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.

one of the models that can be used to study the relationship between boolean random sets and explanatory variables is growth regression model which is defined by generalization of boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. this model can be used in the study of behavior of boolean random sets when their coverage regions variation...

To model noncompatible events, a quantum logic was chosen among various algebraic structures as the suitable one. This paper deals with a characterization of a center in various types of quantum logics by means of special bivariable functions defined on them. Any quantum logic can be described as a union of blocks (a block in a given quantum logic L is the maximal Boolean subalgebra of L) [16]....

Moisil logic, having as algebraic counterpart Lukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of Lukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative a...

Let L be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of L contained in the center of L and endomorphisms j of L satisfying the Borceux-Van den Bossche conditions.

A method to extract the cubes of the Generalized Reed-Muller form (GRM) of a Boolean function with a given polarity is presented. The method does not require exponential space and time complexity and it achieves the lower bound time complexity. The proof of the method’s correctness constitutes the first half of this paper. Also, a separate heuristic algorithm to find the optimal polarity that r...