Generalized Kripke semantics for Nelson’s logic

Abstract

A completeness theorem for logics N4 N and N30 is proved. A characterization by classes of N4 N - and N30-models is presented, and it is proved that all logics of four types η(L), η 3(L), η n (L), and η 0(L) are Kripke complete iff so are their respective intuitionistic fragments L. A generalized Kripke semantics is introduced, and it is stated that such is equivalent to an algebraic semantics. The concept of a p-morphism between generalized frames is defined and basic statements on p-morphisms are proved.