Henry --
At 09:02 AM 2/7/2005 +0100, you wrote:
I am looking for a way to state
that a relation is an equivalence relation.
Here is a way of doing that using rules:
- some-item is used in the equivalence relation
- ------------------------------------------------
- that-item is related by equivalence to that-item
- some-item1 is related by equivalence to some-item2
- --------------------------------------------------
- that-item2 is related by equivalence to that-item1
- some-item1 is related by equivalence to some-item2
- that-item2 is related by equivalence to some-item3
- ------------------------------------------------
- that-item1 is related by equivalence to that-item3
- this-item1 is related by equivalence to this-item2
- ==================================================
-
A
B
-
B
C
- some-item1 is related by equivalence to some-item2
- --------------------------------------------------
- that-item1 is used in the equivalence relation
- some-item1 is related by equivalence to some-item2
- --------------------------------------------------
- that-item2 is used in the equivalence relation
The first three rules state that the relation is reflexive,
symmetric, and transitive, respectively.
Next is a table saying that [A B] and [B C] are in the relation.
You can run these rules by pointing a browser to
www.reengineeringllc.com
and selecting the example called EquivalenceRelation1 .
(Non commercial use of the system is free.)
HTH, -- Adrian
INTERNET BUSINESS LOGIC (R)
www.reengineeringllc.com
Adrian Walker
Reengineering LLC
PO Box 1412
Bristol
CT 06011-1412 USA
Phone: USA 860 583 9677
Cell: USA 860 830 2085
Fax: USA 860 314 1029