Antisymmetric relation

Set Theory for Concept Modeling

Published in Richard M. Golden, Statistical Machine Learning, 2020

For example, if S ≡ {1, 2, 3}, then R ≡ {(1, 2), (2, 3), (1, 1)} is an antisymmetric relation but the relation R ≡ {(1, 2), (2, 1), (2, 3), (1, 1)} is not an antisymmetric relation on {1, 2, 3}.

A note on the complexity of S4.2

View Article

Journal Information

Published in Journal of Applied Non-Classical Logics, 2021

Aggeliki Chalki, Costas D. Koutras, Yorgos Zikos

Recalling that a relational frame is a set equipped with a binary relation, we proceed to review a few useful properties of binary relations. A binary relation is reflexive iff ; it is irreflexive iff . It is a transitive relation iff . It is an antisymmetric relation iff ; it is a symmetric relation iff . It is weakly directed iff and directed iff .

Antisymmetric relation

Explore chapters and articles related to this topic

Set Theory for Concept Modeling

A note on the complexity of S4.2