Definition of Atheism

[Angrboda]

lacks belief + lacks knowledge + there is no god (agnostic atheist? weak atheist)
has belief + lacks knowledge + there is no god (strong atheist)
has belief + has knowledge + there is no god (gnostic atheist)

lacks belief + lacks knowledge + there is a god (apostatic theist)
has belief + lacks knowledge + there is a god (weak theist; faith based theism)
has belief + has knowledge + there is a god (strong theist; fundamentalist)

???

It suggests to me, because there are two variables, and a proposition that can be stated in the affirmative or the negative, there are a large range of possible positions. I don't think you can determine what the term atheism means by applying a sort of linguistic calculus, because words aquire meaning through convention, not logic. In the case of the word 'atheism', there are competing conventions. Because lexicographers have traditionally been theists, they've tended to frame the definition in ways that are understandable from the perspective of theism. This is somewhat proscriptive, however since atheist's proper are a minority language group, there's some sense to this. Then there's the sociological approach, that those to whom a term applies have the say in how it is defined; this has led to the "lack of belief" definition, possibly because it is the most inclusive. So you have two separate social conventions for the term, neither is necessarily more right than the other.