Valerie J. Harvey, RT(R ), PhD, C&IS,
Strict Partial Orders in Discrete Mathematics for IS/ISM
Manna and Waldinger distinguish between strict (transitive, irreflexive) partial order and partial order which is transitive and reflexive. They prefer asymmetric instead of antisymmetric for strict partoal order, stating that asymmetry implies irreflexivity - Zohar Manna and Richard Waldinger, The Logical Basis for Computer Programming, Vol. 1: Deductive Reasoning (Addison Wesley, 1985), pp. 201-203.
Many IS/ISM partial order application examples are irreflexive.
A link on strict partial order:
Acknowledgements: Thanks to the following persons who contributed dialog on strict partial order: Joe Mott, Emeritus Professor, Mathematics, Florida State University, Tallahassee, FL; Ada C. Dong, Mathematics and Computer Science, Lawrence Technological University, Southfield, MI; Mary-Angela Papalaskari, Computing Sciences, Villanova University Villanova, PA; Judith Gersting, Chair, Computer Science Department, University of Hawaii at Hilo, Hilo, HI.