query about 'ka'

[ucleaar <ucleaar@UCL.AC.UK>]

I find myself rather confused about 'ka'. If we look at duhu or nu,
we find that the following pair mean the same:
  le nu/duhu mi nelci do
  le nu/duhu do se nelci me
i.e. the event of me liking you/you being liked by me, or the
proposition that I like you or that you are liked by me.
But it seems to me that "the property of me liking you" and
"the property of you being liked by me" don't make sense,
and instead I would want to express these different meanings:
   the property of liking you (the property of being the liker of you)
   the property of being liked by me
But to express these, it seems that 'ka' would have to mark
a sumti rather than a bridi, as in:
   le ka nelci do
   le ka se nelci mi
or
   le ka le nelci do kei
   le ka le se nelci mi kei

That is, to me it seems that whereas nu/duhu express aspects of
a bridi, ka expresses an aspect of a sumti.

Could someone please explain...

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And