The Definition Problem

Given: an abstraction knowledge.
Problems:
  1. develop the facility to accept and store a definition for the abstraction.
  2. Given an instance, use the learned definition to determine if
     the given instance satisfy the definition of a specific
     abstraction.  In other words, answer the question: 
     "Is the given instance the specific abstraction?".
    
e.g.,
An abstraction knowledge: greatest common factor
Problems:
1. Develop an internal "definition" class to allow 
   its definition to be taught and stored.
2. Answer the question, given a reference collection of input and a target,
   is the target the greatest common factor of the reference collection?


Goal:
Develop theory and program to teach the definitions of all kinds of
knowledge, not just one specific piece of knowledge.