Logical Structures in Computation Seminar

Piecewise Boolean Algebra

Boolean algebra governs the logical calculus of observations. But in many applications it doesn't make sense to consider all pairs of observations to be compatible. Rather, the fundamental structures originally studied by Boole are piecewise Boolean algebras. I will survey a domain-theoretic description. Inspiration will be taken from quantum theory, where much about a quantum system is captured by the collection of its classical subsystems.