Audiences and level 

I left a comment to this effect on Talk:Boolean algebra (structure), but maybe here is a more appropriate place: I think a lot of this argument is over the wrong thing. Whether we're looking at these things as rings or lattices or fragments of formal logic or whatever is the wrong question. The right question is: who is the audience? And the answer is: there is more than one of them. At least as the current US college system is set up, many beginning computer science students need an article like Boolean algebra (logic) or Boolean logic, and would be baffled and lost by the mathematical formalism in Boolean algebra (structure). On the other hand, mathematicians from the advanced undergraduate level upwards would find those articles simplistic and useless, and need instead something like Boolean algebra (structure) or Boolean algebras canonically defined. We don't have to hide the fact that they're all really the same thing, but I think trying to make the freshman computer scientists learn ring theory in order to look up de Morgan's laws, or trying to make the math majors wade through lots of truth tables, would be a bad idea in either case.  And I think that trying to please both audiences in a single article would lead to a mess that's even worse than the current mess in Boolean logic. So, please do consider some merges — we have too many articles — but please don't take your one unified theory and insist that it's the only way the subject can be presented. —