Dealing with sign relations containing many types of signs — icons, indices, symbols, and more complex varieties — calls for a flexible and powerful organizational framework, one with the ability to grow and develop over time.  This is one of those applications where I found it useful to consider a “relative membership” relation, adding a parameter for the interpreter to the ordinary set-theoretic membership.

I laid out the details of a formalization in the following paragraphs:

• Inquiry Driven Systems • Part 1
• Objective Plans and Levels
• Formalization of OF : Objective Levels
• Application of OF : Generic Level
• Application of OF : Motive Level

It begins as follows:

In accounting for the special characters of icons and indices that arose in previous discussions, it was necessary to open the domain of objects coming under formal consideration to include unspecified numbers of properties and instances of whatever objects were initially set down.  This is a general phenomenon, affecting every motion toward explanation whether pursued by analytic or synthetic means.  What it calls for in practice is a way of organizing growing domains of objects, without having to specify in advance all the objects there are.