An n-ary relation on the sets
is a set of ordered tuples
∀0≤i≤n-1 S=Si, then we write
We say that the relation holds for an n-tuple
A relation on pairs is called a binary relation.
Sometimes binary relations are written
aRb for the relation
A binary relation that has no infite path,
aRbRcR..., is called well-founded.
The following are examples of binary relations:
R is a binary relation on the set
Ris called reflexive if
Ris called transitive if
Ris called symmetric if
Ris called antisymmetric if
Deransart, Pierre, Maluszynski, Jan. A Grammatical View of Logic Programming. MIT Press, 1993.
Doets, Kees. From Logic to Logic Programming. MIT Press, 1994.
Copyright © 2014 Barry Watson. All rights reserved.