I Lattice of truth values for a paraconsistent logic?

[nomadreid]

Usually the truth values of propositions of a logic are structured into a lattice, with 0 (False) on (say) the bottom and 1(True) on (say) the top, and the connecting lines being implication. In paraconsistent logics, there is at least one node which is not implied by 0. Can one safely say that a paraconsistent logic would not be able to refer to a lattice of truth values? If not, what would a lattice for the truth values of a paraconsistent system look like?

 

[sysprog]

Here's an example that's part of a general article on para-consistent logics: https://plato.stanford.edu/entries/logic-paraconsistent/#ManyValuLogi

 

[nomadreid]

thanks, sysprog; I know the article, but it is not clear to me how one would get a distributive lattice out of these truth tables. I found a more thorough answer in the following article, that I am still working through: "Lattice-baed Paraconsistent Logic", by Wendy McCaull and Dimiter Vakarelov, Lecture Notes in Computer Science 3929, Relational Methods in Computer Science ; Springer Verlag, ed. McCaull & WInter, 2006, pages 173-187.