Metric Boolean Algebras and an Application to Propositional Logic
Let B be a Boolean algebra and Ω be the set of all homomorphisms from B into D, and μ be a probability measure on Ω . We introduce the concepts of sizes of elements of B and similarity degrees of pairs of elements of B by means of μ , and then define a metric on B . As an application, we propose a kind of approximate reasoning theory for propositional logic.