Lecture note on Boolean algebra to understand logical model of geologic structure (Part 1): Minterm Canonical form of Boolean expression

Logical Aggregation Based on Interpolative Realization of Boolean Algebra

In this paper, aggregation is treated as a logical and/or pseudo-logical operation what is important from many points of view such as adequacy and interpretations.

Approaches to realize Canonical Form of Boolean Expression by using Reversible COG Gates

Nowadays, reversible logic is one of the most important issue which has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology and optical computing. Reversible logic circuits give less power dissipation as well as distinct output that is assigned for each distinct input. The classical set of gates such as the NAND, AND, NOR, OR, XOR and X...

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

The Hodge Structure on a Filtered Boolean Algebra

Let (Bn) be the order complex of the Boolean algebra and let B(n, k) be the part of (Bn) where all chains have a gap at most k between each set. We give an action of the symmetric group Sl on the l-chains that gives B(n, k) a Hodge structure and decomposes the homology under the action of the Eulerian idempontents. The Sn action on the chains induces an action on the Hodge pieces and we derive ...

Omega-almost Boolean rings

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.