Abstract
This paper reports a computational model of Boole's discovery of Logic
as a part of Mathematics. George Boole (1815-1864) found that the
symbols of Logic behaved as algebraic symbols, and he then rebuilt the
whole contemporary theory of Logic by the use of methods such as the
solution of algebraic equations. Study of the different historical
factors that influenced this achievement has served as background for
our two main contributions: a computational representation of Boole's
Logic before it was mathematized; and a production system, BOOLE2,
that rediscovers Logic as a science that behaves exactly as a branch
of Mathematics, and that thus validates to some extent the historical
explanation. The system's discovery methods are found to be general
enough to handle three other cases: two versions of a Geometry due to
a contemporary of Boole, and a small subset of the Differential
Calculus.
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