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== The Schematic Completion and The Schematic Lattice ==
[[File:Schematic Lattice.png|thumb|The Schematic lattice formed from the schematic completion on the set <math>A=\{111, 011, 001\}</math>. Here the schematic lattice <math>(\mathcal{S}(A),\leq)</math> is shown as a [[Hasse diagram]]. ▼
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For a set <math>A \subseteq \Sigma^l</math>, we call the process of calculating the compression on each subset of A, that is <math>\{{\downarrow}X | X \subseteq A\}</math>, the schematic completion of <math>A</math>, denoted <math>\mathcal{S}(A)</math>.<ref name="Fletcher"/>
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The [[poset]] <math>(\mathcal{S}(A),\leq)</math> always forms a [[complete lattice]] called the schematic lattice.
▲[[File:Schematic Lattice.png|thumb|The Schematic lattice formed from the schematic completion on the set <math>A=\{111, 011, 001\}</math>. Here the schematic lattice <math>(\mathcal{S}(A),\leq)</math> is shown as a [[Hasse diagram]].
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The schematic lattice is similar to the concept lattice found in [[Formal concept analysis]].
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