The properties of binary relations such as reflexivity, symmetry, transitivity are ubiquitous. What about ternary relations, which properties can we consider fundamental? For motivation here is the one that looks like generalized transitivity:
R(e,a,b) & R(d,e,c) & R(f,b,c) -> R(d,a,f)
This is a well known algebraic law disguised in relational notation (which one?-).