1 Abstract The network reliability analysis problem consists of evaluating a measure of the reliability of a network. A more general context than the network reliability analysis is the stochastic coherent binary system (SCBS) analysis. One approach used in determining the reliability of a system involves Boolean algebra, and in particular a sum of disjoint products (SDP) technique. This paper ...

We give a formulation of the Nielsen-Schreier theorem (subgroups free groups are free) in homotopy type theory using presentation as pointed connected 1-truncated types. show special case finite index subgroups holds constructively and full follows from axiom choice. an example boolean infinity topos where our does not hold stronger "untruncated" version is provably false theory.

The variety of interpretations exhibited by sentences with reciprocals is a longstanding challenge for semantic and pragmatic theories. This puzzle is related to some hard questions about the interpretation of plural predicates in general. In this paper we study the implications of relations between reciprocity and plurality for the account of reciprocals in Dalrymple et al. (1994). It will be ...

For suitable groups G we will show that one can add a Boolean algebra B by forcing in such a way that Aut(B) is almost isomorphic to G . In particular, we will give a positive answer to the following question due to J. Roitman: Is אω a possible number of automorphisms of a rich Boolean algebra? In [Ro], J. Roitman asked, is אω a possible number of automorphisms of a rich Boolean algebra? A Bool...

I argue that research on organizational configurations has been limited by a mismatch between theory and methods. While configurational theory stresses nonlinearity, synergistic effects, and equifinality, empirical research has largely drawn on methods that assume linearity, additive effects, and unifinality. I introduce set-theoretic methods as a viable alternative for overcoming this mismatch...

Starting from quasi-Wajsberg algebras (which are generalizations of Wajsberg algebras), whose regular sets are Wajsberg algebras, we introduce a theory of quasi-algebras versus, in parallel, a theory of regular algebras. We introduce the quasi-RM, quasi-RML, quasi-BCI, (commutative, positive implicative, quasi-implicative, with product) quasi-BCK, quasi-Hilbert and quasi-Boolean algebras as gen...

The following problem of algebraic logic is investigated: to determine those Boolean algebras which admit the structure of a nondiscrete cylindric algebra. A partial solution is found, and is then used to give an algebraic characterization of the Lindenbaum algebras of formulas of several broad classes of countable theories.

We use information theory to study recovering sets RL and strongly cancellative sets CL on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in the papers of Simonyi, Frankl, and Füredi. We mainly focus on the lattices Bn and D k l . Specifically, we find upper bounds and constructions for the sets RBn , CBn , and CDk l .

Vectorial Boolean functions play an important role in cryptography, sequences and coding theory. Both affine equivalence EA-equivalence are well known relations between vectorial functions. In this paper, we give exact formula for the number of classes, asymptotic classes