Geodesic
Generalized Kripke semantics for Nelson's logic
Algebra i logika, Tome 49 (2010) no. 5, pp. 630-653

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A completeness theorem for logics $N4^N$ and $N3^0$ is proved. A characterization by classes of $N4^N$- and $N3^0$-models is presented, and it is proved that all logics of four types $\eta(L)$, $\eta^3(L)$, $\eta^n(L)$, and $\eta^0(L)$ 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.
Keywords: Nelson logic, Kripke semantics, algebraic semantics, generalized frame. 
@article{AL_2010_49_5_a3,
     author = {E. I. Latkin},
     title = {Generalized {Kripke} semantics for {Nelson's} logic},
     journal = {Algebra i logika},
     pages = {630--653},
     publisher = {mathdoc},
     volume = {49},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_5_a3/}
}
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E. I. Latkin. Generalized Kripke semantics for Nelson's logic. Algebra i logika, Tome 49 (2010) no. 5, pp. 630-653. http://geodesic.mathdoc.fr/item/AL_2010_49_5_a3/