We define an interpretation of modal languages with polyadic operators
in modal languages that use monadic operators (diamonds) only.
We also define a simulation operator which associates a logic $\simL$ in the
diamond language with each logic $\La$ in the language with polyadic modal
connectives.
We prove that this simulation operator transfers several useful properties
of modal logics, such as finite/recursive axiomatizability, frame
completeness and the finite model property, canonicity and first-order
definability.