A relation "
"
is called a preorder (or quasiorder) on a set 
if it satisfies:
1. Reflexivity: 
for all 
.
2. Transitivity: 
and 
implies 
.
A preorder that also has antisymmetry is a partial order.
Preorder
See also
Partial Order, Total OrderThis entry contributed by Michael Clarkson
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References
Harel, D.; Kozen, D.; and Tiuryn, J. Dynamic Logic. Cambridge, MA: MIT Press, p. 6, 2000.Referenced on Wolfram|Alpha
PreorderCite this as:
Clarkson, Michael. "Preorder." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Preorder.html