 We choose a standard “Kripke-style” possible world semantics for SDL (Kripke 1959,  1963).[30]  We assume that we have a set of possible worlds, \(W\), and a relation, \(A\), relating worlds to worlds, with the intention that \(Aij\) iff \(j\) is a world where everything that holds at \(j\) is acceptable from the standpoint of \(i\), so that everything obligatory at \(i\) holds in \(j\). For brevity, we will call all worlds so related to \(i\), “\(i\)-acceptable” worlds and denote them by  \(A^i\).[31]  We then add that the acceptability relation is “serial”: for every world, \(i\), there is at least one \(i\)-acceptable world. Finally, propositions are either true or false at a world, never both, and when a proposition, \(p\), is true at a world, we will often indicate this by referring to that world as a “\(p\)-world”. The truth-functional operators have their usual behavior at each world.