 The logic \(\bL^{ \{\wedge , \vee \}}\) is not protoalgebraic but it is Fregean. The class of algebras \(\bAlg\bL^{\{\wedge , \vee \}}\) is the variety of bounded distributive lattices, which is the class of algebras naturally expected to be the associated with \(\bL^{ \{\wedge , \vee \}}\), but the class \(\bAlg^*\bL^{ \{\wedge , \vee \}}\) is strictly included in it. In fact, this last class of algebras is not a quasivariety, but still it is good enough to be first-order definable.