 The logic is very unlike Łukasiewicz’s earlier multivalent systems and also very unlike other modal systems. It is unlike his own systems in that it is an extension of classical bivalent logic and includes all bivalent tautologies. This is less surprising when we note that the four-valued matrices for the standard connectives are simply the Cartesian product of the standard bivalent matrices with themselves. It is the modal operators that make the difference. Several features make this very unlike standard modal systems. One is the complete lack of any truths, let alone theorems, of the form \(\Gamma a\), in line with Łukasiewicz’s rejection of truths of “higher dignity”. Other odd theorems are: