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From SMW-Sandbox

A binary relation R over a set X is symmetric if it holds for all A and B in X that if A is related to B then B is related to A.

In mathematical notation, this is:

<math>\forall A, B \in X,\ A R B \Rightarrow \; B R A</math>

In SMW we have to distinguish between semantic symmetry and actual symmetry, i.e., symmetry in the sense that whenever A R B is annotated, also B R A is annotated. The latter implies also that page B exists, hence, that we do not annotate a relation to a non-existing page..

See also:

• http://en.wikipedia.org/wiki/Symmetric_relation
• Owl:SymmetricProperty