Essentially the logic of collapsed systems.

For example,

One might ask 'If there is one move this system
  can make, what is it?'

Or, what is the result of 'formal elapse', that is, moving from the
beginning of the implication of the system, to the end of the
implication of the system?: What is the net result from the
beginning to the end of the implication of the system?

Part of this may be:

What is the 'original' implication?

And, finally:

What is the minimum ultimate implication?

Depending on what formal tools are adopted, close logic can have
multiple type of interpretations. Most typically the formal results
are such as the following:

1. No implication. Relevance of 0.
2. Formal implication. Relevance of some type.
3. Systematic relevance. Translation or implication of some type.
4. Archteypal significance. Change of critical tools.

That's about all I can muster about close logic for now.

Basically, it deals with formal tools that are either purely
theoretical or even hypothetical. However, it has the effect of
fielding certain types of theoretical questions.