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- Half of lattice, semilattice.
- Structure of implication in [set
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If the set is as shown in the upper left diagram, drawing a line through the inclusion relation such as “A encompasses B” will result in the upper right diagram. (Christmas) tree.
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In reality, however, there are relationships where “one does not encompass the other, but neither is it unrelated,” as in B and C in the figure below left.
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If we draw this in a diagram with inclusions, we get the lower right figure. In this figure, B and C meet at E.
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This is not a tree. Such a structure is called semilachis.
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That is, [Inclusion” and “irrelevance” are not two choices.
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