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Graham Priest, The sun may not, indeed, rise tomorrow: a reply to Beall, Analysis, Volume 72, Issue 4, October 2012, Pages 739–741, https://doi.org/10.1093/analys/ans120
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A well-known feature of standard paraconsistent logics, such as LP, is that they are weak in a certain sense. Thus, they do no validate the Disjunctive Syllogism, even though there are clearly cases where we would want to use it. I have argued that a way around this apparent problem is to employ a non-monotonic extension of LP, LPm, which is stronger.1LPm can be applied to any situation, and in that sense it is a universal logic: it gives classical reasoning in consistent situations and an inference engine at least as generous as LP in inconsistent situations.
There has to be more to matters than this, though. After all, reasoning classically in all situations would do that job as well. This is why what I called Reassurance is important. It guarantees that if a theory is non-trivial under LP consequence, it is non-trivial under LPm consequence as well – unlike classical consequence, which explodes any inconsistent information, producing triviality. In other words, taking triviality to be some kind of incoherence, LPm will never turn a coherent situation into an incoherent one.2
