  Clauses \(({\sim})\) and \((\rightarrow)\) simply describe the standard truth table behavior for negation and material implication respectively. According to (5), \(\Box A\) is true (at a world \(w)\) exactly when \(A\) is true in all possible worlds. Given the definition of \(\Diamond\), (namely, \(\Diamond A = {\sim}\Box{\sim}A)\) the truth condition (5) insures that \(\Diamond A\) is true just in case \(A\) is true in some possible world. Since the truth clauses for \(\Box\) and \(\Diamond\) involve the quantifiers ‘all’ and ‘some’ (respectively), the parallels in logical behavior between \(\Box\) and \(\forall x\), and between \(\Diamond\) and \(\exists x\) noted in section 2 will be expected.