predicates {relations} | R Documentation |
Predicate functions for testing for binary relations and endorelations, and special kinds thereof.
relation_is_antisymmetric(x) relation_is_asymmetric(x) relation_is_bijective(x) relation_is_binary(x) relation_is_complete(x) relation_is_coreflexive(x) relation_is_endorelation(x) relation_is_equivalence(x) relation_is_functional(x) relation_is_injective(x) relation_is_irreflexive(x) relation_is_left_total(x) relation_is_linear_order(x) relation_is_partial_order(x) relation_is_reflexive(x) relation_is_right_total(x) relation_is_strict_linear_order(x) relation_is_strict_partial_order(x) relation_is_surjective(x) relation_is_symmetric(x) relation_is_tournament(x) relation_is_transitive(x) relation_is_weak_order(x) relation_is_preference(x) relation_is_preorder(x) relation_is_quasiorder(x)
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an object inheriting from class relation . |
A binary relation is a relation with arity 2. An endorelation R on a set X is a relation with domain D(R) = (X, X), i.e., a binary relation on X.
Let us write x R y iff (x, y) is contained in R.
A binary relation R is called
An endorelation R is called
Some combinations of these basic properties have special names because of their widespread use:
If R is a weak order (“weak preference relation”), I = I(R) defined by x I y iff x R y and y R x is an equivalence, the indifference relation corresponding to R.
There seem to be no commonly agreed definitions for order relations: e.g., Fishburn (1972) requires these to be irreflexive.
P. C. Fishburn (1972), Mathematics of decision theory. Methods and Models in the Social Sciences 3. Mouton: The Hague.
H. R. Varian (2002), Intermediate Microeconomics: A Modern Approach. 6th Edition. W. W. Norton & Company.