  In classical logic, the meaning of \(\phi\) is simply its truth-value. But in modal logic, it is the set of possible worlds where \(\phi\) is true: \({\llbracket}\phi{\rrbracket}\). So \(\phi\) is true in w, relative to v and R, just in case \(w\in{\llbracket}\phi{\rrbracket}^R_v\):