Three-valued paraconsistent logics and their extensions : Three-valued paraconsistent logics

We first prove that
any [conjunctive/disjunctive/implicative]
3-valued paraconsi-tent logic
with subclassical negation (3VPLSN) is defined by a
unique {modulo isomorphism} [conjunctive/disjunctive/implicative]
3-valued matrix and provide
effective
algebraic criteria of any 3VPLSN's
"being subclassical"|$"being maximally
paraconsistent"|"having no (inferentially) consistent non-subclassical extension"
implying that any [conjunctive/disjunctive]|conjunctive/"both disjunctive
and {non\}subclassical''/"refuting Double Negation
Law"'|"conjunctive/disjunctive subclassical''
3VPLSN "is subclassical if[f]
its defining 3-valued matrix has a 2-valued submatrix"|"is
{pre-}maximally paraconsistent"|"has a theorem but no consistent non-subclassical extension''.
Next, any disjunctive/implicative 3VPLSN has no proper consistent
non-classical disjunctive/axiomatic extension, any classical extension being
disjunctive/axiomatic and relatively axiomatized by the "Resolution
rule"'/"Ex Contradictione Quodlibet axiom''.
Further, we provide an effective
algebraic criterion of a [subclassical] "3VPLSN with lattice conjunction and
disjunction"''s having no proper [consistent non-classical] extension
but that [non-]inconsistent one which is relatively axiomatized by the
Ex Contradictione Quodlibet rule
[and defined by the product of any defining 3-valued matrix
and its 2-valued submatrix].
Finally, any disjunctive and conjunctive 3VPLSN
with classically-valued connectives
has an infinite increasing chain of finitary
extensions.