Finitary Relation

References

(Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Finitary_relation Retrieved:2019-9-25.
- In mathematics, a finitary relation is a property that assigns truth values to finite tuples of elements. Typically, the property describes a possible connection between the components of a -tuple. For a given set of -tuples, a truth value is assigned to each -tuple according to whether the property does or does not hold. When $k = 2$ , one has the most common version, a binary relation.

(OEIS, 2019) ⇒ https://oeis.org/wiki/Relation Retrieved:2019-9-25.
- QUOTE: A finitary relation is defined by one of the formal definitions given below.
  - The basic idea is to generalize the concept of a two-place relation, such as the relation of equality denoted by the sign “[math]\displaystyle{ = }[/math]” in a statement like [math]\displaystyle{ 5+7=12 }[/math] or the relation of order denoted by the sign “[math]\displaystyle{ \lt }[/math]” in a statement like [math]\displaystyle{ 5\lt 12 }[/math]. Relations that involve two places or roles are called binary relations by some and dyadic relations by others, the latter being historically prior but also useful when necessary to avoid confusion with binary (base 2) numerals.
  - The concept of a two-place relation is generalized by considering relations with increasing but still finite numbers of places or roles. These are called finite-place or finitary relations. A finitary relation involving [math]\displaystyle{ k }[/math] places is variously called a [math]\displaystyle{ \kappa }[/math]-ary, [math]\displaystyle{ \kappa }[/math]-adic, or [math]\displaystyle{ \kappa }[/math]-dimensional relation. The number [math]\displaystyle{ \kappa }[/math] is then called the arity, the adicity, or the dimension of the relation, respectively.

(Freund & Lehmann, 1994) ⇒ Freund, Michael, and Daniel Lehmann (1994). "Nonmonotonic reasoning: from finitary relations to infinitary inference operations". Studia Logica, 53(2), 161-201.