Editing Formal concept analysis (section)

== Arrow relations ==
Formal concept analysis has elaborate mathematical foundations,<ref name="GW" /> making the field versatile. As a basic example we mention the ''arrow relations'', which are simple and easy to compute, but very useful. They are defined as follows: For {{math|1=''g'' ∈ ''G''}} and {{math|1=''m'' ∈ ''M''}} let

: {{math|1=''g'' ↗ ''m'' ⇔ (''g, m'') ∉ ''I'' and if ''m''⊆''{{prime|n}}'' and ''{{prime|m}} ≠ {{prime|n}} '', then (''g, n'') ∈ ''I'',}}

and dually

: {{math|1=''g'' ↙ ''m'' ⇔ (''g, m'') ∉ ''I'' and if ''{{prime|g}}''⊆''{{prime|h}}'' and ''{{prime|g}} ≠ {{prime|h}} '', then (''h, m'') ∈ ''I''.}}

Since only non-incident object-attribute pairs can be related, these relations can conveniently be recorded in the table representing a formal context. Many lattice properties can be read off from the arrow relations, including distributivity and several of its generalizations. They also reveal structural information and can be used for determining, e.g., the congruence relations of the lattice.