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On the Representation of N4-Lattices

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Abstract

N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. Finally, subdirectly irreducible N4-lattices are described.

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  1. Sobolev Institute of Mathematics, Koptyug prosp. 4, 630090, Novosibirsk, Russia

    Sergei P. Odintsov

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  1. Sergei P. Odintsov
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Odintsov, S.P. On the Representation of N4-Lattices. Studia Logica 76, 385–405 (2004). https://doi.org/10.1023/B:STUD.0000032104.14199.08

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