boolean algebra is an axiomatic system like euclidian geometry.
the writing up of a system into axioms (or postulates), theorems and rules of inference is much like describing a machine in blue print form.
methods of proof within such axiomatic systems are either algorithmic (exhaustive and precise) or heuristic (short cuts and uncertain)
algorithms will never produce machine intelligence.
programmed heuristics on the other hand can make the computer provide results that are at once efficient and intelligent.
again intelligence is proving to be more than just syntactic or semantic.