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You may want to check with some professors who specialize in a branch of mathematics called "Functional Analysis". They are probably going to use a bunch of lingo like set theory and spaces unless you talk to them in person or by phone. Their whole field is about this kind of stuff.
As for programming, I don't know that this is possible without just running through and testing each combination of operators on the data. If it can not only be simple but can include multi-level compounding, yikes!
Simple:
y = (a&b) ! (c^d) ^ (e|f)
A lot more difficult:
z = (a&b) ! ((c^d) ^ (e|f))
If you want to go it alone, I would put a lot of constraints on it (Only 2 pairs deep) and see how it scales when you take them off. First try the simple examples on paper and develop an algorithm. If you can do that, start making them more complex and see what changes need to be made. If you find a pattern, great.
PS I don't know what the symbol for NOR is so i used !.
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