Theory-Driven Historical Discovery: Boole’s Abstract Formalization of Logic

Luis de Ledesma, Aurora Perez, Daniel Borrajo, and Luis M. Laita

There is a trend in the field of Machine Discovery that has undertaken the task of approaching Scientific Discovery from a computational viewpoint. Such an approach is a very promising, and in some way fascinating, field of research in Artificial Intelligence. Its ultimate goal is to recognize and learn patterns of previous discovery, which can improve one’s chances for future discovery significantly (Oliver 1991). Most studies have dealt with empirical laws of physics and chemistry but, so far, almost no theory driven discovery has been contemplated. The present paper deals with a computational approach to the real history of the genesis of a mathematical discovery: an abstractalgebraic method called "the method of separation of symbols", and its role in the creation of George Boole’s logic. We have studied the different historical factors that influenced this creation. The real history of the discovery under consideration has suggested a computational model that provides the basis for a theory of this kind of discovery. The paper presents a sketch of the history of Boole’s discovery as well as the influence of Duncan F. Gregory on it, and describes the system BOOLE2. This program embodies Boole’s method of discovering, discovers Logic and Geometry as parts of Algebra, and is also ready to be used on a variety of sciences.

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