to formalize many types
of patterns, such as itemsets, intervals, graph and sequence sets. Moreover,
FCA provides generic algorithms to generate irredundantly all closed patterns,
the only condition being that the pattern space is a meet-semilattice. This
does not always hold, e.g., for sequential and graph patterns. Here, we discuss
pattern setups consisting of descriptions making just a partial order. Such a
framework can be too broad, causing several problems, so we propose a new
model, dubbed pattern multistructure, lying between pattern setups and pattern
structures, which relies on multilattices. Finally, we consider some techniques
, namely completions, transforming pattern setups to pattern structures using
sets/antichains of patterns.
