Relation

Naseer Ahmed Chandio · #1 Wednesday, July 05, 2006

Hi dears,

Relation

In logic, a relation R is defined as a set of ordered pairs, triples, quadruples, and so on.

A set of ordered pairs is called a two-place (or dyadic) relation; a set of ordered triples is a three-place (or triadic) relation; and so on. In general, a relation is any set of ordered n-tuples of objects. Important properties of relations include symmetry, transitivity, and reflexivity. Consider a two-place (or dyadic) relation R. R can be said to be symmetrical if, whenever R holds between x and y, it also holds between y and x (symbolically, (∀x) (∀y) [Rxy ⊃ Ryx]); an example of a symmetrical relation is "x is parallel to y." R is transitive if, whenever it holds between one object and a second and also between that second object and a third, it holds between the first and the third (symbolically, (∀x) (∀y) (∀z ) [(Rxy ∧ Ryz) ⊃ Rxz]); an example is "x is greater than y." R is reflexive if it always holds between any object and itself (symbolically, (∀x) Rxx); an example is "x is at least as tall as y" since x is always also "at least as tall" as itself.

Expressions used:

Einstein's mass energy relation
Equivalence relation
International relations
National Labor Relations Board
Public relations
Labor Management Relations Act
National Labor Relations Act
Industrial and organizational relations
Organizational relations

1: the act of telling or recounting : ACCOUNT
2 : an aspect or quality (as resemblance) that connects two or more things or parts as being or belonging or working together or as being of the same kind <the relation of time and space> specifically : a property (as one expressed by is equal to, is less than, or is the brother of) that holds between an ordered pair of objects
3 : the referring by a legal fiction of an act to a prior date as the time of its taking effect ― usually used with back

4 a (1) : a person connected by consanguinity or affinity : RELATIVE (2) : a person legally entitled to a share of the property of an intestate b : relationship by consanguinity or affinity : KINSHIP

5 : REFERENCE, RESPECT <in relation to>

6 : the attitude or stance which two or more persons or groups assume toward one another <race relations>

Relation

"The relations in which concepts in a state of mind can stand to one another are those of identity and difference, of agreement and opposition, of the inner and the outer, and finally of the determinable and the determination (matter and form)....Before constructing any objective judgment we compare the concepts to find in them identity (of many representations under one concept) with a view to universal judgments, difference with a view to particular judgments, agreement with a view to affirmative judgments, opposition with a view to negative judgments, etc." There seems to be an interesting way in which the manner that intuitions are applied to concepts depends on the relations in which the intuition and concepts stand to each other, as well as on the relations which intuitions stand to intuitions and concepts to concepts; here, however, Kant is concerned with emphasizing that an amphiboly takes place if we try to determine the relations holding between things in themselves.

(1) A statement with one or more arguments implying a constraint among cooccurring values of these arguments. E.g., a mathematical function such as the logarithm, an ordering such as "is greater than" or "causes", a statement of association such as "is married to", a correspondence, a code. Equivalently (2), a subset of elements of a cartesian product set (Wiener). When that subset contains observed or permissible cooccurrences, its complement in the same product set is called a constraint and contains conceivable cooccurrances that did not occur or are excluded. Relations are of different ordinality. Unary relations or properties are of order one. binary relations are of order two, etc. Relations may be combined to form new relations, e.g., the simple ternary relation of "off-spring" which relates a father, a mother and a child can be used recursively (see recursion ) to generate a whole family tree. More than one relation may be defined in the same Cartesian product set as the relations "talked to", "is married to", "exchanged goods with" all of which are subsets of the product of two sets of people. (Krippendorff )

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