Overview

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.

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