The Horn theory of Boole's partial algebras (Q2837764)

The paper under review concerns one of the two components of Boole's algebra of logic, namely his algebra of classes. Boole claimed that, with one exception, the laws of his algebra of classes agreed with the laws of the common algebra of numbers -- the one exception was the idempotent law for variables. The paper augments \textit{T. Hailperin}'s efforts (cf. his book [Boole's logic and probability. A critical exposition from the standpoint of contemporary algebra, logic and probability theory. Amsterdam etc.: North-Holland Publishing Company (1976; Zbl 0352.02002); second edition (1986; Zbl 0611.03001)]) to place Boole's algebra of logic on a solid footing. The authors use Horn sentences to give a modern formulation of the principle that Boole adopted in 1854 as \textit{the} foundation for his algebra of logic -- this principle is called in the present paper \textit{The Rule of 0 and 1}.