In the Peirce universe “the role that human institutions play in establishing grounding and associated frames of reference and standards” (Hans Polzer) is articulated by reference to “communities of inquiry” and “communities of interpretation”. Invoking communities as extended agents of inquiry and interpretation equips us with a better handle on “contexts of interpretation” and the structures involved in this array of constructs are found to be of triadic sign relations all compact.
Over the years I have found the hardest thing to convey about sign relations has been what it’s like to think and work within an extended sign relational environment. A “setting” like that consists of a large number of individual sign-relational triples called “elementary sign relations”, each having the form where is the object, is the sign, and is the interpretant sign of the triple.
This means that any given sign relation is a subset of a cartesian product where is the object domain, is the sign domain, and is the interpretant sign domain of the sign relation in view.
Taking this point of view on sign relations makes a big difference in the conjoined theories of inquiry and interpretation that develop from this point on.