 The logic \(\bSilK\) is not protoalgebraic and is not truth-equational. It is selfextensional but it is not Fregean. Its algebraic counterpart \(\bAlg \bSilK\) is the class of bounded distributive lattices with a binary operation with the properties of the strict implication of \(\blK\). This class of algebras is introduced and studied in Celani &amp; Jansana 2005, where its members are called Weakly Heyting algebras. \(\bAlg \bSilK\) does not coincide with \(\bAlg^* \bSilK\).