 In order to do this, the signature \(C_0\) just containing \(\neg\) and \(\to\) is taken into consideration, and so \(\neg_1\) is identified with \(\neg_2\) in \(C_1 \oplus C_2\), as well as \(\to_1\) is identified with \(\to_2\). The resulting signature is \(C\), which just contains the connectives \(\neg\), \(\to\), \(\square_1\) and \(\square_2\). In the resulting logic \({{\cal L}}\), defined over \(C\), there is now just one rule of Modus Ponens: