2.1 More about Relations

A binary relation seen as a directed graph on n points is completely determined by its degree and its list of edges. This information is represented in the form of a successors list which, for each single point i in {1, ..., n} contains the set i^R of succesors of i. Here each single set of successors is represented as a subset of {1, ..., n} by boolean list (see chapter "Boolean Lists").

A relation R of degree n is represented by a record with the following category components.

isRelation:

is always set to true.

domain:

is always set to Relations.

Moreover a relation record has the identification component

successors:

containing a list which has as its ith entry the boolean list representing the successors of i.

A relation record rel can aquire the following knowledge components.

isReflexive:

set to true if rel represents a reflexive relation (see IsReflexive)

isSymmetric:

set to true if rel represents a symmetric relation (see IsSymmetric)

isTransitive:

set to true if rel represents a transitive relation (see IsTransitiveRel) isPreOrder:
set to true if rel represents a preorder (see IsPreOrder)

isPartialOrder:

set to true if rel represents a partial order (see IsPartialOrder)

isEquivalence:

set to true if rel represents an equivalence relation (see IsEquivalence)

  
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