A COMPUTATIONAL APPROACH TO BOOLE,GEORGE DISCOVERY OF MATHEMATICAL LOGIC

This paper reports a computational model of Boole's discovery of Logic as a part of Mathematics. George Boole (1815-1864) found that the sym bols of Logic behaved as algebraic symbols, and he then rebuilt the wh ole contemporary theory of Logic by the use of methods such as the sol ution of algebraic equations. Study of the different historical factor s that influenced this achievement has served as background for our tw o main contributions: a computational representation of Boole's Logic before it was mathematized; and a production system, BOOLE2, that redi scovers Logic as a science that behaves exactly as a branch of Mathema tics, and that thus validates to some extent the historical explanatio n. The system's discovery methods are found to be general enough to ha ndle three other cases: two versions of a Geometry due to a contempora ry of Boole, and a small subset of the Differential Calculus. (C) 1997 Published by Elsevier Science B.V.