In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.

We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.

one for each variable. These transition functions map an input of the Boolean variables in X to a Boolean value (0 or 1). We call a Boolean vector x(t) = (x1(t), . . . , xn(t)) the state of the network at time t. Then, the next state of the network x(t+ 1) is calculated by applying all transition functions fi(x(t)). In a biological context, genes can be modeled as Boolean variables (active/expr...

We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the ca...

A Boolean algebra carries a strictly positive exhaustive submeasure if and only if it has a sequential topology that is uniformly Fréchet.

Boolean logic appears to be unable to draw conclusions in the presence of inconsistent and/or incomplete information. Fortunately, what seems to be impossible to solve applying binary logic can be achieved using nonbinary logic. In this work we use the theory of many-value logic to facilitate the deductive process of knowledge assessment. Key–Words: Web-based assessment, learning, intelligent t...

An interval algebra is a Boolean which isomorphic to the of finite unions half-open intervals, linearly ordered set. hereditary if every subalgebra an algebra. We answer question M. Bekkali and S. Todorcevic, by showing that it consistent σ-centered size $$\mathfrak{b}$$ hereditary. also show there is, in ZFC, cardinality ℵ1.

The Facebook discussion with Stephen King about Stone spaces led to a highly interesting development of ideas concerning Boolean, algebras, Stone spaces, and p-adic physics. I have discussed these ideas already earlier but the improved understanding of the notion of Stone space helped to make the ideas more concrete. The basic ideas are briefly summarized. p-adic integers/numbers correspond to ...

Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction technique...

There would seem to be a significant degree of interest in the Yi Jing from computer literate people. The number of web sites devoted to the changes is substantial (see the web site listed as [ICh98] in Section 7 for a comprehensive selection of crossreferences) and there are a wide range of Yi Jing consultation programs available, as freeware, shareware and commercial software. There is also a...