Quasi-order is not defined uniformly
In the literature, some authors define “quasi order” as transitive and reflexive
, others define it as transitive and irreflexive
.
No such discrepancy seems to exist in using “preorder” for the former (transitive and reflexive) and “strict partial order
” for the latter (transitive and irreflexive).
It seems wise to use only the unambiguous terminology, and start any text where the term “quasi order” is felt with a proper warning.
Just for completeness: a partial order is transitive, reflexive and antisymmetric.