Suppose I have a set containing 'normal items' and other sets, of which the items would indicate a possibility in the encompassing set. For example, I have (AC, AS, AH, AD), eg the aces of all four suites. In a case I am not so certain what I have, I may end up with: (AC, AS, (AH, AD), (4H, 5H)), which would mean I have one card that's either AH or AD, and another that is either 4H or 5H.
Now take the set: ((AH, AD), (AH, AD, AC, AS), (AH, AD, AC, AS)). By logical deduction, one can say all the possible 'result sets' are still the same when it is simplified to: ((AH, AD), (AC, AS), (AH, AD, AC, AS)). Here it was simplified from 10 'choices' to 8 'choices'.This however is a very simplistic set, with only four cards and none unrelated cards in the choices. (e.g. a 4H being a possibility somewhere.) The goal is that it becomes easier to find out things about the total set of cards. In the example above: 'Do I have a red ace?'
The problem: finding the constraints and rules at which sets can be simplified. Simplifying meaning that, while readjusting one or more sets of choices, the possible result-sets remain the same while the total amount of choices goes down. I have dozens of things written out on paper, but those are rather hard to copy here. :)