boolean decisions

[Robin Becker]

I have a couple of business decisions to make that essentially use 6 binary 
input variables. After the business users have gone back and forth for two weeks 
trying to build special case rules I asked them to make up a table containing 
all of the input possibilities and specify what should happen in each case. 
There are only 64 rows and some of the decisions are obviously explainable in 
simple ways ie

if a and not b do action 1

is there a way to derive simplified rules for each binary outcome? I'm sure this 
is a standard sort of problem and probably some python code is out there. It 
seems to me I need to solve an overdetermined binary equation system and then 
choose the solution with the shortest number of terms or something, but perhaps 
I am daft.
-- 
Robin Becker