Boole’s object in inventing an “algebra of logic” [12, 13] was to reduce the processes of reasoning to those of calculation. He showed that a system of logical equations, unlike a system of ordinary equations, can be reduced to a single equivalent equation (we consider the reduction-process in Chapter 4). He chose the standard reduced form f = 0, where f is a Boolean function. Reasoning is carried out in Boole’s formulation by solving that equation for certain of its arguments in terms of others.
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