Boolean algebra (aka propositional calculus, propositional logic) is as simple a transformation system as you can find. To make it useful, the system needs to be extended to include equality and quantification and functions and relations. Each of these can be handled separately, with quantification and equality being fundamental.
Much of the work on Predicate Logic is yet to be added to this page. Coming attraction: a Predicate Logic engine for database queries and deduction based entirely on boundary math (spatial) concepts.