Correction of the dot-matrix conditions
I think these conditions match the dot-matrix test better than the ones I proposed earlier. They are more complicated, but closer to the matrices and not too unnatural:
A property F is natural to the extent that the following conditions are satisfied, where (1), (3) and (5) weigh heavier than (2), (4) and (6).
1) The Fs resemble each other intrinsically.
2) The Fs resemble each other extrinsically.
3) Anything that exactly resembles an F intrinsically is itself F.
4) Anything that exactly resembles an F extrinsically is itself F.
5) There are few intrinsic F-gaps.
6) There are few extrinsic F-gaps.
Something y is an intrinsic (extrinsic) F-gap if it isn't F and there are Fs x and z such that y intrinsically (extrinsically) resembles both of them more closely than x intrinsically (extrinsically) resembles z.
RL satisfies all conditions except (3), whereas R only properly satisfies (1).