Abstract
LP$^{\supset,F}$ is a three-valued paraconsistent propositional
logic which is essentially the same as J3.
It has most properties that have been proposed as desirable properties
of a reasonable paraconsistent propositional logic.
However, it follows easily from already published results that there are
exactly 8192 different three-valued paraconsistent propositional logics
that have the properties concerned.
In this paper, properties concerning the logical equivalence relation of
a logic are used to distinguish LP$^{\supset,F}$ from the others.
As one of the bonuses of focussing on the logical equivalence relation,
it is found that only 32 of the 8192 logics have a logical equivalence
relation that satisfies the identity, annihilation, idempotent, and
commutative laws for conjunction and disjunction.
For most properties of LP$^{\supset,F}$ that have been proposed as
desirable properties of a reasonable paraconsistent propositional logic,
its paracomplete analogue has a comparable property.
In this paper, properties concerning the logical equivalence relation of a logic are also used to distinguish the paracomplete analogue of LP$^{\supset,F}$ from the other three-valued paracomplete propositional
logics with those comparable properties.
Preprint available:
arXiv:1702.03414v7 [cs.LO]