:::I'm not arguing for the inclusion of anything about paraconsistent logical systems, I am arguing against that.  If I'm not mistaken, paraconsistent logics are a species of non-Boolean logic and your contention  if I am understanding it  that the article lead should possess a generality that does not preclude non-Boolean logics amounts to a position that paraconsistent logics  amongst other non-Boolean logics  should bear on the composition of the lead.  If you write a thorughly generic lead it will retain the vagueness and lack of clarity that was originally complained about.  The special relevance of propositional calculus and first-order predicate logic is that they are the most likely context in which a novice will encounter the operator and will seek clarification from an encyclopedia.  I believe I know what you mean but I don't agree with the completely generic form of the lead that you support.  Such an article will be a useless piece of formalism.  Anyone that is even aware that there are logical systems that are non-Boolean will have no need to consult a general encyclopedia regarding the material conditional.  Those that are likely to consult an encyclopedia  those encountering the material conditional in the conext of Boolean first-order logic  will not gain anything from a generic article that takes account of non-Boolean logics in all of its descriptions.  Technically what you are arguing is correct but from a pragmatic and pedagocial position it is misguided.