Re: Ontolog Forum • Joseph Simpson

JS:

A binary relation is a set of ordered pairs of the elements of some other set.

That is the first definition I learned for binary relations.

Slightly more generally, a binary relation is a subset of a cartesian product of two sets, and   In symbols,   Of course and could be the same, but that’s not always the case.

I have long used the adjectives, 2-place, binary, and dyadic pretty much interchangeably in application to relations but I developed a bias toward dyadic on account of computational contexts where binary is reserved for binary numerals.

Once again, partly due to computational exigencies, I would now regard this first definition as the weak typing version.

The strong typing definition of a -place relation includes the cartesian product as an essential part of its specification.  This serves to harmonize the definition of a -place relation with the use of mathematical category theory in computer science.

When I get more time, I’ll go through the material I linked on relation theory in a slightly more leisurely manner …

Resources

• Sign Relations
• Triadic Relations
• Relation Theory

cc: Ontolog Forum • Structural Modeling • Systems Science