We study the problem of decomposing a Boolean function into a set of functions with fewer arguments. This problem has considerable practical importance in VLSI. For example, for digital circuits designed with eld-programmable gate arrays, it is necessary to express Boolean functions in terms of`smaller' functions that t the cells of the array. The decomposition problem is old, and well understo...

The Boolean prime ideal theorem is a very slightly weaker version of the axiom of choice. In 2011, Andreas Blass showed that models of set theory (with atoms) in which the Boolean prime ideal theorem holds but the full axiom of choice fails correspond with a certain type of topological group. The path taken to prove this surprising result draws not just from set theory but also from combinatori...

Negation, conjunction, and disjunction are major building blocks in the formation of concepts. This article presents a new model-based theory of these Boolean components. It predicts that individuals simplify the models of instances of concepts. Evidence corroborates the theory and challenges alternative accounts, such as those based on minimal descriptions, algebraic complexity, or structural ...

We consider how to develop types corresponding to propositions and questions. Starting with the conception of Propositions as Types, we consider two empirical challenges for this doctrine. The first relates to the putative need for a single type encompassing questions and propositions in order to deal with Boolean operations. The second relates to adjectival modification of question and proposi...

The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent com...

Being the crossroads between Algebra, Topology, Logic, Set Theory and the Theory of Order; the class of Boolean algebras over partially ordered sets were look at as one of the sources, providing over time, new insights in Boolean algebras. Some constructions and their interconnections will be discussed, motivating along the way a list of open problems. Mathematics Subject Classification (MSC 20...