 Quantified modal logic is the system that combines pure quantificational logic with propositional modal logic. Propositional modal logic investigates the logic of the modal operators \(\Box\) and \(\Diamond\) and is discussed in the entry on  modal logic.  The language of propositional modal logic supplements the language of propositional logic with the sentential operator \(\Box\), and \(\Diamond\) may then be explicitly defined as \(\neg \Box \neg\). A weak propositional modal logic called K logic includes as axioms all tautologies and all instances of schema K: