Changes

When a relation happens to be a function, it may be excusable to use the same name for it in both applications, writing out explicit type markers like <math>P : X \times Y,</math>&nbsp;&nbsp; <math>P : X \to Y,</math>&nbsp;&nbsp; <math>P : X \leftarrow Y,</math> as the case may be, when and if it serves to clarify matters.

When a relation happens to be a function, it may be excusable to use the same name for it in both applications, writing out explicit type markers like <math>P : X \times Y,</math>&nbsp;&nbsp; <math>P : X \to Y,</math>&nbsp;&nbsp; <math>P : X \leftarrow Y,</math> as the case may be, when and if it serves to clarify matters.

From this current, perhaps transient, perspective, it appears that our next task is to examine how the known properties of relations are modified when an aspect of functionality is spied in the mix.

From this current, perhaps transient, perspective, it appears that our next task is to examine how the known properties of relations are modified when an aspect of functionality is spied in the mix. Let us then return to our various ways of looking at relational composition, and see what changes and what stays the same when the relations in question happen to be functions of various different kinds at some of their domains. Here is one generic picture of relational composition, cast in a style that hews pretty close to the line of potentials inherent in Peirce's syntax of this period.

 

Let us then return to our various ways of looking at relational composition, and see what changes and what stays the same when the relations in question happen to be functions of various different kinds at some of their domains.

 

Here is one generic picture of relational composition, cast in a style that hews pretty close to the line of potentials inherent in Peirce's syntax of this period.

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"

|}

|}

From this we extract the "hypergraph picture" of relational composition:

From this we extract the ''hypergraph picture'' of relational composition:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"

|}

|}

All of the relevant information of these Figures can be compressed into the form of a "spreadsheet", or constraint satisfaction table:

All of the relevant information of these Figures can be compressed into the form of a spreadsheet, or constraint satisfaction table:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"