 The first clause says: \(\varphi \wedge \psi\) is true when using assignment \(g\) if and only if \(\varphi\) and \(\psi\) are true when the assignment \(g\) is used. In the second clause assignments \(h\) are introduced (by \(\sim_x g)\) which are equal to \(g\) except maybe for the value they assign to variable \(x\). Montague uses the same format, with the difference that besides \(g\) he also has \(i\), the time of reference and \(j\), the possible world, as superscripts.