Eigenlogic in the spirit of George Boole

This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of boolean functions in the original form introduced by George Boole. It is then shown that this algebraic polynomial formulation can be naturally extended to operators in finite vector spaces. Logical operators will appear as commuting projectors and the truth values, which take the binary values {0, 1}, are the respective eigenvalues. In this view the solution of a logical proposition resulting from the operation on a combination of arguments will appear as a selection where the outcome can only be one of the eigenvalues. In this way propositional logic can be formalised in linear algebra by using elective developments which correspond here to combinations of tensored elemantary projectors.