|Imaginary and Reentrant Forms
Shoup, Kauffman and Varela have done the most significant work on imaginary forms, I have elected not to focus there. I did use imaginary logic in a contradiction maintenance system (it is not yet on the site) that does deduction in the presence of logical contradictions. In Numerics, the James calculus uses a new numerical imaginary.
Here are some miscellaneous pieces that use imaginaries. Quantum Logic plays with mathematical models of a polarized light paradox, and Dr. Fischell is quoted at the end of Imaginary Booleans: "The soul is the real root of the mind, and the imaginary root of the body."