 Note that \(R\) could be defined on \(W\times W\times L_2\), letting \(R_A(w)\) depend on the syntactic form of \(A\) (instead of the proposition \(\lvert A\rvert^M\) expressed by \(A\)). The main effect of this modification is to block the substitution of equivalent antecedents, a feature called for by several theorists on separate grounds (see  section 3.5).