£199.30

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

Algebra

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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.

Product Specifications

Format: paperback
ASIN: B095GRW3QK
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 22 May 2021
Listed Since: 22 May 2021

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

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