Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions.
Other logical systems have more than two truth-values instead of a binary of such values.
Some assume the system in question is classical propositional logic.
The universe of "possible worlds" depends upon the axioms and rules of the logical system in which one is working, but given some logical system, any logically consistent collection of statements is a possible world.
The relationship between modalities (if there is any) is the subject of debate and may depend upon how one views logic, as well as the relationship between logic and metaphysics, for example, many philosophers following Saul Kripke have held that discovered identities such as "Hesperus = Phosphorus" are metaphysically necessary because they pick out the same object in all possible worlds where the terms have a referent.