Relations

Definition (Reference Books)

Classification (Immanuel Kant)
Classification (Richard E. Mayer)
Classification (J. Brian McLoughlin)
Classification (Gerald Runkle)
Classification (Wesley C. Salmon)
Classification (Mickey A. Palmer)

Definition

Reference Books

The Shorter Oxford English Dictionary (Third Edition, First Edition 1983)
“That feature or attribute of things which is involved in considering them in comparison or contrast with each other; the particular way in which one thing is thought of in connection with another; any connection, correspondence, or association, which can be conceived as naturally existing between things.”

Classification

[1990, First Published 1781] Immanuel Kant, The Critique of Pure Reason
“All relations of thought in judgements are those
(a) of the predicate to the subject;
(b) of the principle to its consequence;
(c) of the divided cognition and all the members of the division to each other.”
(Book 1, Section II, Of the Logical Function of the Understanding in Judgements)
The Categories of Relation
- Of inherence and subsistence (substantia et accidens)
- Of causality and dependence (cause and effect)
- Of community (reciprocity between the agent and patient)
(Book 1, Section III, Of the Pure Conceptions of the Understanding, or Categories)

[1992, Second edition] Richard E. Mayer, Thinking, Problem Solving, Cognition
- Relation of degree (A is less/more than B - e.g. from hunger to starvation)
- Relation of causation (cause-effect - A leads to B)
- Relation part-to-whole (A is part of B - e.g. leaf to branch)
- Relation of coordination (A and B belong to the same category - e.g. teacher, lawyer, etc.)
- Relation of superordination (A belongs to category B - e.g. breakfast, lunch, dinner under: ‘meals’) (from Chapter 11, p. 326)

[1973, First Edition 1969] J. Brian McLoughlin, Urban and Regional Planning
“Three levels of relationship between two (or more) sets of observations may be distinguished :
- deterministic causality in which whenever A occurs B also occurs, i.e. A causes B;
- probabilistic causality in which whenever A occurs there is a probability p that B will also occurs, i.e. A has probability p of causing B;
- correlation in which A occurs in association with B (which association can be measured statistically) but there is no observable cause-and-effect relationship between them.” (Chapter 8, pp. 169-170)

[1981, Second edition] Gerald Runkle, Good Thinking
A) Symmetry
- Symmetrical. “A relation is said to be symmetrical when it goes both ways.” (examples : ... is identical to...; ... is married to...; ...is parallel with...; ...is the obverse of...)
- Asymmetrical. “If the relation is such as to forbid the reversal it is said to be asymmetrical.” (examples : ... parent of ... ; ... hotter than ... ; ... is to the left of ...).
- Nonsymmetrical. “A relation which is neither symmetrical nor asymmetrical is nonsymmetrical”. (examples : ... loves ... ; ... brother of ... ; ... votes for ... ; ... understands ...).
B) Reflexivity.
- Reflexive. “A relation is reflexive if and only if things must bear that relation to themselves.”
(examples : ... identical to ... ; ... equal ... ; ... not less than ...)
- Irreflexive. “If however the relation is such that things can never bear that relationship to themselves, the relation is irreflexive.” (examples : ... less than ... ; ... is ancestor of ... ; ... taller than ...)
- Nonreflexive. “Those relations which are neither reflexive nor irreflexive are non-reflexive.”
(examples : ... loves ... ; ... shoots ...; ... gives haircut to ...)
C) Transitivity.
- Transitive. (example : ... descendant of ...)
- Intransitive. (example : ... mother of ...)
- Non-transitive. (example : ... cousin of ...)

Note: “Relations can be assigned qualities in terms of symmetry, reflexivity, and transitivity. Sometimes the assignment is analytic: it follows simply from the meaning of the relation. Sometimes the assignment is synthetic: it is based on actual fact.” (from pp. 171-174)

[1973, Second Edition] Wesley C. Salmon, Logic
- Symmetrical. Whenever the relation holds between two objects A and B it also holds between B and A ” [e.g. Tom is the sibling of Harry].
- Asymmetrical. e.g. Tom is the father of Lucy.
- Nonsymmetric. e.g. a loves b .
- Reflexive. A relation is said to be reflexive if objects always bear that relation to themselves.” (e.g. any number is equal to itself).
- Irreflexive. A relation which an object never bears to itself is irreflexive.
(e.g. greater than...).
- Nonreflexive. Loves is a nonreflexive relation, since some people love
themselves and others do not.
- Transitive. e.g. if Tom is older than Sam and Sam is older than Marc then Tom is older than Marc.
- Intransitive. e.g. if x is father of y and y is father of z then x cannot be father of z.
- Nontransitive. e.g. if x is friend of y and y is friend of z then x may or may not be friend of z.
Note. Transitivity is used to define two extremely important types of relations :
- Ordering relations such as greater then, earlier than;
- Equivalence relations, i.e. relations that are transitive, symmetrical and reflexive
(Ordering relations and equivalence relations can be fruitfully combined to provide a basis for quantitative measurement).
(from Chapter II, pp. 70-74)

[1981] Mickey A. Palmer, The Architect's Guide to Facility Programming
Listing of relational dimensions :

- linkage
- connection
- attraction
- mutual influence
- selection
- preferential relation
- interdependence
- exchange
- communication
- dysfunction
- disassociation
- adjacency
- proximity
- social/physical distance
- movement
- direction
- grouping
- cluster
- pattern
- arrangement
- organization
- hierarchy

(from Chapter 4, p. 125)

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