 A quasivariety can be an \(\iEq\)-algebraic semantics for a logic and an \(\iEq'\)-algebraic semantics for another logic (with \(\iEq\) and \(\iEq'\) different). For example, due to Glivenko’s theorem (see the entry on  intuitionistic logic)  the class of Heyting algebras is a \(\{\neg \neg p \approx 1\}\)-algebraic semantics for classical logic and it is the standard \(\{p \approx 1\}\)-algebraic semantics for intuitionistic logic. Moreover, different quasivarieties of algebras can be an \(\iEq\)-algebraic semantics for the same logic. It is known that there is a quasivariety that properly includes the variety of Boolean algebras that  is also a \(\{p \approx 1\}\)-algebraic semantics for classical propositional logic. It is also known that for some logics with an algebraic semantics (relative to some set of equations), the natural class of algebras that corresponds to the logic is not an algebraic semantics (for any set of equations) of it. One example where this situation holds is in the local normal modal logic \(\blK\). Finally, there are logics that do not have any algebraic semantics.