On some connections between Boolean algebras and Heyting algebras
Trillas ([1]) has defined a relational probability on an intuitionistic algebra and has given its basic properties. The main results of this paper are two. The first one says that a relational probability on a intuitionistic algebra defines a congruence such that the quotient is a Boolean algebra. The second one shows that relational probabilities are, in most cases, extensions of conditional probabilities on Boolean algebras.
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.
We show that all finite Brouwerian semilattices have strong endomorphism kernel property (SEKP), give a new proof that all finite relative Stone algebras have SEKP and also fully characterize dual generalized Boolean algebras which possess SEKP.