Compossibility is a philosophical concept from Leibniz. According to Leibniz a complete individual thing (for example a person) is characterized by all its properties, and these determine its relations with other individuals. The existence of one individual may contradict the existence of another. A possible world is made up of individuals that are compossible — that is, individuals that can exist together. Possible worlds exist as possibilities in the mind of God. One world among them is realized as the actual world, and this is the most perfect one.
According to the Stanford Encyclopedia of Philosophy article on Leibniz's Modal Metaphysics by Brandon C. Look, views on "compossibility" and the closely related best of all possible worlds argument are to be found in On the Ultimate Origination of Things, The Discourse in Metaphysics, On Freedom, and throughout his works. The term itself is found in Die philosophischen Schriften III when Leibniz writes to Bourguet.
Gilles Deleuze uses it in Cinema II taking support from Leibniz's explanation of the problem of future contingents. He then creates the notion of in-compossible, and drawing on Jorge Luis Borges explains that several mutually contradictory worlds do in fact exist.