Geodesic
The Lattice of Extensions of the~Minimal Logic
Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 60-108

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In this article, we survey the results on the lattice of extensions of the minimal logic $\mathbf{Lj}$, a paraconsistent analog of the intuitionistic logic $\mathbf{Li}$. 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 {\tt Int} of intermediate logics, the class {\tt Neg} of negative logics with a degenerate negation, and the class {\tt Par} of properly paraconsistent extensions of the minimal logic. The classes {\tt Int} and {\tt Neg} are well studied, whereas the study of {\tt Par} can be reduced to some extent to the classes {\tt Int} and {\tt Neg}. 
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     author = {S. P. Odintsov},
     title = {The {Lattice} of {Extensions} of {the~Minimal} {Logic}},
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S. P. Odintsov. The Lattice of Extensions of the~Minimal Logic. Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 60-108. http://geodesic.mathdoc.fr/item/MT_2006_9_2_a3/