Sign Relations, Triadic Relations, Relations • 7

Re: Ontolog ForumJS

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 L is a subset of a cartesian product X \times Y of two sets, X and Y.  In symbols, L \subseteq X \times Y.  Of course X and Y 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 k-place relation L \subseteq X_1 \times \ldots \times X_k includes the cartesian product X_1 \times \ldots \times X_k as an essential part of its specification.  This serves to harmonize the definition of a k-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

This entry was posted in C.S. Peirce, Inquiry Driven Systems, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations and tagged , , , , , , , , , , , , , . Bookmark the permalink.

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