Noneism is a theory in logic and metaphysics first coined by Richard Routley and appropriated again in 2005 by Graham Priest. It holds that some things do not exist. That is, we can quantify over non-existent things using the particular quantifier (also known —misleadingly in the view of noneists— as the existential quantifier). They also hold that "there is" is like "exist", rather than like the particular quantifier. Thus, they deny that there are things that do not exist. On this theory, there are no empty names, wherefore the "problem of empty names" that afflicts many theories about names (in particular, Millianism), is not a problem at all. 
While Priest also espouses dialetheism, he maintains that his dialethiesm is mostly capable of being separated out from his noneism. The connection is that impossible objects may exist in impossible worlds, much as nonexistent objects may exist in possible (but not actual) worlds.
Routley's book, Exploring Meinong's Jungle and Beyond: An Investigation of Noneism and the Theory of Items, was published in 1980, while Priest's 2005 book is entitled Towards Nonbeing: The Logic and Metaphysics of Intentionality.
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