I like your attitude about being careful when we try to develop a new logical system.
Therefore my basic attitude is to find ways to associate between opposite concepts in such a way that at least they do not contradict each other.
And after that we can check if they can associate and define more interesting results then the state of not being associated.
This is the main idea of Complementary Logic.
Because I am not familiar with the standard formal mathematical notations form one hand, and I did not find any existing model in pure Mathematics from the other hand, I had no choice but to write my ideas in the best way I can, which is not an easy task for professionals to understand it, and I am aware of it.
One of the things that I cared about was to use the simplest possible way to organize my ideas.
For example, I associated in a coherent way between concepts like redundancy, uncertainty and symmetry to construct a very simple model of symmetry break levels.
Then I have found that addition and multiplication are complement operations, and there is a beautiful and simple way to order them when using their complement associations on each other.
My non-formal paper with some examples can be found here
(Hyrkyl helped me to write the first 9 lines of it):
http://www.geocities.com/complementarytheory/ET.pdf
I am here in this forum to share my ideas with you, and learn from your experience, remarks and insights.
I think no man's work can really be done alone, and maybe one of the most beautiful and meaningful (and also powerful, therefore dangerous) languages, which is Math language, has to be developed by team work.