Metric Boolean Algebras and an Application to Propositional Logic (Global Journal of Science Frontier Research, 2011)
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.
Keywords: Boolean algebra; probability measure; size; similarity degree; approximate reasoning; propositional logic