 On the other hand, the opposite (or dual) situation may also be problematic: suppose, to help intuition, that the logic of classical negation is combined with the logic of classical disjunction. These logics can be presented, for instance, axiomatically (through Hilbert calculi) or semantically, say, through valuations over \(\{0,1\}\) (that is, by means of classical truth-tables). The semantical presentation of the logic of classical negation consists of the set of all valuations over \(\{0,1\}\) satisfying the following clause:  \[v(\neg\varphi)=0 \textrm{ iff } v(\varphi)=1.\]   On the other hand, the logic of classical disjunction can be characterized by the set of all valuations over \(\{0,1\}\) such that:   \[v(\varphi \vee \psi)=0  \textrm{ iff } v(\varphi)=0 \textrm{ and  } v(\psi)=0.\]   