Abstract characterization of a four-valued logic

A four-valued logic defined by the four-element De Morgan lattice together with its two prime filters is treated. For certain classes of abstract logics, several characterizations in terms of De Morgan lattices and projective generation of logics by sets of homomorphisms or by a single epimorphism (a biological morphism) are described. A similar treatment is shown for the three-valued logic generated by the three-element chain together with its two prime filters, and for the incorporation of the falsum connective, which brings out the classes of all De Morgan algebras and all Kleene algebras.<>