  We consider all 16 unary operations that, given a homogeneous binary relation
R, define a new one by a boolean combination of xRy and yRx. Operations can be
composed, and connected by pointwise-defined logical junctors. We consider the
usual properties of relations, and allow them to be lifted by prepending an
operation.
  We investigate extensional equality between lifted properties (e.g. a
relation is connex iff its complement is asymmetric), and give a table to
decide this equality. Supported by a counter-example generator and a resolution
theorem prover, we investigate all 3-atom implications between lifted
properties, and give a sound and complete axiom set for them (containing e.g.
"if R's complement is left Euclidean and R is right serial, then R's symmetric
kernel is left serial").
