Research on Boolean Algebra to Switching Theory

The Extension of an Arbitrary Boolean Algebra to an Implicative Boolean Algebra

Ternary Boolean Algebra

Boolean Algebra Approximations

Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof u...

Free Boolean Algebra

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

Lattices and Boolean Algebra from Boole to Huntington to Shannon and Lattice Theory

The study of computer design and architecture includes many topics on formal languages and discrete structures. Among these are state minimizations, Boolean algebra, and switching algebra. In minimization, three approaches are normally used that are based on equivalence relations. Partial order relations are used today in constructions of Boolean algebra. In this paper we survey this important ...