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The lattice of extensions of the minimal logic

Abstract

In this article, we survey the results on the lattice of extensions of the minimal logic Lj, a paraconsistent analog of the intuitionistic logic Li. Unlike the well-studied classes of explosive logics, the class of extensions of the minimal logic has an interesting global structure. This class decomposes into the disjoint union of the class Int of intermediate logics, the class Neg of negative logics with a degenerate negation, and the class Par of properly paraconsistent extensions of the minimal logic. The classes Int and Neg are well studied, whereas the study of Par can be reduced to some extent to the classes Int and Neg.

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Original Russian Text © S. S. Odintsov, 2006, published in Matematicheskie Trudy, 2006, Vol. 9, No. 2, pp. 60–108.

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Odintsov, S.P. The lattice of extensions of the minimal logic. Sib. Adv. Math. 17, 112–143 (2007). https://doi.org/10.3103/S1055134407020034

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Key words

  • Johansson’s logic
  • j-algebra
  • paraconsistency
  • lattice of logics
  • negative equivalence