Relation Theory

Two further classes of incidence properties will prove to be of great utility.

Regional Incidence Properties

The definition of a local flag can be broadened from a point to a subset of a relational domain, arriving at the definition of a regional flag in the following way.

Let be a -place relation

Choose a relational domain and a subset

Then is a subset of called the flag of with at or the -flag of a mathematical object with the following definition.

Numerical Incidence Properties

A numerical incidence property of a relation is a local incidence property predicated on the cardinalities of its local flags.

For example, is said to be -regular at if and only if the cardinality of the local flag is for all in — to write it in symbols, if and only if for all

In a similar fashion, one may define the numerical incidence properties, -regular at -regular at and so on.  For ease of reference, a few definitions are recorded below.

Resources

• Sign Relations
• Triadic Relations
• Survey of Relation Theory
• Peirce’s 1870 Logic Of Relatives

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