Class IRREFLEXIVE-RELATION

• Defined in theory: Frame-ontology
• Source code: frame-ontology.lisp

Slots on this class:

Documentation:

Relation R is irreflexive if if R(a,a) never holds.

Instance-Of: Class

Subclass-Of: Binary-relation

Superclass-Of: Asymmetric-relation

Equivalence Axioms:

(<=> (Irreflexive-Relation ?R)
     (And (Binary-Relation ?R) (Forall (?X) (Not (Holds ?R ?X ?X)))))

Axioms:

(Forall (?X) (Not (Holds ?R ?X ?X)))

(Binary-Relation ?R)

Other Related Axioms:

(<=> (Asymmetric-Relation ?R)
     (And (Antisymmetric-Relation ?R) (Irreflexive-Relation ?R)))

(<=> (Irreflexive-Relation ?R)
     (And (Binary-Relation ?R) (Forall (?X) (Not (Holds ?R ?X ?X)))))

Notes:

• This is a change in definition. Used to mean (not reflexive).
• Formerly: antireflexive-relation