Boole’s logic revisited from computer algebra Original Research Article

The article deals with computer algebra emulation and generalization of the main ideas that were the basis of Boole’s logic, as they were produced by him, and not as they were frequently misinterpreted in the history of Logic. The article begins with a historical account of the genesis of Boole’s logic. Next, Boole’s ideas on inference are examined and the following items are checked. First, Boole’s use of MacLaurin series expansions in the translation of logical formulae into polynomials can be justified and extended using a computer algebra system (CAS). Second, his method of inference in ‘hypotheticals’ can be related directly with a polynomial ideal membership. Third, the final results of his method of inference in ‘categoricals’ (based on MacLaurin series expansions) can also be emulated using a CAS. Implementations of the three items are provided. The study of the consistency of a many-valued logic based expert system is outlined as an application of the ideal membership mentioned above to a current problem in computer science.