I doubt if there's anything like the best of all possible formal languages for boolean expressions, but there are many ways of coming up with calculi that are more efficient than most of the ones currently in common use.

You might enjoy exploring the possibilities of using [minimal negation operators][1] as the fundamental primitives of a propositional calculus.


  [1]: http://ncatlab.org/nlab/show/minimal+negation+operator


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temporary work area for testing latex and unicode —
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code = `![⦗x﹐y﹐z⦘](http://latex.mathoverflow.net/png?%u2997x%uFE50y%uFE50z%u2998)`

result →

![⦗x﹐y﹐z⦘](http://latex.mathoverflow.net/png?%u2997x%uFE50y%uFE50z%u2998)

this displays okay in the latex sidebar, but doesn't show up here ???

code = `![⦗ x ﹐ y ﹐ z ⦘](http://latex.mathoverflow.net/png?%26%23x2997%3B%20x%20%26%23xFE50%3B%20y%20%26%23xFE50%3B%20z%20%26%23x2998%3B)`

result →

![⦗ x ﹐ y ﹐ z ⦘](http://latex.mathoverflow.net/png?%26%23x2997%3B%20x%20%26%23xFE50%3B%20y%20%26%23xFE50%3B%20z%20%26%23x2998%3B)