  In propositional logic, a valuation of the atomic sentences (or row of a truth table) assigns a truth value \((T\) or \(F)\) to each propositional variable \(p\). Then the truth values of the complex sentences are calculated with truth tables. In modal semantics, a set \(W\) of possible worlds is introduced. A valuation then gives a truth value to each propositional variable for each of the possible worlds in \(W\). This means that value assigned to \(p\) for world \(w\) may differ from the value assigned to \(p\) for another world \(w'\).