I thought that “symmetric” and “inverse” constraints only made sense for the main snak of a statement, but @Sjoerddebruin pointed out the symmetric qualifier property “together with” (P​1706), e. g. on “award received” statements: if person A received award X together with person B, then person B should also have received award X together with person A.

• Do we need to support this? Are there any more properties like this?
• Are there any inverse qualifier properties, too?
• Are there any such properties for references, or just qualifiers?
• What are the precise semantics? Should we also require that the other statement with the symmetric qualifier has the same other qualifiers (e. g. point in time)?