[FOM] Question about Congruence

A. Mani a_mani_sc_gs at yahoo.co.in
Tue Jan 29 18:35:53 EST 2008

On Tuesday 29 Jan 2008 10:14:01 pm hdeutsch at ilstu.edu wrote:
> Let me clarify the point of my posting "A Question About Congruence."
> I was asking two questions in my earlier posting.  First, is the
> simple fact about closer under equivalence well-known?  Secondly, does
> anyone have anything to say about the philosophical import of the
> principle?
In the general sense * says that B is closed under R iff A \cap B is a 
definite (or crisp) set in the rough set terminology. I used a related notion 
in a recent paper, but that was about relative approximations. What you have 
defined is not a frequently used notion in rough set theory in this 

If B is a subset of A, then "B is closed under R" is exactly the same thing 
as "B is a definite/crisp set in the approximation space <A, R>" in classical 
rough set theory. So it is well-known.

The "Temporal parts" that you mention in your earlier posting are dealt with 
in rough mereological approaches too... especially  in coherence with 
Leibnitz's theory of indiscernibles. (I need to see a copy of your paper 
before commenting further). 


A. Mani
A. Mani
Member, Cal. Math. Soc

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