 A logic satisfying this weaker replacement property is called selfextensional by Wójcicki (e.g., in Wójcicki 1969, 1988) and congruential in Humberstone 2005. We will use the first terminology because it seems more common —at least in the abstract algebraic logic literature. It has to be mentioned that all fragments of a selfextensional logic are selfextensional and that the analogous fact also holds for Fregean logics. Moreover, the difference between being selfextensional and being Fregean is not only encountered among protoalgebraic logics like the mentioned local consequence relations of normal modal logics, it is also encountered among non protoalgebraic logics. The four-valued logic of Belnap and Dunn (see Font 1997 for information) is selfextensional, non-protoalgebraic, and non-Fregean.