  The truth value of the atomic sentence \(p\) at world \(w\) given by the valuation \(v\) may be written \(v(p, w)\). Given this notation, the truth values \((T\) for true, \(F\) for false) of complex sentences of modal logic for a given valuation \(v\) (and member \(w\) of the set of worlds \(W)\) may be defined by the following truth clauses. (‘iff’ abbreviates ‘if and only if’.)