I'd prefer you to tell us what's the aim of all this.
I do not exclude the possibility there's a much simpler approach to it.
It's all about building software to solve logical problems. So in logic implication (p > q) is equal to (~p v q) and disjunction is equal to conjunction (p v q) = ~(~p & ~q). Even more difficult is equivalence: (p <-> q) = (p > q) & (q > p)
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